A method and apparatus for fabricating a guide plate for dental implant crown removal.

Abstract

A method and apparatus for fabricating a guide plate for dental implant crown removal are disclosed, relating to the field of dental implant crown removal technology. The method involves acquiring three-dimensional image data and oral scan data of the patient with the implant to be removed; processing the three-dimensional image data and oral scan data to obtain a three-dimensional voxel mesh; constructing a three-dimensional probability cloud map based on each voxel in the three-dimensional voxel mesh; calculating the local path cost value for each voxel in the three-dimensional probability cloud map according to the clinical goals of the implant to be removed; using the surface voxels of the implant to be removed as the starting point and the voxel corresponding to the top of the central screw hole of the implant as the ending point, and guided by the local path cost value, solving for the final safe crown removal path in the three-dimensional probability cloud map; analyzing the final safe crown removal path and combining it with the surface morphology of adjacent teeth in the digital three-dimensional scene to generate a three-dimensional guide plate template. This method solves the problem of insufficient tolerance control in existing technologies.

Description

Technical Field

[0001] This application relates to the field of dental implant crown removal technology, specifically to a method and apparatus for manufacturing a guide plate for dental implant crown removal. Background Technology

[0002] With the rapid development of digital dental technology, dental implant restoration has become the mainstream solution for tooth loss reconstruction. However, after long-term use, dental implant crowns often require removal and maintenance due to porcelain chipping, loosening of abutment screws, or peri-implantitis. To achieve precision medicine, digital surgical guide technology has been widely used in the implant placement stage. Preoperative 3D imaging planning assists doctors in clinical operations, providing a technological foundation for digital and minimally invasive maintenance throughout the entire implant lifecycle.

[0003] Currently, in the field of dental implant crown removal, existing assisted removal techniques mainly rely on general-purpose digital restoration design software. This technology acquires intraoral scan data and CT data from the patient for three-dimensional registration, reconstructs the relative position of the crown and implant in virtual space, and uses software to calculate a virtual cutting path leading to the central screw hole of the implant. Then, a guide mold with a fixed channel is manufactured using 3D printing to guide the cutting tool into place.

[0004] However, the path planning and guidance design of the above-mentioned prior art are based on simple rigid avoidance based on static spatial geometric distance, and fail to consider the probability of dynamic mechanical deviation when the cutting tool approaches the implant due to high-speed rotation during actual cutting. This results in a large deviation in the tolerance control of the designed guide channel, and the prepared guide plate still has extremely high uncertainty in clinical application, and cannot achieve safe and precise guidance. Summary of the Invention

[0005] This application provides a method and apparatus for fabricating a guide plate for dental implant crown removal. This method solves the problem of insufficient tolerance control in the prior art, reduces the uncertainty of clinical operation, and achieves safe and precise guidance for dental implant crown removal.

[0006] In a first aspect, this application provides a method for fabricating a guide plate for the removal of dental implant crowns. The method includes: acquiring three-dimensional image data of the patient's oral and maxillofacial region where the dental implant crown to be removed is located, and oral scan data containing tooth tissue morphology; registering and fusing the three-dimensional image data and oral scan data in a unified coordinate system to obtain a digital three-dimensional scene containing anatomical structures; performing voxelization processing on the digital three-dimensional scene to obtain a three-dimensional voxel mesh containing multiple voxels; calculating the conditional probability of triggering various preset failure events when the cutting tool passes through the target voxel based on the spatial geometric distance from the target voxel, and constructing a three-dimensional probability cloud map for the conditional probabilities corresponding to all voxels, wherein the target voxel is any voxel in the three-dimensional voxel mesh; acquiring the clinical target of the dental implant crown to be removed, and based on the clinical target, matching the target voxel in the three-dimensional probability cloud map with respect to the clinical target. The conditional probabilities of various factors are calculated to obtain the local path cost value. In the three-dimensional probability cloud map, the surface voxel of the implant crown to be removed is taken as the exploration starting point, and the voxel corresponding to the top of the central screw hole of the implant is taken as the exploration ending point. Guided by the local path cost value, the optimal path voxel set with the minimum cumulative local path cost value is solved. The optimal path voxel set is fitted and smoothed to obtain the final safe crown removal path in three-dimensional space. Based on the final safe crown removal path, rigid cutting envelope analysis is performed to determine the rigid axial cutting track of the cutting tool. Combined with the surface morphology of adjacent teeth in the digital three-dimensional scene, a three-dimensional guide plate template is generated for physical processing and fabrication according to the three-dimensional guide plate template. The three-dimensional guide plate template includes a main body for matching the surface of adjacent teeth and a guide channel. The geometric constraint boundary of the guide channel corresponds to the rigid axial cutting track.

[0007] By employing the above technical solution, three-dimensional image data of the patient's oral and maxillofacial region and oral scan data including tooth tissue morphology are acquired. These two data are then registered and fused in a unified coordinate system. The digital three-dimensional scene is voxelized and a three-dimensional voxel mesh is constructed. By building a three-dimensional probability cloud map, multidimensional clinical risks are quantified into a continuous probability distribution, fundamentally solving the problem of insufficient tolerance control in existing technologies. Furthermore, the clinical objective of the implant crown to be removed is obtained. Based on the clinical objective, the conditional probabilities corresponding to the target voxels are calculated to obtain the local path cost value. This enables the path planning algorithm to adaptively respond to different clinical needs, overcoming the limitations of existing technologies that rely on fixed strategies. This addresses the limitations of differentiated treatment goals. In solving for the optimal path voxel set that minimizes the cumulative local path cost, probabilistic cost is used as a guide rather than simple geometric distance, ensuring an optimal balance between safety and operability in the planned path. By fitting and smoothing the optimal path voxel set, a final safe crown removal path is obtained. Based on rigid cutting envelope analysis, the rigid axial cutting trajectory of the cutting tool is determined. The geometric constraint boundary of the generated three-dimensional guide plate template accurately corresponds to the actual cutting trajectory, effectively addressing the dynamic mechanical deviation during high-speed rotation of the cutting tool, reducing the uncertainty of clinical operation, and achieving safe and precise guidance for implant crown removal.

[0008] Optionally, the 3D image data and oral scan data are registered and fused in a unified coordinate system to obtain a digital 3D scene containing anatomical structures. Specifically, this includes: extracting point clouds of the hard tissue surface of the crown from the 3D image data and extracting point clouds of the crown surface from the oral scan data; using principal component analysis algorithm, calculating the initial rotation matrix and translation vector of the point clouds of the hard tissue surface of the crown and the point clouds of the crown surface; iteratively optimizing the initial rotation matrix and translation vector until the root mean square error between the point clouds of the hard tissue surface of the crown and the point clouds of the crown surface is less than a preset threshold to obtain a spatial transformation matrix; transforming the 3D image data and oral scan data to a unified coordinate system based on the spatial transformation matrix for 3D fusion to generate a fused data model; performing semantic segmentation on the fused data model to obtain a digital 3D scene containing anatomical structures, including implants, abutments, crowns to be removed, adjacent teeth, important nerve canals of the inferior alveolar ridge, and gingival soft tissue.

[0009] By employing the aforementioned technical solution, point clouds of the hard tissue surface of the crown are extracted from 3D image data and point clouds of the crown surface are extracted from oral scan data. Principal component analysis algorithm is used to calculate the initial rotation matrix and translation vector of the hard tissue surface point cloud and the crown surface point cloud. The initial rotation matrix and translation vector are iteratively optimized until the root mean square error is less than a preset threshold. Fine alignment is achieved on the basis of coarse registration, ensuring the high accuracy of the spatial transformation matrix. This enables the fusion of 3D image data and oral scan data based on the spatial transformation matrix to achieve sub-millimeter registration accuracy. The generated fusion data model integrates bone tissue and implant internal structure information from the image and soft tissue and crown surface detail information from the oral scan data. Semantic segmentation of the fusion data model yields a digital 3D scene of the anatomical structure, fundamentally ensuring the safety of path planning.

[0010] Optionally, based on the spatial geometric distance from the target voxel to the anatomical structure, the conditional probability of triggering various preset failure events when the cutting tool passes through the target voxel is calculated, and a three-dimensional probability cloud map is constructed for the conditional probabilities corresponding to all voxels. Specifically, this includes: obtaining a set of preset failure events, which includes mechanical damage events to the implant, mechanical damage events to the abutment, damage events to adjacent teeth or restorations, bone tissue damage to the implant due to heating, and events where the crown cannot be easily separated by the instrument after cutting; calculating the Euclidean distance from the target voxel to the corresponding surface of each structure in the anatomical structure to obtain the spatial geometric distance; when the preset failure events are mechanical damage events to the implant, mechanical damage events to the abutment, and damage events to adjacent teeth or restorations, Substituting the spatial geometric distance into the first probability mapping function, the conditional probability of triggering a preset failure event when the cutting tool passes through the target voxel is calculated. When the preset failure event is damage to the bone tissue around the implant due to heating, the spatial geometric distance is substituting into the second probability mapping function to calculate the conditional probability of triggering the preset failure event when the cutting tool passes through the target voxel. When the preset failure event is that the crown cannot be easily separated by instruments after cutting, the spatial geometric distance is substituting into the third probability mapping function to calculate the conditional probability of triggering the preset failure event when the cutting tool passes through the target voxel. Traversing all voxels in the three-dimensional voxel grid, the conditional probabilities corresponding to each voxel are spatially arrayed and mapped to construct a three-dimensional probability cloud map containing multiple probability dimensions.

[0011] By adopting the above technical solution, a preset set of failure events is obtained, achieving comprehensive coverage of multidimensional clinical risks during implant crown removal. The spatial geometric distance is obtained by calculating the Euclidean distance from the target voxel to the corresponding surface of each anatomical structure. Differentiated probability mapping strategies are adopted for the differences in the physical mechanisms of different failure events. This classification mapping scheme can accurately reflect the nonlinear decay characteristics of different risk factors with distance, making the calculated conditional probabilities more consistent with the actual clinical situation. By traversing all voxels in the three-dimensional voxel grid and mapping the conditional probabilities corresponding to each voxel in a spatial array, a continuous risk probability field is obtained. This changes the existing path planning mode based on hard binary judgment, achieving global optimization of the path while ensuring safety margin.

[0012] Optionally, the clinical target of the dental implant crown to be removed is obtained. Based on the clinical target, the conditional probabilities of each item corresponding to the target voxel in the three-dimensional probability cloud map are calculated to obtain the local path cost value. Specifically, this includes: obtaining the clinical target of the dental implant crown to be removed; determining the corresponding set of weight coefficients based on the clinical target, wherein the set of weight coefficients includes weight factors corresponding one-to-one with each preset failure event; and using the set of weight coefficients to perform a weighted summation calculation on the multi-channel conditional probabilities corresponding to the target voxel to obtain the corresponding local path cost value. The formula for calculating the local path cost value is as follows: ; Where x represents the target voxel, C(x) represents the local path cost at target voxel x, N represents the total number of preset failure events, and P(E) i |x) represents the conditional probability of triggering the i-th preset failure event when the cutting tool passes through the target voxel x, w i Let G(x) represent the weight factor corresponding to the i-th preset failure event, and let each weight factor in the set of weight coefficients satisfy the normalization mapping constraint. Let G(x) represent the geometric constraint penalty term of the guidance path, and let γ represent the geometric constraint adjustment coefficient.

[0013] By adopting the above technical solution, the clinical target of the implant crown to be removed is obtained, and a set of weight coefficients containing weight factors corresponding to each preset failure event is determined based on the clinical target. This enables the path planning algorithm to adapt to different clinical needs, fundamentally changing the limitation of existing technologies that cannot meet differentiated treatment goals by using fixed strategies. The local path cost value is obtained by weighted summation of the multi-channel conditional probabilities corresponding to the target voxel using the set of weight coefficients. This allows the path planning process to both prioritize avoiding anatomical damage for the target crown to be preserved and actively seek easily separable cutting positions for the target crown to be discarded.

[0014] Optionally, the clinical goal includes either the goal of preserving the crown or the goal of discarding the crown. Based on the clinical goal, a corresponding set of weighting coefficients is determined. Specifically, this includes: constructing a three-dimensional stress distribution field of the implant crown to be removed under a preset removal load, and identifying stress concentration areas based on the three-dimensional stress distribution field; calculating the spatial geometric distance from each voxel to the corresponding surface of the anatomical structure based on the digital three-dimensional scene, and constructing a spatial distance sensitivity function; when the clinical goal is to preserve the crown, based on the spatial geometric distance sensitivity function, assigning weights to the preset failure events related to anatomical damage. The weighting factor is determined as a positive penalty function negatively correlated with spatial geometric distance, and the weighting factor corresponding to the event that the cut crown cannot be easily separated by instruments is determined to be zero; when the clinical goal is to discard the crown, the weighting factor corresponding to the event that the cut crown cannot be easily separated by instruments is determined as a negative reward function positively correlated with the distance of the stress concentration area, and the weighting factors corresponding to the preset failure events related to anatomical damage are kept as positive penalty functions; the determined weighting factors are dynamically normalized and mapped, and the normalized weighting factors are vectorized and combined to obtain the set of weight coefficients corresponding to the clinical goal.

[0015] By employing the above technical solution, a three-dimensional stress distribution field of the implant crown to be removed under a preset removal load is constructed, and stress concentration areas are identified. Based on the digital three-dimensional scene, the spatial geometric distance from each voxel to the corresponding surface of the anatomical structure is calculated, and a spatial distance sensitivity function is constructed. When the clinical goal is to preserve the crown, the weight factors corresponding to the preset failure events related to anatomical damage are determined as positive penalty functions negatively correlated with spatial geometric distance, ensuring that the planned path protects the crown integrity to the maximum extent. When the clinical goal is to discard the crown, the weight factors corresponding to the event that the cut crown cannot be easily separated by instruments are determined as negative reward functions positively correlated with the distance to the stress concentration area, keeping the weight factors related to anatomical damage as positive penalty functions to maintain basic safety constraints. The determined weight factors are dynamically normalized and mapped, and quantitatively combined to obtain a set of weight coefficients, realizing intelligent switching and smooth transition of path optimization strategies under different clinical goals.

[0016] Optionally, in the 3D probability cloud map, the surface voxel of the implant crown to be removed is used as the exploration starting point, and the voxel corresponding to the top of the central screw hole of the implant is used as the exploration ending point. Guided by the local path cost value, an optimal set of path voxels with the minimum cumulative local path cost value is solved. Specifically, this includes: pushing the exploration starting point into a dynamic priority queue, and initializing the cumulative path cost value of all voxels in the 3D voxel grid except the exploration starting point to infinity, and initializing the cumulative path cost value of the exploration starting point to zero; popping the voxel with the minimum current cumulative path cost value from the dynamic priority queue, and traversing the neighboring voxels of the voxel to be evaluated in 3D space; calculating the temporary cumulative path cost value from the exploration starting point through the voxel to be evaluated to the target neighboring voxel, where the temporary cumulative path cost value is the cumulative cost value of the voxel to be evaluated. The cumulative path cost is the sum of the cumulative path cost, the local path cost at the neighboring voxel, and the spatial step cost between two adjacent voxels. The target neighboring voxel is any neighboring voxel in 3D space. If the temporary cumulative path cost is less than the historical cumulative path cost recorded by the target neighboring voxel, the historical cumulative path cost of the target neighboring voxel is updated using the temporary cumulative path cost. The parent node pointer of the target neighboring voxel is set to the voxel to be evaluated, and the target neighboring voxel is updated in the dynamic priority queue. The step of updating the cumulative path cost is repeated until the exploration endpoint is popped. When the exploration endpoint is popped, the process starts from the exploration endpoint and backtracks along the parent node pointers of each voxel until the exploration starting point is reached. All voxels passed during the backtracking process are arranged in order to generate the optimal path voxel set.

[0017] By adopting the above technical solution, the surface voxel of the implant crown to be removed is pushed into a dynamic priority queue as the exploration starting point. The cumulative path cost of all voxels in the 3D voxel mesh, except for the exploration starting point, is initialized to infinity. The cumulative path cost of the exploration starting point is initialized to zero. The voxel with the smallest current cumulative path cost is popped from the dynamic priority queue, and its neighboring voxels in 3D space are traversed. This achieves a greedy strategy that always prioritizes exploration along the lowest-cost direction, avoiding the waste of computational resources caused by blind searching. The temporary cumulative path cost from the exploration starting point through the voxel to be evaluated to the target neighboring voxel is calculated to ensure the final solution's path... The algorithm achieves cost optimization globally rather than locally. By determining whether the temporary cumulative path cost is less than the historical cumulative path cost recorded in the target neighborhood voxels, and updating the historical cumulative path cost, parent node pointer, and dynamic priority queue based on the comparison result, the algorithm repeatedly executes the step of updating the cumulative path cost until the exploration endpoint is popped. This ensures that the algorithm can find the true global optimum by traversing all feasible paths. When the exploration endpoint is popped, the algorithm backtracks from the endpoint along the parent node pointer back to the exploration starting point and arranges all the voxels passed through in order to generate the optimal path voxel set. This backtracking can efficiently reconstruct the complete optimal path.

[0018] Optionally, the optimal path voxel set is fitted and smoothed to obtain the final safe crown removal path in three-dimensional space. Specifically, this includes: extracting the center three-dimensional coordinates of each voxel in the optimal path voxel set to construct a discrete control point sequence; based on the discrete control point sequence, using a fitting algorithm to perform continuous interpolation fitting to generate an initial continuous three-dimensional path curve; in the three-dimensional probability cloud map, retrieving the conditional probabilities corresponding to each voxel traversed by the initial continuous three-dimensional path curve; if the conditional probability corresponding to the current voxel is greater than a preset safety threshold, then the current voxel is marked as a conflict voxel, where the current voxel is any voxel traversed by the initial three-dimensional path curve; based on the spatial location of the conflict voxels... The system applies a normal repulsive force to the initial continuous 3D path curve, deviating from the conflict voxel, and iteratively adjusts the control point positions of the initial continuous 3D path curve until all conditional probabilities of the regions traversed by the initial continuous 3D path curve are less than or equal to a preset safety threshold, thus obtaining the final safe crown removal path. It then calculates the overall geometric features of the final safe crown removal path; based on these geometric features, it uses a preset strategy classifier to identify the topology strategy of the final safe crown removal path; and based on the identified topology strategy, it automatically configures the geometric configuration of the guide channel in the 3D guide plate template so that the geometric constraint boundary of the guide channel matches the motion envelope space of the rigid cutting tool when executing the corresponding topology strategy.

[0019] By employing the above technical solution, the three-dimensional coordinates of the center of each voxel in the optimal path voxel set are extracted to construct a discrete control point sequence. Based on the discrete control point sequence, a fitting algorithm is used to continuously interpolate and fit to generate an initial continuous three-dimensional path curve. The conditional probabilities corresponding to each voxel traversed by the initial continuous three-dimensional path curve are retrieved in the three-dimensional probability cloud map. The current voxel with a conditional probability greater than a preset safety threshold is marked as a conflict voxel. Based on the spatial position of the conflict voxel, a normal repulsive force away from the conflict voxel is applied to the initial continuous three-dimensional path curve, and the control point position is iteratively adjusted until the conditional probabilities of each region traversed are less than or equal to the preset safety threshold. The overall geometric morphology features of the final safe crown removal path are calculated, and a preset strategy classifier is used to identify the topology strategy, realizing automatic mapping from geometric features to clinical operation strategies. Based on the identified topology strategy, the geometric configuration of the guide channel in the three-dimensional guide plate template is automatically configured, so that the geometric constraint boundary of the guide channel is precisely matched with the motion envelope space of the rigid cutting tool when executing the corresponding topology strategy, which completely changes the limitation of the existing technology that uses a fixed channel structure and cannot adapt to dynamic operation deviations.

[0020] A second aspect of this application provides an apparatus for fabricating a guide plate for the removal of dental implant crowns. The apparatus includes an acquisition unit, a processing unit, a calculation unit, and a planning unit. The acquisition unit acquires three-dimensional image data of the patient's oral and maxillofacial region where the dental implant crown to be removed is located, as well as oral scan data containing tooth tissue morphology. The processing unit registers and fuses the three-dimensional image data and oral scan data in a unified coordinate system to obtain a digital three-dimensional scene containing anatomical structures. The digital three-dimensional scene is voxelized to obtain a three-dimensional voxel mesh containing multiple voxels. Based on the spatial geometric distance from the target voxel to the anatomical structure, the conditional probability of triggering various preset failure events when the cutting tool passes through the target voxel is calculated, and a three-dimensional probability cloud map is constructed for the conditional probabilities corresponding to all voxels, where the target voxel is any voxel in the three-dimensional voxel mesh. The calculation unit acquires the clinical target of the dental implant crown to be removed, and based on the clinical target... The conditional probabilities of the target voxels in the 3D probability cloud map are calculated to obtain the local path cost value. Using the surface voxel of the implant crown to be removed as the starting point and the voxel corresponding to the top of the central screw hole of the implant as the ending point, guided by the local path cost value, an optimal set of path voxels with the minimum cumulative local path cost value is obtained. A planning unit is used to fit and smooth the optimal path voxel set to obtain the final safe crown removal path in 3D space. Based on the final safe crown removal path, a rigid cutting envelope analysis is performed to determine the rigid axial cutting trajectory of the cutting tool. Combined with the surface morphology of adjacent teeth in the digital 3D scene, a 3D guide plate template is generated for physical fabrication. The 3D guide plate template includes a main body for matching the surface of adjacent teeth and a guide channel. The geometric constraint boundary of the guide channel corresponds to the rigid axial cutting trajectory.

[0021] In a third aspect, this application provides an electronic device including a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory, causing the electronic device to perform any of the methods described above in this application.

[0022] In a fourth aspect, this application provides a computer-readable storage medium storing instructions that, when executed, perform any of the methods described above in this application.

[0023] In summary, one or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages: 1. Acquire 3D image data of the patient's oral and maxillofacial region and oral scan data including tooth tissue morphology, and register and fuse them in a unified coordinate system. Perform voxelization processing on the digital 3D scene and construct a 3D voxel mesh. By constructing a 3D probability cloud map, multidimensional clinical risks are quantified into a continuous probability distribution, fundamentally solving the problem of insufficient tolerance control in existing technologies. 2. Obtain the clinical objective of the implant crown to be removed. Based on the clinical objective, calculate the local path cost value for the conditional probabilities corresponding to the target voxels. This achieves adaptive response of the path planning algorithm to different clinical needs, changing the limitations of existing technologies that use fixed strategies and cannot meet differentiated needs. Limitations of treatment goals; in the process of solving for the optimal path voxel set that minimizes the cumulative local path cost, probabilistic cost is used as the guide rather than simple geometric distance, ensuring the optimal balance between safety and operability in the planned path; by fitting and smoothing the optimal path voxel set, the final safe crown removal path is obtained, and the rigid axial cutting track of the cutting tool is determined based on rigid cutting envelope analysis. The geometric constraint boundary of the guide channel of the generated three-dimensional guide plate template can accurately correspond to the actual cutting track, thereby effectively dealing with the dynamic mechanical deviation when the cutting tool rotates at high speed, reducing the uncertainty of clinical operation, and realizing safe and precise guidance for implant crown removal. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a method for fabricating a guide plate for removing dental implant crowns, as provided in an embodiment of this application. Figure 2 This is a schematic diagram of the structure of an electronic device disclosed in an embodiment of this application.

[0025] Explanation of reference numerals in the attached figures: 200, electronic device; 201, processor; 202, memory; 203, user interface; 204, network interface; 205, communication bus. Detailed Implementation

[0026] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0027] In the description of the embodiments of this application, the words "for example" or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design that is described as "for example" or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design options. Rather, the use of the words "for example" or "for instance" is intended to present the relevant concepts in a specific manner.

[0028] In the description of the embodiments of this application, the term "multiple" means two or more. For example, multiple systems means two or more systems, and multiple screen terminals means two or more screen terminals. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. The terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0029] Therefore, how to overcome the insufficient tolerance control of existing technologies, reduce the uncertainty of clinical operations, and achieve safe and precise guidance for implant crown removal is an urgent problem to be solved. This application provides a method for fabricating a guide plate for implant crown removal, applied in a server. The server in this application can provide a platform for generating guide plates for implant crown removal. Figure 1 This is a flowchart illustrating a method for fabricating a guide plate for dental implant crown removal, as provided in an embodiment of this application. (Refer to...) Figure 1 The method includes the following steps S101-S108.

[0030] S101: Obtain three-dimensional image data of the patient's oral and maxillofacial region where the implant crown to be removed is located, as well as oral scan data including tooth tissue morphology.

[0031] In the above S101, in order to achieve precise removal of dental implant crowns and avoid implant damage caused by limited field of vision and improper depth control in traditional manual operation, three-dimensional image data of the patient's oral and maxillofacial region where the dental implant crown to be removed is located, as well as oral scan data containing tooth tissue morphology, are first obtained.

[0032] The dentist performs cone-beam computed tomography (CBCT) scans on the patient's maxillofacial region, where dental implants are implanted. The CT scanner acquires DICOM format 3D images of the jawbone, implant, abutment, and hard tissue morphology of the implant to be removed. This 3D image data clearly shows the precise 3D position of the implant within the bone, the connection between the abutment and implant, the axial orientation of the implant's central screw hole, and the spatial distribution of important anatomical structures such as the inferior alveolar nerve canal. This provides imaging evidence for avoiding sensitive areas around the implant. Because CT scans have limitations in capturing detailed features of the crown surface and gingival soft tissue morphology, an intraoral scanner is used to directly digitize the patient's oral cavity or indirectly obtain STL format oral scan data through a scanned plaster model. This oral scan data records the external surface geometry of the implant to be removed, the surface contours of adjacent natural teeth or other restorations, and the 3D undulations of the gingival soft tissue with sub-millimeter precision. By simultaneously acquiring 3D image data and oral scan data, intraoral scan data including the implant, abutment, implant to be removed, adjacent teeth, important nerve canals, and gingival soft tissue is obtained.

[0033] S102: Register and fuse 3D image data and oral cavity scan data in a unified coordinate system to obtain a digital 3D scene containing anatomical structures.

[0034] In step S102 above, the 3D image data and oral scan data are registered and fused in a unified coordinate system to obtain a digital 3D scene containing anatomical structures. Specifically, this includes: extracting point clouds of the hard tissue surface of the crown from the 3D image data and extracting point clouds of the crown surface from the oral scan data; using principal component analysis algorithm, calculating the initial rotation matrix and translation vector of the point clouds of the hard tissue surface of the crown and the point clouds of the crown surface; iteratively optimizing the initial rotation matrix and translation vector until the root mean square error between the point clouds of the hard tissue surface of the crown and the point clouds of the crown surface is less than a preset threshold to obtain a spatial transformation matrix; transforming the 3D image data and oral scan data to a unified coordinate system based on the spatial transformation matrix for 3D fusion to generate a fused data model; performing semantic segmentation on the fused data model to obtain a digital 3D scene containing anatomical structures, including implants, abutments, crowns to be removed, adjacent teeth, important nerve canals of the inferior alveolar ridge, and gingival soft tissue.

[0035] Specifically, DICOM format 3D image data is imported into medical image processing software. By setting appropriate window width and level parameters, the grayscale range of the hard tissue of the crown is clearly distinguished from the surrounding soft tissue. Then, a threshold segmentation algorithm is used to automatically identify the high-density hard tissue voxels in the area where the implant crown to be removed is located. A 3D surface reconstruction algorithm, such as the moving cube algorithm, is used to extract the triangular mesh model of the outer surface of the crown hard tissue. Then, through uniform sampling or feature point extraction methods, a point cloud containing thousands to tens of thousands of spatial coordinate points is obtained from the surface of the triangular mesh model. This point cloud realistically reflects the 3D geometric contour of the crown in the CT image. Simultaneously, STL format oral scan data is imported into the 3D processing software. Since the oral scan data itself is a surface model stored in triangular mesh form, the crown surface point cloud is directly extracted from the mesh area corresponding to the implant crown to be removed through vertex coordinate reading or surface sampling. The point cloud has higher surface detail resolution and can clearly present the pit and fissure morphology of the occlusal surface of the crown and the anatomical features of the buccal and lingual surfaces. Since the two point clouds come from different scanning devices and at different times, they are each in an independent device coordinate system, and their spatial positions, rotation angles, and scaling ratios are inconsistent. Therefore, a registration algorithm is needed to find the spatial transformation relationship that aligns the two points.

[0036] To achieve initial coarse registration, principal component analysis (PCA) was used to calculate the initial rotation matrix and translation vector of the point cloud on the hard tissue surface of the crown and the point cloud on the crown surface, respectively. PCA first calculates the centroid coordinates of all points in the point cloud on the hard tissue surface of the crown, i.e., the arithmetic mean of the three-dimensional coordinate components of all points. The point cloud is then translated so that the centroid coincides with the origin. The covariance matrix of the point cloud is constructed and eigenvalue decomposition is performed to obtain three mutually orthogonal eigenvectors. These three eigenvectors represent the main distribution direction of the point cloud data in space. Arranging these three normalized eigenvectors in columns constitutes the principal direction rotation matrix of the point cloud on the hard tissue surface of the crown. Following the above process, the point cloud on the crown surface is analyzed to obtain the centroid position and the principal direction rotation matrix. The principal directions of the two point clouds are aligned, i.e., an initial rotation matrix is ​​constructed so that the principal axis of the point cloud on the hard tissue surface of the crown is parallel to the principal axis of the point cloud on the crown surface. Simultaneously, the translation vector required to make the centroids of the two point clouds coincide is calculated, thus completing the initial coarse alignment based on the geometric distribution characteristics.

[0037] After obtaining the initial rotation matrix and translation vector, these spatial transformation parameters are iteratively optimized to achieve accurate registration. The iterative nearest-point algorithm is used as the core method for fine registration. In each iteration, this algorithm first searches for the closest spatial counterpart for each point in the crown hard tissue surface point cloud, establishing a point-to-point correspondence. Then, based on these corresponding point pairs, it calculates the optimal rotation matrix and translation vector that minimizes the overall distance between the two point clouds. Using this updated transformation parameter, the crown hard tissue surface point cloud is spatially transformed, and the point correspondence is re-established and the transformation parameter is updated. This process is repeated iteratively until the registration accuracy between the two point clouds meets the requirements. To quantitatively evaluate the registration quality, the root mean square error (RMSE) between the crown hard tissue surface point cloud and the crown surface point cloud is calculated after each iteration. The RMSE is defined as the square root of the average of the squared Euclidean distances between all corresponding point pairs; a smaller value indicates better spatial overlap between the two point clouds. The iterative optimization process continues until the root mean square error (RMSE) is less than a preset threshold. This threshold is set between 0.2 mm and 0.5 mm based on clinical accuracy requirements. When the RMSE converges below this threshold, it indicates that the CT image surface of the crown and the intraoral scan surface have achieved spatial alignment with sub-millimeter precision. At this point, the accumulated rotation matrix and translation vector together constitute the final spatial transformation matrix. This iterative optimization process, by gradually correcting the spatial transformation parameters, fully utilizes the rich geometric features of the crown surface, such as the cusp-fossa morphology of the occlusal surface and the contact area contour of the proximal surface, as registration constraints. This ensures that the final spatial transformation matrix accurately describes the complete mapping relationship from the CT coordinate system to the intraoral scan coordinate system.

[0038] After obtaining the spatial transformation matrix, the 3D image data and oral scan data are transformed to a unified coordinate system for 3D fusion to generate a fused data model. The coordinate system of the oral scan data is chosen as the unified target coordinate system because the oral scan data directly reflects the true anatomical morphology of the patient's oral cavity and has higher surface accuracy. Using the oral scan data as the reference coordinate system is beneficial for the fitting and positioning during subsequent guide design. The spatial transformation matrix is ​​applied to the voxel mesh of the 3D image data, and the spatial coordinates of each voxel are rotated and translated. This ensures that the spatial positions of hard tissue structures such as implants, abutments, and jawbones in the CT data are accurately mapped to the oral scan coordinate system. This achieves the superposition of internal hard tissue information, which CT images excel at displaying, and surface morphology information, which oral scan data excels at capturing, within the same spatial reference frame. After completing the coordinate transformation, the transformed 3D image data and the original oral scan data are fused together to construct a comprehensive data model in a unified coordinate system. This model includes 3D spatial information of internal structures such as the axial position of the implant, the interface between the abutment and the implant, the central axis of the screw hole, and the path of the inferior alveolar nerve canal from the CT scan, as well as a high-precision mesh representation of external morphology such as the fine surface geometry of the crown, the occlusal relationship of adjacent teeth, and the morphology of the gingival papilla from the oral scan. The two sets of data are seamlessly connected in the crown area through the aforementioned precise registration, forming a fused data model.

[0039] To extract specific anatomical tissues from the fused data model and establish their spatial relationships, semantic segmentation was performed on the fused data model to obtain a digital 3D scene containing anatomical structures. In the CT voxels corresponding to the 3D image data, high-density implant metal structures were separated using threshold segmentation combined with region growing algorithms based on grayscale and morphological features. The complete 3D volume and central axis of the implant were determined by identifying the implant's unique thread morphology and cylindrical outline. The connection position to the abutment was identified at the implant apex by detecting density abrupt changes. Further upwards, the abutment's tabletop outline and sidewall morphology were identified. Simultaneously, the apical opening of the implant's central screw hole was located in the abutment's central region by detecting low-density or cavity features. Using a similar method, the important inferior alveolar nerve canal running within the mandible was identified in the CT data. This nerve canal appears as a continuous low-density strip structure in CT images. The spatial relationship of the nerve canal relative to the implant was determined by tracing the 3D path of this strip. In the surface mesh corresponding to the oral scan data, curvature analysis and geometric feature recognition algorithms were used to segment the surface mesh of the implant crown to be removed from the surface mesh of adjacent teeth. Anatomical landmarks such as the contact area between the crown and adjacent teeth and the gingival margin were used as segmentation criteria to extract the complete surface model of the implant crown to be removed. Based on the surface normal vector and positional relationship, the lighter-colored mesh areas located at the root of the teeth in the oral scan data were identified as gingival soft tissue. The spatial distribution range of the soft tissue was determined by constructing a three-dimensional contour of the gingival surface.

[0040] S103: Perform voxelization on the digitized 3D scene to obtain a 3D voxel mesh containing multiple voxels.

[0041] In S103 above, the spatial resolution parameters required for voxelization are first determined. Spatial resolution directly determines the fineness of the generated three-dimensional voxel mesh. Considering that the diameter of the bur in the implant crown removal operation is usually 1.0 mm to 2.0 mm and the clinical operation accuracy requirement is to be controlled within 0.5 mm, the side length of a single voxel is set to 0.4 mm. This value can capture the spatial distribution of key anatomical details such as implant threads and abutment edges, and can also avoid the problem of increased computation and excessive memory usage caused by excessively small voxels, ensuring the feasibility of completing subsequent path planning calculations on a regular workstation. After determining the voxel edge length, the size of the required 3D voxel mesh is calculated based on the spatial envelope of the digital 3D scene. The vertex coordinates of all anatomical structure models in the digital 3D scene are traversed to find the minimum and maximum values ​​in the X, Y, and Z directions, thereby determining the 3D bounding box of the entire scene. Based on the bounding box, a certain margin, such as 5 to 10 millimeters, is added outward to accommodate the peripheral areas that may be involved in subsequent path planning. The expanded bounding box is divided by the voxel edge length in the X, Y, and Z directions respectively and rounded up to obtain the number of voxels in each direction of the 3D voxel mesh. For example, if the bounding box size is 30 mm × 25 mm × 20 mm and the voxel edge length is 0.4 mm, the generated 3D voxel mesh will have a size of 75 × 63 × 50 voxels, totaling approximately 236,250 voxel units.

[0042] After determining the spatial range and resolution of the three-dimensional voxel mesh, the ray casting method combined with the inside-outside point determination algorithm is used to convert each anatomical structure model in the digital three-dimensional scene into a voxel. For solid tissue structures such as implants, abutments, crowns to be removed, and adjacent teeth, a virtual ray is emitted from the center point of each voxel in the three-dimensional voxel mesh along any fixed direction, such as the positive Z-axis. The number of intersections between the virtual ray and the surface mesh of the target anatomical structure is counted. If the number of intersections is odd, the voxel center is located inside the structure; if the number of intersections is even, the voxel center is located outside the structure. This odd-even determination rule can accurately identify which voxels are occupied by specific anatomical tissues. While performing the internal and external point determination, a semantic label is attached to each voxel to record the type of anatomical structure to which it belongs. For example, voxels located within the implant geometry are labeled as "implant voxels" and assigned a label value of 1; voxels located within the abutment geometry are labeled as "abutment voxels" and assigned a label value of 2; voxels located within the crown to be removed geometry are labeled as "crown voxels" and assigned a label value of 3; voxels located within the adjacent tooth geometry are labeled as "adjacent tooth voxels" and assigned a label value of 4; voxels located within the gingival soft tissue geometry are labeled as "soft tissue voxels" and assigned a label value of 5; and voxels not occupied by any solid tissue are labeled as "air voxels" and assigned a label value of 0. For tubular structures like the inferior alveolar nerve canal, whose diameter is typically between 2 and 3 millimeters, the diameter needs to be considered as the spatial influence range of the risk area during voxelization. This involves discretizing the central path curve of the nerve canal into a series of sampling points, identifying all voxels in the 3D voxel grid that are less than a preset safety distance, such as 5 millimeters, from each sampling point, and marking these voxels as "nerve canal influence area voxels" and assigning them a label value of 6. In this way, even if the geometric volume of the nerve canal itself is small, the surrounding safe avoidance area can be clearly identified in the voxel grid.

[0043] After completing the voxelization labeling of all anatomical structures, the transition between voxel labels of adjacent anatomical structures is first checked for rationality. For example, implant voxels and abutment voxels should be spatially adjacent and form a continuous interface, and crown voxels should completely surround the top area of ​​abutment voxels. If label jumps or spatial gaps are found, morphological closing operations are used to locally repair the voxel labels, filling isolated cavities caused by surface mesh defects or sampling errors. Special treatment is applied to the central screw hole area of ​​the implant. Since the screw hole is the target endpoint of the subsequent crown removal path, its position needs to be accurately marked in the voxel mesh. Based on the screw hole top opening coordinates identified in the semantic segmentation stage, the voxel closest to these coordinates is found in the three-dimensional voxel mesh and marked as "screw hole top voxel" with a special label value of 7. At the same time, voxels are traced downwards along the implant central axis to a certain depth, such as 3 mm to 5 mm, and these voxels are marked as "screw hole channel voxels" to ensure that the path planning algorithm can accurately locate the exploration endpoint. In a three-dimensional voxel grid, the outer surface voxels of the crown to be removed are identified. These surface voxels will serve as the starting point for subsequent path searches. The specific identification method is to traverse all voxels marked as "crown voxels" and check whether there is a voxel marked as "air voxel" among the six adjacent voxels in the top, bottom, left, right, front, and back. If it exists, the crown voxel is located at the interface between the crown and the outside air, and is marked as "crown surface voxel" and assigned a label value of 8. Through this neighborhood detection method, the expression of the complete outer surface of the crown in the voxel space can be automatically extracted.

[0044] Through the above voxelization process, the digital 3D scene originally represented by a continuous triangular mesh is converted into a 3D voxel mesh containing multiple voxels. Each voxel in the 3D voxel mesh not only has a clear 3D spatial location, but also carries rich semantic information, namely the anatomical structure type to which it belongs.

[0045] S104: Based on the spatial geometric distance from the target voxel to the anatomical structure, calculate the conditional probability of triggering various preset failure events when the cutting tool passes through the target voxel, and construct a three-dimensional probability cloud map for the conditional probabilities corresponding to all voxels.

[0046] In S104 above, based on the spatial geometric distance from the target voxel to the anatomical structure, the conditional probability of triggering various preset failure events when the cutting tool passes through the target voxel is calculated, and a three-dimensional probability cloud map is constructed for the conditional probabilities corresponding to all voxels. Specifically, this includes: obtaining a set of preset failure events, which includes mechanical damage events to the implant, mechanical damage events to the abutment, damage events to adjacent teeth or restorations, bone tissue damage to the implant due to heating, and events where the crown cannot be easily separated by the instrument after cutting; calculating the Euclidean distance from the target voxel to the corresponding surface of each structure in the anatomical structure to obtain the spatial geometric distance; and when the preset failure event is a mechanical damage event to the implant, abutment, or damage event to adjacent teeth or restorations... When the cutting tool passes through the target voxel, the spatial geometric distance is substituted into the first probability mapping function to calculate the conditional probability of triggering a preset failure event. When the preset failure event is damage to the bone tissue around the implant due to heating, the spatial geometric distance is substituted into the second probability mapping function to calculate the conditional probability of triggering the preset failure event. When the preset failure event is that the crown cannot be easily separated by the instrument after cutting, the spatial geometric distance is substituted into the third probability mapping function to calculate the conditional probability of triggering the preset failure event. All voxels in the three-dimensional voxel grid are traversed, and the conditional probabilities corresponding to each voxel are spatially arrayed and mapped to construct a three-dimensional probability cloud map containing multiple probability dimensions.

[0047] Specifically, a pre-defined set of failure events is obtained. This set is systematically summarized based on clinical experience and literature reports of common complications in implant crown removal. The pre-defined set of failure events includes, but is not limited to, five major categories of key risk events. The first category is mechanical damage to the implant, which refers to the cutting tool, such as a diamond bur, directly contacting and cutting the titanium alloy surface of the implant, resulting in damage to the implant threads, changes in surface roughness, or localized material defects. This type of damage weakens the mechanical strength of the implant and may affect the long-term stability of its integration with bone tissue. The second category is mechanical damage to the abutment, which refers to the cutting tool accidentally cutting into the abutment components connecting the implant and the crown, including the abutment's tabletop, sidewalls, or screw mounting slots. Abutment damage can lead to inaccurate placement of the new crown, abnormal occlusion, or decreased retention. The third category is damage to adjacent teeth or restorations, which refers to the cutting tool deviating from the intended area during the removal of the target crown, accidentally damaging the enamel, dentin, or existing porcelain crowns, all-ceramic crowns, or other restorations of adjacent natural teeth. The fourth category is peri-implant bone tissue damage caused by heating. This originates from the frictional heat generated during the cutting process by the high-speed rotating bur. When the heat is conducted through the abutment to the implant and further to the implant-bone interface, if the local temperature exceeds 47 degrees Celsius and lasts for more than one minute, it can cause thermal necrosis of bone cells and irreversible damage to bone tissue, leading to peri-implant bone resorption or even implant loosening and failure. The fifth category is cases where the crown cannot be easily separated by instruments after cutting. This refers to situations where, although the cutting operation itself does not directly damage the implant or abutment, insufficient cutting depth, improper cutting position, or unreasonable cutting direction can prevent the effective separation of the adhesive layer or mechanical connection between the crown and the abutment. During the operation, instruments such as pry bars or crown removers are still required to apply significant external force to remove the crown.

[0048] Each voxel in the 3D voxel mesh is selected sequentially as the current target voxel for distance calculation. For each target voxel, the 3D spatial coordinates of the target voxel, i.e., the X, Y, and Z coordinates of the voxel's center point, are first determined. These coordinates can be obtained by multiplying the voxel's index position in the mesh by the voxel's side length and adding the coordinates of the voxel mesh origin. For each type of event in the preset set of failure events, the corresponding anatomical structure associated with the event is identified. For example, for mechanical damage to the implant, the corresponding structure is the 3D geometric model of the implant; for mechanical damage to the abutment, the corresponding structure is the 3D geometric model of the abutment; for damage to adjacent teeth or restorations, the corresponding structure is the set of 3D geometric models of all adjacent teeth and restorations; for bone tissue damage around the implant due to heating, the corresponding structure is still the implant model because heat is mainly conducted through the implant; for events where the crown cannot be easily separated by instruments after cutting, the corresponding structure is the bonding interface area between the top surface of the abutment and the bottom surface of the crown.

[0049] After determining the corresponding structure, the shortest Euclidean distance from the center point of the target voxel to the surface of the corresponding structure is calculated. Since each anatomical structure in the digital 3D scene is represented by a triangular mesh, and the surface is composed of numerous triangular facets, it is necessary to calculate the distances from the center point of the target voxel to all triangular facets of the corresponding structure and find the minimum value as the spatial geometric distance from the target voxel to the surface of that structure. For each triangular facet, a point-to-triangle shortest distance calculation algorithm is used. This algorithm first determines whether the projection point of the target voxel's center point on the triangular plane falls inside the triangle. If the projection point is inside the triangle, the shortest distance is the perpendicular distance from the point to the plane. If the projection point is outside the triangle, it is necessary to further calculate the distances from the point to the three sides of the triangle and the distances from the point to the three vertices of the triangle, and take the minimum value as the distance from the point to that triangular facet. Considering that the triangular mesh of the corresponding structure may contain tens of thousands or even hundreds of thousands of triangular faces, calculating the distance from the target voxel to all triangles one by one would be computationally intensive. Therefore, a spatial acceleration structure such as an octree is used to preprocess the triangular mesh, dividing the space into multiple sub-regions and recording the list of triangles contained in each sub-region. When calculating the distance, most triangles far away from the target voxel are quickly excluded by spatial indexing, and the accurate distance is calculated only for local triangles near the target voxel.

[0050] For implant mechanical injury events, the shortest Euclidean distance from the center point of the target voxel to the triangular mesh on the implant surface is calculated. This distance reflects the space margin for the cutting tool to contact the implant surface when moving or extending in any direction from the target voxel location. For abutment mechanical injury events, the shortest Euclidean distance from the center point of the target voxel to the triangular mesh on the abutment surface is also calculated. Since the abutment is usually located above the implant and partially enclosed by the crown, the abutment surface includes the tabletop and sidewalls exposed at the bottom of the crown. When calculating the distance, the complete geometry of the abutment needs to be considered to ensure that the spatial proximity between the target voxel and any part of the abutment can be identified. For injury events involving adjacent teeth or restorations, since there may be multiple adjacent teeth, the distance from the target voxel to the surface of each adjacent tooth needs to be calculated separately, and the minimum value is taken as the distance from the target voxel to the set of adjacent teeth. This ensures that even if there are multiple adjacent structures around the crown to be removed, the structure closest to the target voxel can be identified as the primary source of risk.

[0051] For events involving peri-implant bone damage due to heating, the risk depends not only on the direct contact between the cutting tool and the implant, but also on the spatial thermal impact zone of the cutting operation. Even if the cutting tool does not directly cut the implant, high-speed cutting at close range still generates heat, which is conducted to the implant through the crown and abutment. When calculating the spatial geometry associated with this event, in addition to calculating the distance from the target voxel to the implant surface, the physical processes of heat conduction must also be considered. A thermal impact radius parameter is defined, determined based on temperature distribution measurements during implant crown removal reported in the literature. Therefore, the thermal impact radius parameter is set to 5 mm. This means that when the distance from the target voxel to the implant surface is less than 5 mm, the voxel is located within the thermal impact zone, and cutting operations in this area may cause thermal damage to the bone tissue. The magnitude of the thermal damage risk is assessed based on the relative relationship between distance and the thermal impact radius parameter; the closer the distance, the higher the heat conduction efficiency and the greater the risk.

[0052] For cases where the crown cannot be easily separated by instruments after cutting, risk assessment needs to consider the spatial relationship between the cutting position and the ideal separation plane. This is because the successful removal of the crown depends not only on whether the cutting depth reaches the abutment surface, but also on whether the cutting path can effectively disrupt the adhesive layer or mechanical interlocking between the crown and the abutment. In the digital 3D scene, the contact interface between the top surface of the abutment and the bottom surface of the crown is identified. This interface is geometrically approximated as a planar region parallel to the abutment surface. The spatial orientation of this interface is determined by analyzing the average normal vector of the top surface of the abutment, and the coordinates of the center position and the plane equation of this interface are calculated. For each target voxel, the vertical distance from the center point of the voxel to the abutment-crown contact interface plane is calculated. This vertical distance reflects the distance the cutting tool needs to move from the target voxel position along a direction perpendicular to the contact interface to reach the separation plane. If the vertical distance is positive and large, it indicates that the target voxel is located on the crown surface far from the abutment. A cutting path starting from this position needs to traverse a long distance to reach the bonding interface, making depth control difficult. If the vertical distance is close to zero, it indicates that the target voxel is very close to the ideal separation plane, making it easier to directly damage the bonding layer when cutting from this position. If the vertical distance is negative, it indicates that the target voxel is already on the abutment side and should not be used as the cutting starting point. The distance from the target voxel to the top of the screw hole also needs to be calculated. For screw-retained crowns, the ideal removal method is to drill through the plugging material at the top of the crown along the screw hole axis to directly expose the screw head, rather than cutting along the crown sidewall. Therefore, a target voxel closer to the screw hole is more advantageous as the starting point for direct screw removal. After calculating the spatial geometric distances from all target voxels to their corresponding structural surfaces, a multi-dimensional distance feature vector is obtained for each voxel. This vector includes multiple distance components, which characterize the voxel's relative position and risk profile in anatomical space from different perspectives.

[0053] Furthermore, for the three types of direct mechanical contact risks in the preset failure event set—mechanical damage to the implant, mechanical damage to the abutment, and damage to adjacent teeth or restorations—a unified first probability mapping function is used to convert the calculated spatial geometric distance into the conditional probability of triggering the preset failure event when the cutting tool passes through the target voxel. First, determine... The key parameter in the first probability mapping function is the preset physical radius R of the cutting tool. tool Standard deviation σ of mechanical vibration deviation of preset cutting tool i Preset physical radius R of the cutting tool tool Based on the specifications of the burs used in high-speed turbine handpieces commonly employed in clinical implant crown removal procedures, the removal operation typically uses fissure drills or diamond burs. The working end diameters are mainly concentrated in four categories: 1.0 mm, 1.4 mm, 1.6 mm, and 2.0 mm. Considering the need to minimize the impact on surrounding tissues while ensuring cutting efficiency, a medium-sized 1.4 mm diameter bur is selected as the standard configuration. Therefore, the preset physical radius R of the cutting tool is... tool Set to 0.7 mm, which is half the diameter of the burr. Preset standard deviation σ for cutting tool mechanical vibration. i This reflects the statistical characteristics of the deviation of the cutting tool's center position from the expected trajectory due to factors such as physiological hand tremors, handpiece bearing clearance, bur bounce, and minute patient movements during actual clinical operations. Based on medical literature research on the precision of oral and maxillofacial surgery, σ... i Set to 0.4 mm.

[0054] After the parameters are determined, conditional probability calculations are performed for each target voxel x. The first probability mapping function is shown below: ; Where, d i (x) represents the shortest Euclidean distance from the target voxel x to the surface of the corresponding anatomical structure, P(E) i |x) represents the conditional probability, R0 tool σ represents the physical radius of the preset cutting tool. i This represents the standard deviation of the preset cutting tool's mechanical vibration. For mechanical damage events to the implant, the shortest Euclidean distance d from the target voxel to the implant surface is extracted. i (x), where i represents the specific anatomical structure corresponding to the implant, and this distance value is the distance calculated in the above steps. Determine the shortest Euclidean distance d of the structure. i Is (x) greater than the preset physical radius R of the cutting tool? toolThis judgment essentially distinguishes between two different geometric states: whether the target voxel has entered the physical occupancy range of the cutting tool. i (x)≤R tool For example, the distance from a target voxel to the implant surface is 0.5 mm, while R... tool A value of 0.7 mm means that when the center of the cutting tool is located at the target voxel, the cylindrical working end of the bur must have spatially overlapped with the implant surface. Even without considering any operational jitter or deviation, purely from a geometric perspective, the cutting tool has already contacted the implant, making the triggering of mechanical damage to the implant a deterministic and inevitable outcome. Therefore, the conditional probability P(E) corresponding to the target voxel is directly calculated. i |x) is assigned a value of 1, representing a 100% risk of damage. This approach aligns with physical reality and provides a clear hard constraint for path planning algorithms: any path that passes through such voxels will be deemed an unacceptably high-risk path.

[0055] If the shortest Euclidean distance d of the structure i (x) is greater than the preset physical radius R of the cutting tool tool For example, the distance from a target voxel to the implant surface is 1.2 mm, while R... tool A value of 0.7 mm indicates that when the center of the cutting tool is located at the target voxel, there is still a safe gap between the physical boundary of the bur and the implant surface, and the size of this safe gap is d. i (x)-R tool That is, 1.2 - 0.7 = 0.5 mm. However, this does not mean there is absolutely no risk of damage, because mechanical vibration deviations in actual operation may cause the actual position of the cutting tool to deviate from the center of the target voxel. When the deviation is large enough to offset the original safety clearance, the cutting tool may still come into contact with the implant surface. To quantify this residual risk introduced by operational uncertainty, the system is based on the difference between the shortest Euclidean distance and the physical radius of the cutting tool, i.e., d. i (x)-R tool Combined with the preset standard deviation σ of mechanical vibration of the cutting tool i Perform Gaussian attenuation calculations. Model the deviation of the cutting tool's center position as conforming to a mean of 0 and a standard deviation of σ. i Given a normally distributed random variable, under this assumption, the probability that the cutting tool boundary touches the implant surface is equivalent to the deviation exceeding the safety gap d. i (x)-R tool The probability of , based on the probability density function characteristics of the normal distribution, can be expressed by the complementary cumulative distribution function of a Gaussian function. Considering that the conditional probability needs to vary continuously between 0 and 1 and should approach 1 when the safety gap is zero, an exponentially decaying Gaussian function exp(-(d)) is adopted.i (x)-R tool The conditional probability P(E) is calculated using )² / (2σi²)). i |x).

[0056] For example, d i (x) = 1.2 mm, R tool =0.7 mm, σ i =0.4 mm, first calculate the safety clearance d i (x)-R tool =0.5 mm, then calculate the normalized distance (d) of this gap relative to the standard deviation of the jitter. i (x)-R tool ) / σ i =0.5 / 0.4 = 1.25 times the standard deviation, then calculate the Gaussian decay exponent term -(d i (x)-R tool )² / (2σ i =-(0.5)² / (2×0.4²)=-0.781, and finally calculate the exponential function exp(-0.781)=0.458, that is, the conditional probability P(E) corresponding to the target voxel. i |x) is approximately 45.8%. With d i As (x) increases, the safety clearance d i (x)-R tool As the difference increases, the absolute value of the Gaussian decay exponent term increases, the value of the exponential function decays rapidly exponentially, and the conditional probability decays exponentially as the difference increases.

[0057] Then, conditional probability calculations are performed using the exact same first probability mapping function for both mechanical damage events to the abutment and damage events to adjacent teeth or restorations. The only difference is the input shortest Euclidean distance d. i (x) correspond to different anatomical structures. For mechanical damage events to the abutment, d i (x) represents the shortest distance da from the target voxel to the abutment surface. Similarly, determine whether da is greater than R. tool If da≤R tool The conditional probability is 1 if da > R. tool Then according to exp(-(da-R) tool )² / (2σ i ²)) Calculate the conditional probability. Since the abutment is usually located above the implant and in direct contact with the crown to be removed, the distance from the target voxel to the abutment is generally shorter than its distance to the implant. Therefore, the conditional probability of abutment damage events is often higher at the same voxel location than that of implant damage events. This aligns with clinical observation that abutments are more easily damaged. For damage events to adjacent teeth or restorations, d i(x) represents the shortest distance from the target voxel to the surface of the adjacent tooth assembly. Since this distance is the minimum distance to all adjacent teeth, the conditional probability reflects the risk of damage to the nearest adjacent tooth. If the gap between the crown to be removed and an adjacent tooth is very small, for example, only 1.0 mm, the distance from the target voxel between the two teeth to the surface of the adjacent tooth may be only 0.3 mm to 0.5 mm. After deducting the 0.7 mm bur radius, this is already a negative value or a very small positive value, and the corresponding conditional probability will be close to or equal to 1. This indicates that cutting operations in narrow gaps have a very high risk of damage to adjacent teeth, and the path planning algorithm should avoid such areas as much as possible. After calculating the conditional probabilities of each target voxel in the three-dimensional voxel mesh for mechanical damage events to the implant, mechanical damage events to the abutment, and damage events to adjacent teeth or restorations, three independent probability fields are obtained. Each probability field contains the same number of probability values ​​as the voxel mesh, forming three three-dimensional arrays.

[0058] Furthermore, for the special thermal damage risk of peri-implant bone tissue damage due to heating in the preset failure event set, a second probability mapping function different from mechanical contact damage is used to calculate the conditional probability of triggering the preset failure event when the cutting tool passes through the target voxel. This is because the mechanism of thermal damage is fundamentally different from direct mechanical contact; it is achieved through the conduction and diffusion of heat in the tissue.

[0059] The predicted temperature rise at the target voxel is calculated based on the thermal conductivity index decay law. The calculation process considers the energy attenuation characteristics during heat transfer from the cutting point to the implant and bone tissue. The high-speed rotational cutting operation of the cutting tool at the target voxel location is regarded as a point heat source, and the intensity of this heat source is determined by the maximum source temperature rise ΔT of the cutting tool under full load. max This parameter, ΔT, reflects the maximum temperature rise of the working end of the bur relative to the ambient temperature during continuous cutting of hard dental crown tissue. Based on experimental research literature in the field of oral medical engineering regarding the thermal effects of high-speed turbine handpieces, ΔT... max The setting is 70 degrees Celsius, which means that under the most unfavorable conditions of continuous high-load cutting and insufficient cooling, the temperature at the cutting location itself can rise by up to 70 degrees Celsius.

[0060] After determining the heat source intensity, the temperature decay during the heat transfer from the target voxel to the implant surface and then to the bone tissue is calculated. Due to the multiple interfaces between the implant crown, abutment, and implant body, and the varying thermal properties of the materials, accurate heat conduction calculations require solving complex unsteady-state partial differential equations of heat conduction, which is computationally too intensive and impractical in real-time path planning scenarios. A simplified exponential decay model is used to approximate the temperature variation with distance. This model is based on the analytical solution of steady-state heat conduction, assuming that the temperature field has reached a quasi-steady-state distribution, and that the temperature rise decreases exponentially with spatial distance from the heat source. The predicted temperature rise ΔT(x) at the target voxel is calculated using the formula: ΔT(x) = ΔT max ×exp(-α×d b (x)), where d b (x) represents the shortest Euclidean distance from the target voxel to the surface of the corresponding anatomical structure. Here, the corresponding anatomical structure specifically refers to the implant, because the heat source for thermal damage to bone tissue is mainly conducted through the implant. b (x) is actually the distance from the target voxel to the implant surface calculated above. The parameter α represents the preset thermal attenuation coefficient of the tooth hard tissue, which physically represents the rate attenuation of the temperature field in space. A larger α value indicates that the temperature attenuates faster with distance, while a smaller α value indicates a wider range of heat propagation. Determining the value of the preset thermal attenuation coefficient α of the tooth hard tissue requires comprehensive consideration of the thermal conductivity properties of various materials from the cutting location to the implant and then to the bone tissue. The preset thermal attenuation coefficient α of the tooth hard tissue is set to 0.5.

[0061] For example, the distance d from a target voxel to the implant surface. b (x) = 4 mm. Substituting this distance into the exponential decay formula, we get ΔT(x) = 70 × exp(-0.5 × 4) = 9.5 degrees Celsius. This indicates that when the cutting tool performs a full-load cut at the target voxel position 4 mm away from the implant surface, the temperature rise conducted to the implant surface is approximately 9.5 degrees Celsius.

[0062] After obtaining the predicted temperature rise value ΔT(x) at the target voxel, the magnitude of the thermal damage risk cannot be directly determined. This is because the damage response of bone tissue to temperature increases is not a simple linear relationship, but rather there exists a critical temperature threshold. When the temperature rise is below this threshold, bone tissue can tolerate temperature changes through physiological regulatory mechanisms without permanent damage. When the temperature rise exceeds this threshold, the probability of damage increases rapidly, and the degree and probability of damage increase rapidly with continued temperature increases. To accurately characterize this nonlinear temperature-damage response relationship, the system substitutes the predicted temperature rise value ΔT(x) into the second probability mapping function for normalization calculation to obtain the conditional probability P(E). h |x), the probability function takes the form of a logistic function: ; Where Tth represents the preset critical temperature rise threshold for thermal damage to bone tissue, β represents the preset sensitivity coefficient, and P(E) h |x) represents the conditional probability, and the conditional probability P(E) h The conditional probability function (Tth) increases monotonically with increasing predicted temperature rise, and reaches its maximum slope with temperature near the preset critical temperature rise threshold for bone tissue thermal damage. The preset critical temperature rise threshold for bone tissue thermal damage (Tth) is determined based on extensive biomedical experimental research; therefore, it is set to 10 degrees Celsius. The preset sensitivity coefficient β controls the rate of change of the conditional probability function near the critical temperature rise threshold, and its value determines the speed of transition from a low-risk state to a high-risk state; therefore, the preset sensitivity coefficient β is set to 0.5.

[0063] For example, if the predicted temperature rise of a target voxel is ΔT(x) = 9.5 degrees Celsius, which is slightly below the critical temperature rise threshold Tth = 10 degrees Celsius, we calculate ΔT(x) - Tth = 9.5 - 10 = -0.5 degrees Celsius, then calculate -β × (ΔT(x) - Tth) = -0.5 × (-0.5) = 0.25, then calculate exp(0.25) = 1.284, and finally calculate the conditional probability P(E). h |x)=1 / (1+1.284)=0.438, or 43.8%. This indicates that when the predicted temperature rise at this location is 9.5 degrees Celsius, although it has not yet reached a clear damage threshold, it is very close, with approximately a 44% probability of causing thermal damage to bone tissue. This is a moderate risk level that requires attention. After calculating the conditional probability of bone tissue damage around the implant due to heating for each target voxel in the three-dimensional voxel mesh, a complete thermal damage risk probability field was obtained. This probability field clearly shows the risk distribution pattern radiating outward from the implant. The closer the voxel is to the implant, the higher the predicted temperature rise value and the greater the conditional probability. The further away the voxel is, the lower the risk gradually becomes, forming a layered risk area around the implant, similar to a concentric circle structure of a bullseye.

[0064] Furthermore, regarding the specific operational effectiveness risk of the crown being unable to be easily separated by instruments after cutting within the preset failure event set, a third probability mapping function, distinct from the aforementioned mechanical and thermal damage, is used to calculate the conditional probability of triggering this preset failure event when the cutting tool passes the target voxel. This is because the risk assessment logic for this event is fundamentally different from other events; it focuses not on whether the cutting operation will damage a sensitive structure, but on whether the cutting path can effectively sever the connection between the crown and the abutment and provide the crown with sufficient degrees of freedom for separation, allowing for gentle removal by instruments after cutting without the need for potentially damaging the implant. First, the shortest Euclidean distance d from the target voxel to the inner surface of the crown to be removed needs to be calculated.c (x), this distance is a key geometric indicator for measuring the cutting depth. The inner surface of the crown to be removed refers to the concave surface of the crown, that is, the surface that contacts or is close to the abutment. This surface has been identified through semantic segmentation and stored in the form of a triangular mesh in the digital 3D scene. For each target voxel x, the 3D spatial coordinates, i.e., the X, Y, and Z coordinates of the voxel's center point, are extracted. The Euclidean distance from the center point to all triangular faces of the triangular mesh on the inner surface of the crown is calculated. The same point-to-triangle shortest distance algorithm as the implant distance calculation above is used, that is, the projection position of the point on the triangular plane is determined and the shortest distance to the triangle itself or its boundary is calculated. After traversing all triangular faces on the inner surface of the crown, the minimum value is taken as the shortest Euclidean distance d from the target voxel to the inner surface of the crown to be removed. c (x). To improve computational efficiency, spatial acceleration data structures such as octrees are also used to preprocess the mesh of the inner surface of the crown, so that for each target voxel, only the triangles in the nearby local area need to be searched to find the shortest distance, without having to traverse all triangles of the entire mesh.

[0065] The shortest Euclidean distance d of the crown c The physical meaning of (x) is the penetration depth margin from the center point of the target voxel to the innermost layer of the crown, i.e., the surface closest to the abutment. The larger this distance, the more likely the target voxel is located in the outer region of the crown. After cutting from this position, the cutting tool needs to continue to penetrate a longer distance to reach the inner surface of the crown and further break through to the abutment-crown contact interface. The smaller this distance, the more likely the target voxel is close to the inner surface of the crown. Cutting from this position only requires a small depth to penetrate the crown wall and reach the separation interface. When this distance is zero, it indicates that the target voxel is exactly located on the inner surface of the crown. At this time, the cutting operation can be directly applied to the adhesive layer or mechanical connection site to achieve the most effective separation. However, it should be noted that not all voxels located on the inner surface of the crown are ideal cutting targets. Because the inner surface of the crown is a three-dimensional curved surface, the degree of contact and stress state with the abutment varies at different positions. Even if some positions are cut, the retention force of the crown cannot be effectively released. Therefore, the system also needs to combine other geometric features, such as the distance to the screw hole and the distance to the edge of the abutment, to comprehensively judge the effectiveness of the cutting position.

[0066] To obtain the shortest Euclidean distance d of the crown c After (x), this distance value is mapped to the conditional probability P(E) of the event that the cut crown cannot be easily separated by instruments. s |x). A third probability mapping function in piecewise form, which is based on d c (x) and the preset security penetration threshold D s The size relationship is handled in two cases.

[0067] The third probability mapping function is shown below: ; Among them, P(E) s |x) represents the conditional probability of the event that the crown cannot be easily separated by instruments after cutting, P min d represents the preset minimum allowable probability value. c (x) represents the shortest Euclidean distance from the target voxel x to the inner surface of the crown to be removed, D s This indicates a preset safe penetration threshold. Physically, it's to ensure the crown can be easily separated; the cutting path must penetrate at least to a distance D from the inner surface of the crown. s The depth should be within the millimeter range; otherwise, excessive residual crown wall thickness will lead to separation difficulties. Determining the preset safe penetration threshold requires comprehensive consideration of the mechanical properties of the crown material, the bonding strength of the abutment-crown interface, and the separation capability of the clinical instruments. The preset safe penetration threshold D should be set accordingly. s Set to 1.5 mm.

[0068] In the third probability mapping function, the shortest Euclidean distance d of the crown is determined first. c Is (x) greater than the preset security penetration threshold D? s If d c (x)>D s For example, the distance from a target voxel to the inner surface of the tooth crown is 3.0 mm, while D... s A margin of 1.5 mm indicates that the target voxel is located deep within the outer layer of the crown. The cutting operation from this voxel location leaves a 3.0 mm margin from the inner surface of the crown. Even if the cutting tool reaches the voxel location completely, it still fails to penetrate to the vicinity of the bonding interface, and the crown base retains a relatively thick, intact structure. At this point, the connection between the crown and abutment has not been effectively disrupted, making postoperative crown separation extremely difficult and potentially requiring the use of forceful instruments. Therefore, the system directly determines the corresponding conditional probability P(E). s Setting |x) to 1 indicates that there is a 100% chance of a failure where the crown cannot be easily separated by instruments after cutting.

[0069] If the shortest Euclidean distance of the tooth crown is d c (x) is less than or equal to the preset safe penetration threshold D s This indicates that the target voxel has penetrated into the deep region of the crown, close to the inner surface and bonding interface. Cutting from this location could effectively disrupt the crown-abutment connection, but the ease of separation depends on the specific details. c The specific value of (x) indicates that a smaller distance signifies deeper penetration and easier separation, while a larger distance, although within the safety threshold, still carries a certain risk of separation difficulties. To finely characterize this gradual change in risk, the system employs a linear interpolation model, making the conditional probability P(E)... s |x) With the shortest Euclidean distance d of the crownc (x) decreases linearly as it decreases, until d c When (x) is 0, the conditional probability reaches the preset minimum allowable probability value P. min The specific function form is P(E) s |x)=P min +(1-P min )×d c (x) / D s The geometric meaning of this formula is in d c (x) from D s As the probability linearly decreases to 0, the conditional probability decreases linearly from 1 to P. min This forms a connection point (D) s (1) and point (0, P) min The straight line segment. The preset minimum allowable probability value P. min This indicates that even if the cutting path completely reaches the inner surface of the crown, i.e., d c (x)=0, still representing the minimum probability of failure. This parameter is introduced based on clinical considerations, because even if the cutting operation has theoretically reached the ideal depth, a minimum allowable probability value P is preset. min The value is set to 0.05, or 5%, which means that even with the most ideal cutting depth, a 5% failure probability is still retained as a safety margin. After calculating the conditional probability of the event that the crown cannot be easily separated by the instrument after cutting for all target voxels in the three-dimensional voxel mesh, a probability field reflecting the effectiveness of the cutting is obtained. This probability field exhibits a spatial distribution pattern different from other risk fields.

[0070] After calculating the conditional probabilities of each target voxel in the 3D voxel grid for all five preset failure events, these scattered probability values ​​need to be organized into a unified data structure. This allows subsequent path planning algorithms to efficiently access and comprehensively utilize this risk information. The algorithm traverses all voxels in the 3D voxel grid, mapping the conditional probabilities of each voxel to a spatial array, thus constructing a 3D probability cloud map containing multiple probability dimensions. Essentially, the 3D probability cloud map is a four-dimensional array. The first three dimensions correspond to the spatial dimensions of the 3D voxel grid, i.e., the voxel indices in the X, Y, and Z directions. The fourth dimension corresponds to the probability channel dimension, i.e., the conditional probabilities of different types of preset failure events. The traversal process uses a triple nested loop: the outer loop traverses the X-direction indices from 0 to N1, the middle loop traverses the Y-direction indices from 0 to N1, and the inner loop traverses the Z-direction indices from 0 to N1, ensuring that each voxel in the grid is accessed exactly once. N1 represents the number of voxels in each direction. The probability values ​​obtained by traversal are integrated into a unified four-dimensional array through spatial array mapping operations. After completing the traversal and mapping of all voxels, a complete three-dimensional probability cloud map containing multiple probability dimensions is obtained.

[0071] S105: Obtain the clinical target of the implant crown to be removed, and calculate the conditional probabilities of the target voxels in the three-dimensional probability cloud map based on the clinical target to obtain the local path cost value.

[0072] In step S105 above, the clinical goal of the implant crown to be removed is obtained. Based on the clinical goal, the conditional probabilities corresponding to the target voxels in the three-dimensional probability cloud map are calculated to obtain the local path cost value. Specifically, this includes: obtaining the clinical goal of the implant crown to be removed; determining the corresponding set of weight coefficients based on the clinical goal, wherein the set of weight coefficients includes weight factors corresponding to each preset failure event; and using the set of weight coefficients to perform a weighted summation calculation on the multi-channel conditional probabilities corresponding to the target voxels to obtain the corresponding local path cost value. The clinical goal includes either the goal of retaining the crown or the goal of discarding the crown. Based on the clinical goal, the corresponding set of weight coefficients is determined. Specifically, this includes: constructing a three-dimensional stress distribution field of the implant crown to be removed under a preset removal load, and identifying stress concentration areas based on the three-dimensional stress distribution field. Stress concentration areas are areas that reduce the stability of the crown structure; calculating the spatial geometric distance from each voxel to the corresponding structural surface in the anatomical structure based on the digital three-dimensional scene, and constructing a spatial distance sensitivity function; when the clinical goal is the goal of retaining the crown, based on the spatial geometric distance sensitivity function, the weight factors corresponding to each preset failure event related to anatomical structure damage are weighted... The weighting factor is determined to be a positive penalty function negatively correlated with spatial geometric distance, and the weighting factor corresponding to the event that the cut crown cannot be easily separated by instruments is determined to be zero; when the clinical goal is to discard the crown, the weighting factor corresponding to the event that the cut crown cannot be easily separated by instruments is determined to be a negative reward function positively correlated with the distance of the stress concentration area, and the weighting factors corresponding to the preset failure events related to anatomical damage are kept as positive penalty functions; the determined weighting factors are dynamically normalized and mapped, and the normalized weighting factors are vectorized and combined to obtain the set of weight coefficients corresponding to the clinical goal.

[0073] Specifically, clinical goals are obtained by providing surgeons with explicit options through the user interface. A clinical goal selection control is set up in the planning interface, offering two mutually exclusive options: "Retain Crown" and "Discard Crown." The surgeon selects one based on the specific circumstances of the case. This selection is typically performed in the initial stage of preoperative planning. After completing preparatory work such as importing medical images, 3D reconstruction, voxel mesh generation, and probability cloud map construction, the surgeon needs to clarify the clinical purpose of this crown removal and record their selection to determine the clinical goal.

[0074] Determining the set of weighting coefficients first requires constructing a three-dimensional stress distribution field of the implant crown to be removed under a preset removal load. This is because, as a structure with complex geometry and material properties, the stress on different locations within the crown is not uniform when subjected to external forces. Stress concentration occurs in certain areas due to abrupt changes in geometry, differences in material properties, or constraints of boundary conditions. These stress concentration areas are the weakest parts of the crown structure, and applying external forces to these areas makes it easier for the crown to crack and fracture. For crowns to be retained, the surgeon needs to avoid these stress concentration areas to prevent damage; while for crowns to be discarded, the surgeon should utilize these stress concentration areas, making it easier to fracture and separate the crown during removal, reducing the difficulty of subsequent manual separation. The three-dimensional stress distribution field is constructed using the finite element method. The basic principle of this method is to discretize the continuous crown structure into a mesh model composed of a large number of small elements. Each element is assumed to have a simple stress and strain distribution. The stress field of the overall structure is obtained by solving the equilibrium equations and compatibility conditions between the elements.

[0075] Before performing finite element analysis, it is necessary to extract the geometric model of the dental implant crown to be removed. The geometric model is derived from the digital 3D scene obtained by 3D reconstruction of the medical images in the above steps. From this scene, the triangular mesh surface model belonging to the crown is segmented and extracted. This surface model is composed of thousands to tens of thousands of triangular facets that accurately describe the external shape of the crown. The surface model is then meshed to generate a 3D solid mesh composed of tetrahedral or hexahedral elements. The element size of this solid mesh is usually set to 0.2 mm to 0.5 mm to achieve a balance between computational accuracy and efficiency. For a typical posterior crown, the volume is approximately 500 cubic millimeters. If a 0.3 mm element size is used, the solid mesh contains approximately 15,000 tetrahedral elements. Material properties are assigned to each cell in the solid mesh. The material of the crown is usually an all-ceramic material or a metal-ceramic material. For zirconia all-ceramic material, its elastic modulus is set to 210 GPa, Poisson's ratio is set to 0.30, and density is set to 6.0 g / cm³. These material parameters are derived from the technical data sheets provided by the material supplier or published biomechanical literature. For nickel-chromium alloy porcelain material, the elastic modulus of the metal substrate is set to 200 GPa and Poisson's ratio is set to 0.33, and the elastic modulus of the porcelain layer is set to 69 GPa and Poisson's ratio is set to 0.28. The material type of different locations of the crown is determined based on the gray values ​​of the CT images, and the corresponding material properties are assigned.

[0076] After mesh generation and material assignment, preset removal loads and boundary conditions are defined to simulate the actual stress on the crown during removal. The preset removal load refers to the typical force applied to the crown by instruments during removal. The magnitude and direction of this load are determined based on common clinical removal techniques, such as applying opposing compressive forces simultaneously on the buccal and lingual sides of the crown using a crown remover, with each side having a force of approximately 50 to 100 Newtons, directed perpendicularly to the crown surface and towards the interior of the crown. The system identifies the surface nodes on the buccal and lingual sides of the crown in the finite element model and applies a distributed load to these nodes. The total load of 80 Newtons is evenly distributed across all surface nodes on that side, with each node bearing a force of 80 Newtons divided by the number of nodes. The boundary conditions need to constrain the contact interface between the crown and the abutment. In reality, the crown is fixed to the abutment with adhesive. Under the action of the removal load, the interface will generate a reaction force to support the crown. In the finite element model, the bottom surface of the crown, i.e. the surface in contact with the abutment, is set as a fixed constraint. The displacement degrees of freedom of all nodes on this surface are restricted to zero, that is, these nodes cannot be translated or rotated. Such boundary conditions simplify the modeling requirements of the abutment and implant, while reasonably reflecting the supporting effect on the crown.

[0077] After setting the loads and boundary conditions, the finite element solver is invoked to calculate the stress field. The solver employs a linear statics analysis method, establishing the system's total stiffness matrix and load vector based on the principle of virtual work. It obtains the displacement vector u of all nodes by solving the linear equation system K×u=F, where K is the total stiffness matrix and F is the load vector. The solver uses sparse matrix solving algorithms such as the conjugate gradient method or direct methods such as LU decomposition. For a model containing 15,000 tetrahedral elements, the number of degrees of freedom is approximately 15,000 × 4 nodes × 3 directions = 180,000 degrees of freedom. The solution process typically takes several seconds to tens of seconds on modern multi-core processors. After obtaining the nodal displacements, the system calculates the stress tensor of each element based on the strain-displacement and stress-strain relationships. The stress tensor includes six components: three normal stress components σx, σy, and σz, and three shear stress components τxy, τyz, and τzx. The system further calculates the equivalent stress of each element, using von Mises stress as the measure of equivalent stress. Its calculation formula is σ... eq =√[((σx-σy)²+(σy-σz)²+(σz-σx)²+6(τxy²+τyz²+τzx²)) / 2], von Mises stress can comprehensively reflect the degree of influence of the complex stress state of the element on the material yielding, and is an important indicator for assessing whether the structure will undergo plastic deformation or failure.

[0078] The calculated von Mises stress value of each element is mapped to the geometric center of that element, forming a discrete three-dimensional stress distribution field. The spatial resolution of this distribution field depends on the density of the finite element mesh. To maintain a consistent spatial reference frame with the voxel mesh, the system interpolates the stress field from the finite element mesh onto the voxel mesh. For each voxel in the voxel mesh, the geometric center coordinates of that voxel are calculated. Then, a tetrahedral element containing that coordinate point is searched within the finite element mesh. If the voxel center falls inside a tetrahedral element, the von Mises stress value of that element is assigned to the voxel; if the voxel center is not inside any element (i.e., the voxel is located outside the crown), the stress value of that voxel is set to zero. Through this interpolation mapping, a three-dimensional stress distribution field S[i][j][k] with the same size as the voxel mesh is obtained, where S[i][j][k] represents the von Mises stress value corresponding to the voxel located at spatial position (i, j, k), in megapascals (MPa). A three-dimensional stress distribution field was used to identify stress concentration regions. This identification process combined threshold segmentation and connected component analysis. The distribution characteristics of all non-zero stress values ​​in the three-dimensional stress distribution field were statistically analyzed, and the mean μs and standard deviation σs of the stress values ​​were calculated. For a typical all-ceramic crown, under an 80-Newton removal load, the mean stress value is approximately 50 MPa, and the standard deviation is approximately 30 MPa. The threshold for determining stress concentration was defined as Ts = μs + 2 × σs. This threshold was set based on the statistical criterion of twice the standard deviation; stress values ​​exceeding this threshold were considered significantly higher than the average level, and the corresponding regions were identified as stress concentration areas. Connectivity analysis is performed to identify independent stress concentration regions. A 3D region growing algorithm is used for this analysis. The algorithm starts with any unvisited stress concentration voxel, adds it to the current connected region, and marks it as visited. Then, it checks the voxel's 26 neighboring voxels (including face-adjacent, edge-adjacent, and vertex-adjacent neighbors). If a neighboring voxel is also a stress concentration voxel and has not yet been visited, it is added to the current connected region, and the process continues until the current connected region can no longer be expanded, resulting in a complete connected stress concentration region. Another starting point is selected from the remaining unvisited stress concentration voxels, and the above process is repeated to identify the next connected region until all stress concentration voxels are assigned to a connected region. Through connectivity analysis, scattered high-stress voxels are organized into several independent stress concentration regions, each identified by a unique label.

[0079] Spatial characteristic parameters were calculated for each identified stress concentration region, including the region's geometric center coordinates, the number of voxels contained in the region, the average stress value, and the maximum stress value. The geometric center coordinates of the region were obtained by averaging the coordinates of all voxels within the region. The number of voxels contained in the region is directly equal to the number of voxels assigned to that region in the connected component analysis; this number reflects the spatial scale of the stress concentration region, with larger regions indicating that the stress concentration phenomenon persists over a larger area and has a more significant impact on the stability of the crown structure. The average stress value and maximum stress value of the region were obtained by averaging and maximizing the stress values ​​of all voxels within the region, respectively; these two indicators quantify the severity of the stress concentration. These characteristic parameters were stored in a stress concentration region list, where each element corresponds to a region and contains all the characteristic parameters of that region. This list provides a quantitative reference for subsequently determining weighting factors based on clinical goals.

[0080] After identifying stress concentration areas, the spatial geometric distances from each voxel to its corresponding surface in the anatomical structure are calculated based on the digital 3D scene to construct a spatial distance sensitivity function. The anatomical structures include the implant surface, abutment surface, adjacent tooth surfaces, and adjacent restoration surfaces. These structures have already obtained their respective surface mesh models through 3D reconstruction in the digital 3D scene. For each anatomical structure, the shortest distance from all voxels in the voxel mesh to the surface of that structure is calculated. The shortest distance is defined as the minimum Euclidean distance from the geometric center of the voxel to any point on the surface of the structure. A spatial index structure, such as an octree or KD tree, is first established for the surface mesh of each anatomical structure. This index structure recursively divides the 3D space into several sub-regions, each recording a list of surface triangles contained within it. For any voxel (i, j, k) in the voxel mesh, the geometric center coordinates (xc, yc, zc) of the voxel are first calculated. The spatial index structure then queries for the candidate triangles closest to these coordinates, typically selecting 10 to 20 triangles closest to the voxel center as candidates. Calculate the shortest distance from the voxel center to each candidate triangle. For triangle T, the calculation requires determining the projection position of the voxel center onto the triangle. If the projection point falls inside the triangle, the shortest distance is the distance from the voxel center to that projection point; if the projection point falls outside the triangle, the shortest distance is the minimum of the shortest distances from the voxel center to the three sides of the triangle and to the three vertices of the triangle. Compare the shortest distances from the voxel center to all candidate triangles, and select the minimum value as the spatial geometric distance from the voxel to the anatomical structure surface.

[0081] The distances di[i][j][k] to the implant surface, da[i][j][k] to the abutment surface, dt[i][j][k] to the adjacent tooth surface, and dr[i][j][k] to the adjacent restoration surface of each voxel are calculated separately. These four distance fields are stored in four independent three-dimensional arrays. For voxels located on or inside the anatomical structure, the distance value is set to zero; for voxels located outside the anatomical structure, the distance value is positive, with a larger distance indicating a greater distance from the anatomical structure. A spatial distance sensitivity function is constructed based on the set of distance fields. This function maps spatial geometric distance to risk sensitivity or weight adjustment coefficient. The basic principle is that locations closer to the anatomical structure pose a greater potential threat and should be given a higher risk weight. The spatial distance sensitivity function adopts a nonlinear mapping form, and commonly used function forms include exponential decay functions, inverse proportional functions, or piecewise linear functions. This application employs a negative exponential function as the spatial distance sensitivity function, expressed as S(d) = α × exp(-d / λ), where d is the spatial geometric distance, S(d) is the corresponding sensitivity value, α is the sensitivity scaling factor, and λ is the distance attenuation feature length. Different sensitivity function parameters are set for different anatomical structures to reflect the differences in the sensitivity of different structures to damage. For the implant surface, a larger sensitivity scaling factor αi = 10.0 and a longer attenuation feature length λi = 2.0 mm are set, so that a larger area of ​​voxels around the implant is given high sensitivity. For the abutment surface, although damage to the abutment will also affect the repair effect, its replacement is relatively easy, so moderate sensitivity parameters αa = 5.0 and λa = 1.5 mm are set. These parameter values ​​are determined based on clinical experience and expert consultation, and can be adjusted according to the specific case in practical applications.

[0082] The spatial distance sensitivity function is applied to various distance fields to calculate the corresponding sensitivity fields. After constructing the spatial distance sensitivity function and the stress concentration region identification results, the weighting factors corresponding to each preset failure event are determined based on the acquired clinical goals. The weighting factor is a coefficient used in the path planning algorithm to adjust the relative importance of different risk types. In the path cost function, the probability value of each risk is multiplied by its corresponding weighting factor and then summed to form the total cost. A larger weighting factor indicates a more significant impact of that type of risk on the decision-making process.

[0083] When the clinical goal is to preserve the crown, the core consideration is to minimize damage to surrounding anatomical structures during crown removal. Preserving the crown implies that the surgeon plans to reuse it after removal or at least wants it to remain relatively intact. In this case, even if the cutting path makes separation of the crown from the abutment difficult, the surgeon can accept achieving separation through more meticulous manual manipulation or auxiliary tools. The risk associated with the crown being unable to be easily separated by instruments after cutting can be ignored. The weighting factors corresponding to various pre-set failure events related to anatomical damage are determined as a positive penalty function negatively correlated with spatial geometric distance. This positive penalty function directly adopts the spatial distance sensitivity function constructed above. For events involving mechanical damage to the implant, the weighting factor is wi[i][j][k] = αi × exp(-di[i][j][k] / λi); for events involving mechanical damage to the abutment, the weighting factor is wa[i][j][k] = αa × exp(-da[i][j][k] / λa); for events involving damage to adjacent teeth or restorations, the maximum sensitivity of the adjacent teeth and restorations is taken as the unified weighting factor, thus ensuring that the weighting factor increases accordingly whenever the voxel approaches any of the adjacent teeth or restorations; for events involving damage to the bone tissue around the implant due to heating, since the impact range of thermal damage is large and related to the distance from the implant, the weighting factor is also set as a function related to the distance from the implant, but a relatively small sensitivity coefficient is used, wt[i][j][k] = αt × exp(-di[i][j][k] / λt), where αt = 3.0 and λt = 3.0 mm. This parameter setting reflects the clinical characteristic that although thermal damage is important, its threshold is relatively tolerant to mechanical damage. The weighting factor corresponding to the event that the cut crown cannot be easily separated by instruments is set to zero, i.e., ws[i][j][k]=0. This setting means that the separation difficulty factor is completely ignored in the path cost calculation. Mathematically, when the weighting factor of a certain risk is zero, even if the conditional probability of the risk is high, its contribution to the total path cost is zero. The path planning algorithm does not consider the differences in separation difficulty among different candidate paths when comparing them. The optimization objective of the algorithm is entirely focused on minimizing the risk of damage to the anatomical structure.

[0084] When the clinical goal is to remove a crown, the surgeon is less concerned with the crown's integrity after removal and more focused on the efficiency of the removal process and the protection of the implant abutment system. The weighting factor corresponding to the event that the crown cannot be easily separated by instruments after cutting is determined as a negative reward function positively correlated with the distance to the stress concentration region. The purpose of the negative reward function is to incentivize the path planning algorithm to actively approach the stress concentration region, because cutting near the stress concentration region makes it easier for the crown to break along the stress concentration point during removal, thus facilitating easy separation by instruments. The negative reward function is a monotonically increasing function with the distance from the voxel to the stress concentration region as the independent variable. It outputs an increasing negative cost value as the distance decreases. The negative cost value means that this value is negative; when added to other positive costs, it reduces the total cost, thus making the path planning algorithm tend to choose a path passing through this location.

[0085] First, the distance from each voxel to the stress concentration region is calculated. For any voxel (i, j, k) in the voxel grid, the system traverses all the previously identified stress concentration regions and calculates the shortest distance from the geometric center of the voxel to each stress concentration region. The shortest distance is defined as the minimum Euclidean distance from the voxel center to the geometric center of any voxel within that region. The distance to the region with the shortest distance among all stress concentration regions is selected as the overall distance from the voxel to the stress concentration region, denoted as ds[i][j][k]. If the voxel itself is a member of a stress concentration region, the distance is zero; if the voxel does not belong to any stress concentration region, its distance is positive, and the larger the distance, the farther the voxel is from the nearest stress concentration region. The system then constructs a negative reward function, using the functional form R(d) = -β × exp(-d / μ), where d is the distance ds from the voxel to the stress concentration region, R(d) is the corresponding reward value, β is the reward intensity coefficient, and μ is the distance decay characteristic length. The characteristic of this function is that R(d) is always negative. When d=0, i.e., the voxel is located inside the stress concentration region, the reward value reaches its maximum negative value of -β, indicating that the maximum cost discount is given to that location. As the distance d increases, the absolute value of the reward value decreases rapidly according to an exponential law. When d is much greater than μ, the reward value approaches zero, indicating that the location is too far from the stress concentration region to obtain a reward. Based on clinical experience, the parameters of the negative reward function are set, with the reward intensity coefficient β set to 6.0. This value needs to ensure that the influence of the negative reward is significant enough to guide the path closer to the stress concentration region, but it cannot be too large, causing the algorithm to excessively pursue proximity to the stress concentration region and ignore other safety constraints. The distance decay feature length μ is set to 1.5 mm. This value represents the effective range of the reward effect. Voxels within 1.5 mm of the stress concentration region can obtain a relatively significant cost discount, while the reward effect decays rapidly beyond this range.

[0086] A negative reward function is applied to calculate the weight factor corresponding to the event that the cut crown cannot be easily separated by instruments, ws[i][j][k]=-β×exp(-ds[i][j][k] / μ). This weight factor takes a larger negative value inside or near the stress concentration area, and a negative value close to zero in locations far from the stress concentration area. When the path planning algorithm evaluates the cost of a path, the path segment passing near the stress concentration area will receive cost reduction due to the effect of the negative weight factor, thus appearing better in the overall cost comparison, and the algorithm is therefore incentivized to choose such a path. Under the goal of discarding the crown, the weighting factors corresponding to the pre-set failure events related to anatomical structural damage are maintained as positive penalty functions. That is, the same spatial distance sensitivity function as for the goal of retaining the crown is still used: wi[i][j][k]=Si[i][j][k], wa[i][j][k]=Sa[i][j][k], wa[i][j][k]=max(St[i][j][k],Sr[i][j][k]), wt[i][j][k]=αt×exp(-dii][j][k] / λt). This means that although the clinical goal becomes discarding the crown, the protection of key anatomical structures such as implants, abutments, and adjacent teeth remains an uncompromising safety bottom line. While guiding the path towards stress concentration areas, the system must ensure that the path does not excessively approach or cross these sensitive structures. By maintaining a positive penalty function, there are two opposing driving forces in the path cost function at the same time. The negative reward function prompts the path to move closer to the stress concentration area to facilitate crown separation, while the positive penalty function constrains the path to stay away from the anatomical structure to avoid damage. The path planning algorithm needs to find a balance between these two forces, and the final generated path is a compromise solution that is as close as possible to the stress concentration area while ensuring safety.

[0087] Furthermore, after determining the functional form and parameters of each weight factor, these weight factors are dynamically normalized to ensure that different weight factors maintain consistency in numerical magnitude, preventing some weight factors from dominating the entire path cost calculation due to excessively large values, thus causing other risk factors to be ignored. A maximum-based normalization method is adopted. For each weight factor, all voxels in the voxel grid are traversed first, and the maximum absolute value of the weight factor at all voxel positions is calculated. The global maximum value among all weight factor maximum values ​​is calculated, and each weight factor is divided by this global maximum value to obtain the normalized weight factor. The absolute values ​​of all normalized weight factors do not exceed 1.0, with the normalized weight factors for the positive penalty function ranging from 0 to 1.0, and the normalized weight factors for the negative reward function ranging from -0.6 to 0. This uniformity of numerical range ensures comparability of different risk types in path cost calculation. The normalized weight factors are then vectorized and combined to obtain a set of weight coefficients corresponding to the clinical objectives. The set of weight coefficients is represented in the data structure as a four-dimensional array W[i][j][k][c], whose structure corresponds completely to the aforementioned three-dimensional probability cloud map. The spatial indices i, j, and k identify the voxel positions, and the channel index c identifies the preset failure event type. Dynamic normalization mapping ensures the numerical balance of the weight coefficients, avoiding the over-amplification or neglect of certain risks due to subjective bias in weight setting.

[0088] Furthermore, after constructing the 3D probability cloud map and the set of weighted coefficients, the multi-channel conditional probabilities corresponding to the target voxels are weighted and summed using the set of weighted coefficients to obtain the corresponding local path cost value. When calculating the local path cost value, the concept and selection method of the target voxel are first clarified. A target voxel refers to a candidate position currently being evaluated by the path planning algorithm during the search process. In graph search-based path planning algorithms such as A* or Dijkstra's algorithm, the algorithm maintains a priority queue of nodes to be evaluated. Each time, the node with the lowest cost is taken from the queue as the current node, and its neighboring nodes are expanded as new candidate nodes. These candidate nodes are the target voxels for which the local path cost value needs to be calculated. In sampling-based path planning algorithms such as the Rapid Expanding Random Tree (RRT) algorithm, the algorithm generates new candidate points in space through random sampling or heuristic sampling. These sampled points are also target voxels for which the cost needs to be evaluated. The target voxel is represented by the symbol x. Mathematically, this symbol represents the spatial index of the voxel in the three-dimensional voxel grid, i.e., x=(i,j,k), where i,j, andk are the index values ​​of the voxel in the X, Y, and Z directions, respectively. Through this index, the position of the voxel in space can be uniquely determined and all attribute data corresponding to the voxel can be accessed, including conditional probability and weight factor.

[0089] The local path cost C(x) is defined as a quantitative measure of the overall risk cost incurred when the cutting tool passes through the target voxel x. A larger value indicates a higher risk of cutting at that location or a more severe deviation from clinical objectives. The goal of the path planning algorithm is to find a path from the starting point to the ending point that minimizes the sum of the local path costs of all voxels along the path. The formula for calculating the local path cost is as follows: ; Where x represents the target voxel, C(x) represents the local path cost at target voxel x, N represents the total number of preset failure events, and P(E) i |x) represents the conditional probability of triggering the i-th preset failure event when the cutting tool passes through the target voxel x, w i Let G(x) represent the weight factor corresponding to the i-th preset failure event, and let each weight factor in the set of weight coefficients satisfy the normalization mapping constraint. Let G(x) represent the geometric constraint penalty term of the guidance path, and let γ represent the geometric constraint adjustment coefficient.

[0090] The formula for calculating the local path cost consists of two main parts. The first part is the weighted risk term Σ(i=1 to N)[w i ×P(E i The second part is the geometric constraint penalty term γ×G(x). The calculation process of the weighted risk term is to quantify the comprehensive risk level of the target voxel by weighted summation of the conditional probabilities of all preset failure events.

[0091] In the calculation of the weighted risk term, N represents the total number of pre-defined failure events. This application defines five categories of pre-defined failure events, therefore N=5. These five categories are: mechanical damage to the implant (E1), mechanical damage to the abutment (E2), damage to adjacent teeth or restorations (E3), peri-implant bone tissue damage due to heating (E4), and the inability of the cut crown to be easily separated by instruments (E5). The symbol P(E) i |x) represents the conditional probability of triggering the i-th preset failure event when the cutting tool passes through the target voxel x. The value of this conditional probability is extracted from the previously constructed 3D probability cloud map. For the target voxel x=(i,j,k), the probability value corresponding to the voxel is read from the i-th channel of the probability cloud map, i.e., P(E1|x)=P[i][j][k][0], P(E2|x)=P[i][j][k][1], P(E3|x)=P[i][j][k][2], P(E4|x)=P[i][j][k][3], P(E5|x)=P[i][j][k][4]. These probability values ​​are all floating-point numbers between 0 and 1, where 0 indicates that the event is completely impossible at this position, 1 indicates that the event is almost certain to occur at this position, and the intermediate value indicates the degree of probability of the event occurring.

[0092] symbol w i This represents the weight factor corresponding to the i-th preset failure event. The value of this weight factor is extracted from the previously constructed set of weight coefficients. For the target voxel x=(i,j,k), the weight value corresponding to the voxel is read from the i-th channel of the set of weight coefficients, i.e., w1=W[i][j][k][0], w2=W[i][j][k][1], w3=W[i][j][k][2], w4=W[i][j][k][3], w5=W[i][j][k][4]. The value range of the weight factor varies depending on the clinical goal. For the goal of preserving the crown, the first four weight factors w1 to w4 are positive values ​​between 0 and 1, and the fifth weight factor w5 is zero. For the goal of discarding the crown, the first four weight factors w1 to w4 are still positive values ​​between 0 and 1, and the fifth weight factor w5 is negative values ​​between -0.6 and 0. Each weight factor in the weight coefficient set satisfies the normalization mapping constraint, which means that the maximum absolute value of all weight factors is limited to 1.0. This is achieved through the aforementioned dynamic normalization process. The normalization constraint ensures that different risk types are comparable in cost calculation and prevents certain weight factors from dominating the entire cost calculation due to excessively large values.

[0093] Perform a weighted summation calculation, and for the target voxel x, sequentially calculate the weighted probability w of each preset failure event. i ×P(E i The five weighted probabilities are summed to obtain the total weighted risk term. First, the first weighted probability, w1×P(E1|x), is calculated. This value represents the weighted contribution of the target voxel to the risk of mechanical damage to the implant. Since w1 uses a positive penalty function related to the distance to the implant, w1 is larger near the implant. If the conditional probability P(E1|x) at that location is also higher, the weighted probability obtained by multiplying the two may reach a large value. For example, at a distance of 0.5 mm from the implant surface, the conditional probability may be 0.8, and the normalized weighting factor may be 0.9, so the weighted probability for this term is 0.9×0.8=0.72. However, at a distance of 3 mm from the implant surface, the conditional probability may drop to 0.1, and the weighting factor also decays to 0.2, so the weighted probability for this term is 0.2×0.1=0.02, only about 3% of the former. Similar calculations are performed on the remaining four preset failure events, yielding w2×P(E2|x), w3×P(E3|x), w4×P(E4|x), and w5×P(E5|x), respectively. The weighted probabilities of these five events are then summed, resulting in the weighted risk term = w1×P(E1|x) + w2×P(E2|x) + w3×P(E3|x) + w4×P(E4|x) + w5×P(E5|x). This summation process is implemented in a computer using simple floating-point addition, achieving extremely high computational efficiency, typically completed on the nanosecond level.

[0094] After calculating the weighted risk term, a geometric constraint penalty term γ×G(x) needs to be added to obtain the complete local path cost value. The geometric constraint penalty term is introduced to address the problem that the weighted risk term generates local minima within safe regions, causing the path planning algorithm to lose its directionality. The geometric constraint penalty term G(x) is designed to provide the algorithm with global directional guidance related to the path goal, ensuring that even in areas with extremely low risk costs, the algorithm can still perceive the location of the destination and move towards it. The Euclidean distance from the target destination is used as the basic form of the geometric constraint penalty term. For the target voxel x=(i,j,k), its geometric center has physical coordinates (xc,yc,zc) in actual space, which can be calculated using the voxel index and voxel size, i.e., xc, yc, and zc. In crown removal, the target endpoint of the path planning is usually set as the position that the cutting tool should reach after the crown is cut and separated. The determination of this position is based on the surgical plan. For example, if the plan is to enter from the buccal side of the crown and cut along a specific direction until the crown is completely separated, the endpoint can be set as the position where the cutting path is expected to exit the crown. This position is marked by the surgeon in the 3D scene during the preoperative planning stage or automatically calculated by the system based on the crown geometry. The physical coordinates of the endpoint are (xg, yg, zg).

[0095] The Euclidean distance from the target voxel x to the destination is calculated, defined as dg(x) = √[(xc-xg)² + (yc-ygoa)² + (zc-zg)²]. This distance reflects the linear spatial distance from the current evaluation position to the destination; a larger distance indicates that the current position is farther from the target. The system uses this distance as the basis for the geometric constraint penalty term, defined as G(x) = dgoa(x). This means the geometric constraint penalty term is smaller when approaching the destination and larger when moving away. When the path planning algorithm compares the costs of different candidate voxels, under the same conditions, voxels closer to the destination have lower total costs due to their smaller G(x) values. Therefore, the algorithm is incentivized to choose a movement direction closer to the destination. The symbol γ represents the geometric constraint adjustment coefficient, which controls the relative weight of the geometric constraint penalty in the total cost. A larger γ value indicates a stronger influence of geometric constraints on path selection, and the algorithm tends to approach the endpoint quickly while paying less attention to subtle differences in risk. A smaller γ value indicates a weaker influence of geometric constraints, and the algorithm may focus more on minimizing risk, potentially allowing the path to travel a longer spatial detour to avoid risky areas. The geometric constraint adjustment coefficient γ needs to be set in a balance between path safety and efficiency; based on clinical experience and pre-experiment results, γ is set to 0.1.

[0096] The weighted risk term and the adjusted geometric constraint penalty term are added together to obtain the local path cost C(x) at the target voxel x. This cost value comprehensively reflects the cost of the target voxel in two dimensions: the first dimension is the risk cost, quantified by the weighted risk term, which represents the comprehensive risk level of various failure events triggered by the cutting operation at this location, adjusted for clinical priority; the second dimension is the geometric cost, quantified by the geometric constraint penalty term, which represents the spatial distance from this location to the task objective. During the search process, the path planning algorithm calculates the local path cost value for each candidate voxel and makes a path expansion decision based on this value. The algorithm tends to select voxels with lower local path cost values ​​to join the path, and simultaneously accumulates the local path cost values ​​of all voxels on the path as the total cost of the entire path. The ultimate goal is to find a path from the starting point to the ending point that minimizes the total cost of the path.

[0097] S106: In the three-dimensional probability cloud map, the surface voxel of the implant crown to be removed is taken as the starting point of exploration, and the voxel corresponding to the top of the central screw hole of the implant is taken as the ending point of exploration. Guided by the local path cost value, the optimal path voxel set with the minimum cumulative local path cost value is solved.

[0098] In S106 above, the surface voxel of the implant crown to be removed is used as the exploration starting point in the three-dimensional probability cloud map, and the voxel corresponding to the top of the central screw hole of the implant is used as the exploration ending point. Guided by the local path cost value, an optimal set of path voxels with the minimum cumulative local path cost value is solved. Specifically, this includes: pushing the exploration starting point into the dynamic priority queue, and initializing the cumulative path cost value of all voxels in the three-dimensional voxel grid except the exploration starting point to infinity, and initializing the cumulative path cost value of the exploration starting point to zero; popping the voxel with the minimum current cumulative path cost value to be evaluated from the dynamic priority queue, and traversing the neighboring voxels of the voxel to be evaluated in three-dimensional space; calculating the temporary cumulative path cost value from the exploration starting point through the voxel to be evaluated to the target neighboring voxel, where the temporary cumulative path cost value is the voxel to be evaluated. The cumulative path cost of a voxel is the sum of the cumulative path cost of the voxel, the local path cost of the voxel in the neighborhood, and the spatial step cost between two adjacent voxels. The target neighboring voxel is any neighboring voxel in the 3D space. If the temporary cumulative path cost is less than the historical cumulative path cost recorded by the target neighboring voxel, the historical cumulative path cost of the target neighboring voxel is updated using the temporary cumulative path cost. The parent node pointer of the target neighboring voxel is set to the voxel to be evaluated, and the target neighboring voxel is updated in the dynamic priority queue. The step of updating the cumulative path cost is repeated until the exploration endpoint is popped. When the exploration endpoint is popped, the voxel is backtracked from the exploration endpoint along the parent node pointers of each voxel until the exploration starting point is reached. All voxels passed during the backtracking process are arranged in order to generate the optimal path voxel set.

[0099] Specifically, after calculating the local path cost, an optimal cutting path from the surface of the implant crown to be removed to the top of the implant screw hole needs to be found in the search space formed by the three-dimensional probabilistic cloud graph. This path should minimize the cumulative local path cost, that is, minimize the overall risk and maximize the space efficiency while satisfying the geometric reachability constraint. An improved Dijkstra's shortest path algorithm is used to search for the path in a three-dimensional voxel grid. This is a classic algorithm in graph theory for solving the single-source shortest path problem. The core idea is to dynamically maintain the current shortest distance from the starting point to each node and gradually expand the exploration range until the optimal path to the destination is found. In the application scenario of this application, each voxel in the three-dimensional voxel grid is regarded as a node in the graph. There are edges connecting adjacent voxels. The weight of the edge is determined by the local path cost and the space step size cost. The goal of the algorithm is to find a path from the starting voxel to the ending voxel that minimizes the sum of the weights of all edges on the path.

[0100] First, determine the spatial locations of the exploration start and end points, and their corresponding voxel indices. The exploration start point is set as the surface voxel of the implant crown to be removed. The selection of this voxel is based on the three-dimensional geometric model of the crown and the surgical approach planning. During the preoperative planning stage, the surgeon marks the expected entry position of the cutting tool in the three-dimensional visualization interface. This position is usually selected in an area that is easy to operate on and has a good field of vision on the buccal side or occlusal surface of the crown. The system maps this marked point to a three-dimensional voxel mesh and finds the voxel containing this point as the exploration start point. Assume that the index of this voxel is (is, js, ks), for example (30, 25, 20). The endpoint of the exploration is set as the voxel corresponding to the top of the central screw hole of the implant. The central screw hole of the implant is the channel connecting the abutment and the implant fixing screw. Its top position is the ideal endpoint of the cutting path because after the cutting tool reaches this position, it can continue to go deeper along the screw hole direction to complete the complete separation of the crown and the abutment. This endpoint position is obtained preoperatively by analyzing the CBCT image or CAD model of the implant. Assuming that the physical coordinates of the top of the screw hole are (xe, ye, ze), the coordinates are converted into voxel indices (ie, je, ke).

[0101] The initialization of the pathfinding algorithm requires data structures including a dynamic priority queue and a cumulative path cost record table. The dynamic priority queue is implemented using a min-heap data structure. Each element in the queue contains the voxel's index and its current cumulative path cost value. The queue is sorted in ascending order of cumulative path cost values, supporting efficient insertion, deletion, and minimum value operations with a time complexity of O(log N²), where N² is the number of elements in the queue. A cumulative path cost record table, CostMap, with the same size as the 3D voxel mesh is created. This table is a 3D floating-point array used to store the current known minimum cumulative path cost value from the exploration start point to each voxel. The array is initialized by iterating through all voxels. For all voxels (i, j, k) except the exploration start point, CostMap[i][j][k] = ∞ is set to indicate that these voxels have not yet been explored. The setting of infinity is represented in computers using special floating-point values ​​such as positive infinity in the IEEE 754 standard. For the exploration start point voxel, CostMap[is][js][ks] = 0 is set to indicate that the cumulative cost from the start point to itself is zero. A parent node pointer record table PM is also created. This table is also an array of the same size as the 3D voxel mesh. Each element stores a triple representing the index of the predecessor voxel in the optimal path. Initially, the parent node pointers of all voxels are set to NULL to indicate that the predecessor has not yet been determined.

[0102] Push the exploration starting point into the dynamic priority queue. The specific operation is to call the insertion function of the queue q((is, js, ks), 0), where the first parameter is the voxel index and the second parameter is the cumulative path cost value of 0. At this time, the queue only contains one element, which is the exploration starting point, and the algorithm enters the main loop to execute the iterative search process. In each iteration, first pop the voxel with the smallest current cumulative path cost value from the dynamic priority queue as the voxel to be evaluated. This operation is implemented by calling the function to pop the minimum value of the queue, cv = qmin(). This function returns the voxel index with the minimum cumulative cost in the queue and removes it from the queue. Since the queue is sorted by cost, this operation ensures that the algorithm always preferentially processes the currently known optimal candidate voxels, which is the core mechanism for the correctness of the Dijkstra algorithm. Suppose the voxel index to be evaluated popped in a certain iteration is (ic, jc, kc), and the cumulative path cost value is cc = CostMap[ic][jc][kc]. Traverse the neighboring voxels of the voxel to be evaluated in the three-dimensional space. The neighborhood definition adopts the 26-connected neighborhood rule. That is, for the voxel (ic, jc, kc), the neighborhood includes all voxels (i, j, k) that satisfy |i - ic| ≤ 1 and |j - jc| ≤ 1 and |k - kc| ≤ 1 and (i, j, k) ≠ (ic, jc, kc), a total of 26 neighboring voxels. These 26 neighboring voxels are divided into three categories: 6 face-adjacent voxels that are adjacent through shared faces, such as (ic ± 1, jc, kc), etc.; 12 edge-adjacent voxels that are adjacent through shared edges, such as (ic ± 1, jc ± 1, kc), etc.; and 8 corner-adjacent voxels that are adjacent through shared vertices, such as (ic ± 1, jc ± 1, kc ± 1), etc. The system traverses all neighboring voxels through three nested loops. The outer loop traverses Δi from -1 to 1, the middle loop traverses Δj from -1 to 1, and the inner loop traverses Δk from -1 to 1. For each group (Δi, Δj, Δk), if not all are zero, calculate the neighboring voxel index (in, jn, kn) = (ic + Δi, jc + Δj, kc + Δk). The system first checks whether the neighboring voxel index is within the valid range of the voxel grid, that is, 0 ≤ in < gx and 0 ≤ jn < gy and 0 ≤ kn < gz. If it exceeds the range, skip this neighboring voxel. If it is within the range, perform subsequent processing.

[0103] The temporary cumulative path cost value for reaching the target neighboring voxel from the exploration starting point via the voxel to be evaluated is calculated. This value consists of three parts. The first part is the cumulative path cost value costc of the voxel to be evaluated, representing the accumulated cost from the starting point to the current voxel. The second part is the local path cost value at the target neighboring voxel, calculated using the aforementioned formula, cost local=C(in, jn, kn), which is read from a pre-calculated local cost cache or calculated in real time. The third part is the spatial step cost between two adjacent voxels, which reflects the geometric distance from the current voxel to the neighboring voxel. For face-adjacent voxels, the step size is one voxel side length, denoted as s cost=1.0voxel-size; for edge-adjacent voxels, the step size is √2 times the voxel side length, denoted as s cost=√2voxel-size; and for corner-adjacent voxels, the step size is √3 times the voxel side length, denoted as s cost=√3voxel-size. The introduction of the spatial step cost ensures that the algorithm prefers more direct paths in space rather than detours in the grid. The step size coefficient is determined based on the relative positional relationship between the neighboring voxels and the current voxel. If |Δi|+|Δj|+|Δk|=1, the step size coefficient is 1.0 for face adjacency; if |Δi|+|Δj|+|Δk|=2, the step size coefficient is √2≈1.414 for edge adjacency; and if |Δi|+|Δj|+|Δk|=3, the step size coefficient is √3≈1.732 for corner adjacency. The temporary cumulative path cost is calculated as cost t=costc+(cost local)+(s coststep coefficient), which comprehensively considers the accumulated cost, the current location risk cost, and the movement geometric cost.

[0104] Compare the temporary cumulative path cost value with the historical cumulative path cost value of the target neighborhood voxel. The historical cumulative path cost value is read from CostMap[in][jn][kn], denoted as cost old. If cost t < cost old, it means a better path to the target neighborhood voxel has been found, and the relaxation operation is performed to update the state of this neighborhood voxel. The specific update process includes three steps: First, update the historical cumulative path cost value of the target neighborhood voxel to the temporary cumulative path cost value, CostMap[in][jn][kn]=cost t; Update the parent node pointer of the target neighborhood voxel to point to the current voxel to be evaluated, ParentMap[in][jn][kn]=(ic, jc, kc). This pointer records the predecessor of this neighborhood voxel in the optimal path to support subsequent path backtracking; Third, insert or update the target neighborhood voxel and its updated cumulative cost into the dynamic priority queue. If this neighborhood voxel was not in the queue before, perform the insertion operation q((in, jn, kn), cost t). If it was already in the queue, perform the priority update operation q.decreasek((in, jn, kn), cost t). The implementation of the priority queue needs to support efficient priority updates, which is usually achieved by maintaining a mapping table from voxel indices to queue positions. If costt≥cost old, it means that reaching the target neighborhood voxel via the current voxel to be evaluated is not better than the known path, and the system does not perform any updates and continues to process the next neighborhood voxel.

[0105] After processing all the neighborhood voxels of the current voxel to be evaluated, return to the main loop to start the next iteration, and pop the voxel with the smallest new cumulative cost from the dynamic priority queue. As the iteration progresses, the number of voxels in the queue changes dynamically. The processed voxels are popped, and the voxels corresponding to newly discovered better paths are added. The algorithm gradually expands the exploration range from the starting point outwards, similar to the spread of ripples on the water surface. Each expansion is carried out along the direction with the currently known smallest cumulative cost. The iteration continues until the termination condition is met, that is, the exploration end voxel (ie, je, ke) is popped from the dynamic priority queue. When the end point is popped, according to the property of Dijkstra's algorithm, the value recorded in CostMap[ie][je][ke] at this time is the global minimum cumulative path cost value from the starting point to the end point, and the path corresponding to this cost can be obtained by backtracking through the parent node pointer chain. In actual implementation, the system checks whether the popped voxel is the end point each time a voxel is popped. If so, it immediately terminates the main loop and enters the path backtracking stage. If the queue is empty but the end point has not been popped, it means there is no reachable path from the starting point to the end point, and the result of path search failure is returned.

[0106] The optimal path voxel set is generated by performing path backtracking. The backtracking process starts from the exploration endpoint and traverses backward along the parent node pointers until the exploration starting point is reached. An empty voxel index list is created to store the voxels on the path. The current backtracking voxel is initialized to the endpoint current=(ie, je, ke), and then the backtracking loop is entered. In the loop, the system adds the current backtracking voxel to the path list p.append(current). Then, the parent node of the current voxel is queried from the parent node pointer record table, parent=ParentMap[current[0]][current[1]][current[2]], and the current backtracking voxel is updated to the parent node current=parent. The next round of the loop continues. The loop continues to execute until the current backtracking voxel is equal to the exploration starting point current=(is, js, ks). At this time, the starting point is also added to the path list, and the backtracking process is completed. Since backtracking is a reverse process from the end point to the starting point, the voxel order in the generated path list is from the end point to the starting point. The list needs to be reversed to get the forward order from the starting point to the end point, and finally the optimal path voxel set is obtained. This set is an ordered list containing all voxel indices passed along the optimal path from the exploration starting point to the exploration ending point.

[0107] The time complexity of this path search algorithm is O(Vlog V+E), where V is the total number of voxels in the voxel grid and E is the total number of adjacent edges between voxels. In a 3D grid, E is approximately 26V, hence the overall complexity is O(Vlog V). For a typical crown removal planning scenario, with a voxel grid size of 100×100×100 (approximately 1 million voxels), the algorithm's computation time on modern processors is typically between 1 and 5 seconds, meeting the real-time requirements of interactive clinical planning. The optimal path voxel set generated by the algorithm provides the foundation for subsequent path smoothing and visualization. It can convert voxel indices into physical space coordinates and generate smooth, continuous trajectories through methods such as spline interpolation, providing precise positional commands for the motion control of the cutting tool, ultimately achieving safe and efficient implant crown removal.

[0108] S107: Fit and smooth the optimal path voxel set to obtain the final safe crown removal path in three-dimensional space.

[0109] In S107 above, the optimal path voxel set is fitted and smoothed to obtain the final safe crown removal path in three-dimensional space. Specifically, this includes: extracting the center three-dimensional coordinates of each voxel in the optimal path voxel set to construct a discrete control point sequence; based on the discrete control point sequence, using a fitting algorithm to perform continuous interpolation fitting to generate an initial continuous three-dimensional path curve; in the three-dimensional probability cloud map, retrieving the conditional probabilities corresponding to each voxel traversed by the initial continuous three-dimensional path curve; if the conditional probability corresponding to the current voxel is greater than a preset safety threshold, then the current voxel is marked as a conflict voxel, and the current voxel is any voxel traversed by the initial three-dimensional path curve; based on the conflict voxel... In terms of spatial location, a normal repulsive force is applied to the initial continuous 3D path curve, deviating from the conflict voxel. The control point positions of the initial continuous 3D path curve are iteratively adjusted until all conditional probabilities of the regions traversed by the initial continuous 3D path curve are less than or equal to a preset safety threshold, thus obtaining the final safe crown removal path. The overall geometric morphological features of the final safe crown removal path are calculated. Based on the geometric morphological features, a preset strategy classifier is used to identify the topology strategy of the final safe crown removal path. Based on the identified topology strategy, the geometric configuration of the guide channel in the 3D guide plate template is automatically configured so that the geometric constraint boundary of the guide channel matches the motion envelope space of the rigid cutting tool when executing the corresponding topology strategy.

[0110] Specifically, after solving for the optimal path voxel set based on Dijkstra's algorithm, the discrete voxel sequence needs to be converted into a continuous three-dimensional spatial path suitable for clinical operation. This path must meet surgical safety requirements in terms of geometry and guide the precise design of the three-dimensional guide plate. Since the path output by Dijkstra's algorithm is a discrete sequence of voxel indices, these voxels are distributed in a stepped manner in three-dimensional space. Directly using this to guide the movement of the cutting tool would result in discontinuous paths and jagged vibrations, failing to meet the requirements for smooth tool movement and trajectory accuracy in clinical surgery. Therefore, the discrete path needs to be fitted and smoothed. Simultaneously, the path must be continuously monitored during processing to ensure it does not cross high-risk areas. If safety issues are detected, the path shape is dynamically adjusted to ultimately generate a safe coronal removal path that meets both geometric continuity and safety constraints.

[0111] The center 3D coordinates of each voxel are extracted from the optimal path voxel set to construct a discrete control point sequence. The optimal path voxel set is an ordered list containing the indices of all voxels traversed along the optimal path from the exploration start point to the exploration end point. Assume this list contains M voxels, denoted as {(i1, j1, k1), (i2, j2, k2), ..., (i...}. M j M k M )}, where (i1, j1, k1) corresponds to the voxel index of the exploration starting point, (iM j M k M ) corresponds to the voxel index of the exploration endpoint. For each voxel index (i) in the list m j m k m Where m ranges from 1 to M, the center coordinates of the voxel in 3D physical space are calculated. The transformation from voxel to physical coordinates is based on the spatial parameters of the voxel mesh. Assuming the physical coordinates of the origin of the voxel mesh are (ox, oy, oz), for example (-25.0, -25.0, -15.0) in millimeters, and the voxel side length vsize is 0.5 millimeters, then the voxel (i m j m k m The center coordinates of ) are calculated as x m =ox+(i m +0.5)*vsize、y m =oy+(j m +0.5)*vsize、z m =oz+(k m +0.5)*vsize, where 0.5 is added because the voxel center is located at the geometric center of the voxel unit rather than a corner point. Traverse all voxels in the path voxel set, calculate the center coordinates of each voxel sequentially, and store these coordinates as a discrete control point sequence in path order, denoted as {P1, P2, ..., P...}. M}, where P m =(x m y m , z m In a typical crown removal path planning scenario, the path length is approximately 10 to 20 millimeters, and the voxel side length is 0.5 millimeters. Therefore, the discrete control point sequence typically contains 20 to 40 control points, which form a stepped polygonal line in space. The turning points of the polygonal line correspond to the positions where the path changes direction in the voxel grid.

[0112] Based on a discrete control point sequence, a continuous interpolation fitting algorithm using B-spline fitting is employed to generate an initial continuous 3D path curve. The B-spline fitting algorithm is a widely used curve fitting method in computer graphics and numerical analysis. Its advantages lie in the local controllability, continuity, and smoothness of the generated curve, making it suitable for modeling complex paths in medical images. Cubic uniform B-spline fitting is used, which constructs the curve by defining a linear combination of basis functions and control points. First, the discrete control point sequence {P1, P2, ..., P...} is... M As data points for the B-spline curve, a parameterized node vector is constructed. This node vector is generated using the cumulative chord length parameterization method, which assigns parameter values ​​based on the Euclidean distance between adjacent control points. For the m-th control point, the parameter value t... mCalculated as t m =t{m-1}+‖Pm-P{m-1}‖ / Lt, where‖Pm-P{m-1}‖ represents the Euclidean distance between adjacent control points, and Lt is the sum of the distances between all adjacent control points, i.e., the total approximate length of the path. The initial parameter t1=0, and the final parameter t M =1, this parameterization method ensures that the curve can obtain denser sampling in spatially uneven control point regions. A cubic B-spline curve is constructed based on the parameterized control point sequence, and the mathematical expression of the curve is: ; Q m Let B be the m-th B-spline control point. {m，3}(u) The function is a cubic B-spline basis function, with parameter u varying in the interval [0, 1]. To ensure the curve passes through the start and end points of the path, interpolation endpoint conditions are used, i.e., C(0) = P1 and C(1) = P1 are required. M This is achieved by repeating nodes at both ends of the node vector, specifically by setting the node vector to {0, 0, 0, 0, t1, t2, ..., t}. M The B-spline control points Q are determined by solving the system of linear equations. m This system of equations is based on the interpolation condition P. m =C(t m The structure requires that the curve be constructed with parameter t. m Data point P m Due to the local support of cubic B-splines, the coefficient matrix of the equation system is a banded matrix, which can be solved efficiently. After obtaining the control points, sampling is performed in the parameter interval [0, 1] with a fixed step size Δu, for example, 0.01, and the coordinates C(u) of the sampling points on the curve are calculated. k )where u k =kΔu and k ranges from 0 to 100. These sampling points constitute a discrete representation of the initial continuous three-dimensional path curve. The sampling point density is one point every 0.01 parameter units, corresponding to a spacing of about 0.1 to 0.2 millimeters in physical space, which is sufficient to meet the accuracy requirements of the surgical path.

[0113] The system retrieves the conditional probabilities corresponding to each voxel traversed by the initial continuous 3D path curve from the 3D probability cloud map to assess the path's safety. For each sampling point on the initial continuous 3D path curve, the system first converts the physical coordinates (xk, yk, zk) of the sampling point into voxel indices using the formulas ik=floor((xk-ox) / vsize), jk=floor((yk-oy) / vsize), and kk=floor((zk-oz) / vsize), where floor represents rounding down, (ox, oy, oz) represents the origin physical coordinates, and vsize represents the voxel side length. After obtaining the voxel indices (ik, jk, kk), the system reads the corresponding conditional probabilities from the 3D probability cloud map, including P(nerve injury|location), P(vascular injury|location), P(implant injury|location), and P(adjacent tooth root apex injury|location). These probability values ​​have been calculated and stored in the corresponding positions of the voxel grid in the previous steps. The system calculates the comprehensive conditional probability of the voxel using a weighted summation method, resulting in the comprehensive conditional probability Pij. total =w1P(nerve injury | location) + w2P(vascular injury | location) + w3P(implant injury | location) + w4P(adjacent tooth root apex injury | location), where the weight parameters w1, w2, w3, and w4 have been determined in the above local path cost calculation, for example, w1=0.5, w2=0.3, w3=0.15, w4=0.05. These weights reflect the clinical severity of different injury types. The calculated comprehensive conditional probability P total Compared to a preset safety threshold, which is set based on a clinically acceptable risk level and can be set to T... safe =0.25, the preset safety threshold indicates that when the overall probability of damage at a certain location exceeds 25%, the risk is considered too high and the path needs to be adjusted. If P total >T safe The system marks the current voxel as a conflict voxel and records its index, physical coordinates, and corresponding sampling point index. The system iterates through all sampling points on the initial continuous 3D path curve to complete the full path safety check, storing all detected conflict voxels as a conflict voxel list. This list contains the coordinates of each conflict voxel and its corresponding comprehensive conditional probability value.

[0114] Based on the spatial location of conflict voxels, a normal repulsive force opposing the conflict voxels is applied to the initial continuous 3D path curve. The path shape is optimized by iteratively adjusting the control point positions of the curve until safety constraints are met. This process employs a physics-based iterative optimization method, treating the path curve as a flexible, elastic object. The repulsive force exerted by the conflict voxels on the curve allows it to avoid high-risk areas while maintaining smoothness. For each conflict voxel in the conflict voxel list, the repulsive force exerted by that voxel on the corresponding sampling point on the path curve is calculated. Assume the center coordinates of a conflict voxel are V. ct =(x v y v , z v The coordinates of the sampling point corresponding to the conflicting voxel on the path curve are P. sa =(x s y s , z s First, calculate the direction vector d=P from the conflict voxel to the sampling point. sa -V ct =(x s -x v y s -y v , z s -z v The direction vector is then normalized to obtain the unit direction vector n = d / |d|, where |d| is the Euclidean norm of vector d. The magnitude of the repulsive force is proportional to the degree of danger of the conflicting voxels and is defined as F. mag =kr*(P total -T safe ), where k r In this embodiment, the repulsive force coefficient is set to 20.0 Newtons. This coefficient was determined experimentally to obtain a suitable convergence rate and stability in iterative optimization. total T represents the combined conditional probability of conflicting voxels. safe To preset a safety threshold, the difference (P) total -T safe () indicates the degree exceeding the safety threshold. The repulsive force vector is calculated as F. re =F mag *n, this force vector points away from the conflict voxel and acts on the corresponding sampling point of the path curve.

[0115] The repulsive forces generated by all conflicting voxels are accumulated and applied to the B-spline control points of the path curve. Since the shape of the B-spline curve is determined by the control points, adjusting the positions of the control points can indirectly change the curve shape. For each sampling point on the path curve, the influence range of the B-spline basis functions is first used to determine which control points affect the sampling point. Each sampling point of a cubic B-spline is typically affected by four adjacent control points. The basis function values ​​corresponding to these four control points are calculated. Then, the repulsive forces acting on the sampling point are distributed to these four control points according to the proportion of the basis function values. The specific distribution formula is ΔQ. m =∑ {k∈ins} B {m，3}(uk) ×F re-k , where ΔQ m Let represent the displacement increment applied to the m-th control point, ins be the set of all sampling points affected by this control point, Fre-k be the repulsive force at the k-th sampling point, uk represent the curve parameters corresponding to the k-th sampling point, and B be the displacement increment applied to the m-th control point. {m，3}(uk) The value of the m-th basis function at parameter uk is used as a weighting coefficient. All control points are iterated over, and the displacement increments at each control point are accumulated. The internal elastic constraints of the curve are considered; these constraints are implemented by penalizing excessive curvature of the curve. The formula for calculating the smoothness energy scalar value of the curve is as follows: ; Among them, E s The energy scalar value representing the smoothness of the curve, Q m+1 Q m Q m-1 Q represents the coordinates of three adjacent control points. m+1 -2Q m +Q m-1 Let E represent the second-order finite difference of the control points, the second derivative of the approximate curve, and ||×||² represent the square of the Euclidean norm of the vector. During the optimization process, E is minimized. s To maintain the smoothness of the curve, considering both repulsive force and smoothness constraints, the control point positions are iteratively updated using the gradient descent method. The update formula is as follows: ; Where α is the repulsive force step size coefficient set to 0.1, and β is the smoothness weighting coefficient set to 0.05. E s For smoothness energy to control point Q m gradient, This represents the new position of the m-th control point after the update. Let α × ΔQ represent the old position of the m-th control point before the update. m β× represents the displacement contribution caused by the repulsive force. E sThis represents the displacement correction caused by the smoothness constraint. An iterative optimization process is performed, updating the positions of all control points in each iteration. Then, the sampling points of the updated curve in the parameter interval [0, 1] are recalculated. A safety check is repeatedly performed on the new sampling point sequence to check whether the updated path still traverses conflict voxels. The iterative process continues until the convergence condition is met. The convergence condition includes two items: the first is a global safety constraint, meaning that the conditional probabilities of all parameters in the region traversed by the initial continuous 3D path curve are less than or equal to a preset safety threshold T. safe The first condition is that the conflict voxel list is empty; the second condition is control point displacement convergence, which means that the maximum value of all control point displacements in two consecutive iterations is less than a preset threshold, such as 0.01 mm, indicating that the curve shape has become stable. The maximum number of iterations is set to 100 to prevent the algorithm from getting stuck in an infinite loop. In practical applications, convergence usually occurs after 10 to 30 iterations. When the convergence condition is met, the current path curve is determined as the final safe coronary removal path. This path satisfies both the continuity and smoothness requirements from the start point to the end point, and ensures that the probability of damage risk along the entire path is within a clinically acceptable range.

[0116] The overall geometric features of the final safe crown removal path are calculated; these features are used for subsequent topology strategy identification and guide plate design. Geometric features include path length, path curvature, the incident angle of the path relative to the crown surface, and the number of path branches. The path length is calculated by accumulating the Euclidean distances between adjacent sampling points on the path curve; the formula for path length is as follows: ; Among them, L p This represents the total arc length of the path curve (unit: millimeters), typically ranging from 8 to 25 mm; C(u k ) indicates that the parameter u is on the curve. k The coordinates of the point, u k Represents the parameter corresponding to the k-th sampling point, ||C(u k )-C(u k-1 || represents the Euclidean distance between adjacent sampling points. Path curvature is defined as the ratio of path length to the straight-line distance between the start and end points, κ=L p The ratio / ‖C(1)-C(0)‖ indicates that the path is closer to a straight line when the ratio is closer to 1, and the path is more curved when the ratio is larger. In this embodiment, the curvature of the straight path is about 1.0 to 1.1, and the curvature of the tortuous path can reach more than 1.5. The incident angle of the path relative to the crown surface is obtained by calculating the angle between the tangent vector at the starting point of the path and the normal vector of the crown surface. The tangent vector at the starting point of the path is T. s =dC / du| {u=0}The derivative is calculated using the analytical derivative of the B-spline curve. The normal vector of the crown surface at the starting point is extracted from the 3D mesh model of the crown. Specifically, the method is to find the crown surface triangular facet closest to the starting point of the path, read the normal vector Nc of that facet, and the incident angle θ = arccos(T s ×Nc / (‖T s The angle θ reflects the direction in which the cutting tool enters the crown. When entering perpendicularly, θ is close to 0 degrees, and when entering obliquely, θ is larger. The number of path branches is determined by analyzing the topological structure of the path curve. The system checks whether the path branches in the middle or has multiple sub-paths. If the path is a single continuous curve, the number of branches is 1. If the path consists of two or more intersecting curves, the number of branches is the corresponding value. In the single-start-point and single-end-point search scenario of this embodiment, the number of path branches is usually 1 to indicate a single path structure.

[0117] Based on geometric morphological features, a pre-defined strategy classifier was used to identify the topological strategy of the final safe crown removal path. This classifier, implemented using a rule-based decision tree, categorizes the path into one of three typical clinical crown removal strategies based on its geometric feature parameters. The first strategy is the central windowing strategy, which is suitable for cases where the crown structure is intact and the bonding strength is high. This involves weakening the bonding interface by drilling a vertical hole in the center of the crown before removing the crown entirely. The rule for determining whether a path belongs to the central windowing strategy is: path length L... p Less than the preset length threshold T length For example, with a path curvature of 12 mm, the path curvature κ is less than a preset curvature threshold T. curvature For example, 1.15 indicates that the path is approximately a straight line, with the starting point located in the central region of the occlusal surface of the crown. This is determined by checking whether the x and y coordinates of the starting point are within ±3 mm of the center of the crown boundary frame. The incident angle θ of the path relative to the crown surface is less than a preset angle threshold T. angleFor example, a 15-degree angle indicates a near-vertical entry and a single path branch. If the path meets all these conditions, it is identified as a central windowing strategy. The second strategy is the cross-segmentation strategy, which divides the crown into four pieces by cutting two intersecting straight lines on the crown and then removing them piece by piece. This strategy is suitable for difficult cases with large crown volumes or extremely high bonding strength. The system determines the cross-segmentation strategy as follows: the path actually consists of two sub-paths, therefore two independent paths need to be generated during path planning. The starting points of both paths are located on the occlusal surface of the crown, the ending points of both paths are located near the implant screw holes, the two paths intersect in space, the intersection point is located in the central region of the crown, and the angle between the direction vectors of the two paths is between 70 and 110 degrees, approaching a near 90-degree perpendicular intersection. In this embodiment, if the user selects the cross-segmentation mode during preoperative planning, the system will plan two separate paths. The third strategy is the lateral stripping strategy, which weakens the lateral bonding interface by cutting from the occlusal surface of the crown and then turning to the lateral wall in an L-shaped path. This strategy is suitable for cases where the lateral wall bonding of the crown is weak. The rule for determining the lateral stripping strategy is: path length L p Greater than the preset length threshold T length For example, with a path curvature of 15 mm, the path curvature κ is greater than a preset curvature threshold T. curvature For example, 1.3 indicates that there is a clear turning point in the path. The starting point of the path is located on the occlusal surface, and the ending point is located on the buccal or lingual surface of the crown. This is determined by checking whether the y-coordinate or x-coordinate of the ending point is close to the crown boundary. The path exhibits a broken line characteristic in three-dimensional space, which is detected by analyzing the rate of change of the tangent vector direction of the path curve.

[0118] Based on the identified topology strategy, the geometry of the guide channel in the 3D guide plate template is automatically configured to match the geometric constraint boundary of the guide channel with the motion envelope space of the rigid cutting tool when executing the corresponding topology strategy. The 3D guide plate is a personalized surgical guidance device manufactured through 3D printing. During surgery, it is installed on the dentition or gingiva in the patient's mouth, providing precise spatial positioning and motion constraints for the cutting tool, ensuring that the cutting path is strictly executed according to the pre-operative plan. The guide channel is a through-hole or groove structure on the guide plate. The drill bit or saw blade of the cutting tool moves within the guide channel, and the channel wall constrains the tool's degrees of freedom of movement. If a central windowing strategy is identified, the guide channel is configured as a vertical cylindrical hole structure. The central axis of this hole structure coincides with the planned path curve. The diameter of the hole is determined by the drill bit diameter of the cutting tool plus a 0.5 mm operating clearance. Assuming the drill bit diameter is 2.0 mm, the hole diameter is set to 2.5 mm. The hole depth corresponds to the path length plus a 2 mm penetration allowance. The hole entrance is located at the interface between the guide plate and the crown surface, precisely aligned with the starting position of the path. The cylindrical hole structure is designed by performing Boolean difference operations in CAD software with the path curve as the axis. The cylindrical volume is removed from the guide plate solid model along the path curve to generate the guide hole. If a cross-cutting strategy is identified, the guide channel is configured as a bidirectional cross-groove structure. This structure contains two orthogonal grooves, each corresponding to a planned path. The cross-section of the groove is rectangular, with a width equal to the saw blade thickness plus a 0.3 mm operating clearance (e.g., 1.5 mm), and a depth corresponding to the projection height of the path perpendicular to the groove length. The two grooves intersect at the center of the guide plate, forming a cross-shaped opening. This structure allows the saw blade to cut sequentially in two directions. If the lateral stripping strategy is identified, the guide channel is configured as a lateral open chute structure. The chute is L-shaped, matching the zigzag shape of the path. One end of the chute opens on the top surface of the guide plate corresponding to the starting point of the path. The chute extends along the path direction and changes direction at the turning point. The outlet of the chute is located on the side wall of the guide plate corresponding to the ending point of the path. The cross-section of the chute is U-shaped, the width of the chute is the tool diameter plus the clearance, and the depth of the chute is sufficient to accommodate the tool blade. The open design allows the operator to observe the tool position and adjust the cutting depth during the cutting process.

[0119] S108: Based on the final safe crown removal path, a rigid cutting envelope analysis is performed to determine the rigid axial cutting trajectory of the cutting tool. Combined with the surface morphology of adjacent teeth in the digital 3D scene, a 3D guide plate template is generated so that physical processing can be carried out according to the 3D guide plate template.

[0120] In S108 above, after obtaining the final safe crown removal path, it needs to be converted into a rigid axial cutting track that takes into account the physical dimensions of the cutting tool, and the final guide plate template is generated based on this. Since the cutting tool itself has physical dimensions, especially the diameter and working length of the burr have clear geometric parameters, the path centerline cannot be simply used as the cutting track directly, but a rigid cutting envelope analysis must be performed.

[0121] First, the standard specifications of commonly used burs for crown removal surgery are retrieved from the medical device database. A three-dimensional geometric model of the bur, established based on these specifications, is then virtually swept along the final safe crown removal path. The sweeping process employs an evenly spaced sampling method, recording the bur's spatial position and orientation every 0.1 mm along the path. At each sampling location, the shortest distance between the bur surface and surrounding tissue structures is calculated. These surrounding tissue structures include the enamel surface of adjacent teeth, the gingival soft tissue surface, the outer surface of the implant abutment, and the surface of the jawbone cortical bone. The distance calculation uses a point-to-triangular mesh facet algorithm. Specifically, all vertices of the bur surface mesh are traversed. For each vertex, the nearest triangular facet in the surrounding tissue structure mesh is searched, and the perpendicular distance from the vertex to that facet is calculated. If the projected point falls inside the triangle, the distance is the perpendicular distance from the point to the plane; if the projected point falls outside the triangle, the distance is the distance from the point to the nearest side or vertex of the triangle. Statistical analysis is performed on the shortest distances calculated at all sampling locations to ensure a safe clearance between the bur and surrounding structures, avoiding tissue damage caused by accidental contact. After collision detection and necessary path adjustments, the final rigid axial cutting path is determined. This path is defined as the trajectory of the bur's central axis in three-dimensional space, consisting of a starting point, an ending point, and a series of intermediate control points. The starting point is located 2 mm directly above the crown surface, ensuring that the bur reaches a stable rotational and feed speed before contacting the crown. The ending point is located 0.5 mm below the upper surface of the plugging material in the screw hole, a depth sufficient to completely penetrate the plugging material without touching the underlying abutment screw. Intermediate control points are evenly distributed along the path at 1 mm intervals. Each control point records the three-dimensional coordinates of the bur's central axis and the unit vector of the bur's axial direction. The axial direction vector is obtained by calculating the tangent direction of the path at that point; the tangent direction is the normalized vector of the first derivative of the B-spline curve at that point.

[0122] Once the rigid axial cutting path is determined, a physical guide structure needs to be designed. This guide mechanically constrains the movement of the bur during the procedure, ensuring that the bur cuts strictly along the preset path. The guide design relies on precise morphological data of the adjacent tooth surface, as the guide must be stably supported on the adjacent tooth surface to provide a reliable spatial positioning reference for the bur. Mesh data of the adjacent tooth surface of the target implant crown is extracted from the registered composite 3D virtual model. To ensure precise matching between the guide and the adjacent tooth surface, suitable areas on the adjacent tooth surface for support contact need to be identified. Ideally, the support contact surface should be relatively flat with minimal curvature variation; located on the buccal or lingual side of the crown for easy guide placement and fixation; and large enough to provide stable support. After determining the adjacent tooth support contact area, the main structure of the guide is constructed. The main body of the guide employs a negative shape fitting design, meaning the inner surface of the guide forms a precise complementary concave-convex relationship with the outer surface of the adjacent tooth. The three-dimensional geometric model of the guide plate body is generated through the following steps: First, the surface mesh of the supporting contact area is offset outward by 3 mm along the direction of its respective surface normal vector. The offset distance is chosen to ensure sufficient mechanical strength for the guide plate material thickness, while avoiding excessive thickness that could affect the surgical operating space. The offset surface constitutes the inner surface of the guide plate body, with a geometric gap of 3 mm between this inner surface and the adjacent tooth surface. The outer surface of the guide plate body is then expanded outward based on the offset inner surface. A uniform shell thickness design is used during the expansion process, with the shell thickness set at 2.5 mm, determined based on the mechanical properties of the guide plate material.

[0123] After the outer surface of the guide plate body is generated, a guide channel is excised on the body using Boolean operations. The geometric constraint boundary of this guide channel strictly corresponds to the rigid axial cutting track. The inner diameter of the guide channel is slightly larger than the outer diameter of the bur to allow free insertion and axial movement of the bur, but not lateral oscillation or angular deflection. The length of the guide channel needs to cover the entire distance from the outer surface of the guide plate to the crown surface. To further enhance the constraint effect of the guide channel on the bur, a depth marking structure is designed inside the channel. The depth marking is achieved by setting an annular ridge on the inner wall of the channel, and the position of the ridge corresponds to the critical node of the bur cutting depth. After the geometric model of the guide plate body and the guide channel is completed, an auxiliary fixation structure for the guide plate needs to be designed to ensure that the guide plate remains stable during the operation. The auxiliary fixation structure consists of two parts: one is an extension arm added to the buccal side of the guide plate body, with a fixation hole designed at the end of the extension arm. The fixation hole has a diameter of 1.5 mm, through which a temporary fixation pin can be inserted during clinical use to fix the guide plate to the gingival tissue or jawbone surface of the adjacent tooth. The length of the fixation pins is determined based on the patient's gingival thickness, typically 3-5 mm. Secondly, an absorbent pad is designed on the lingual or palatal side of the guide plate body. This pad is made of flexible silicone rubber, and its inner surface shape precisely matches the anatomical morphology of the adjacent tooth's lingual or palatal side. The negative pressure adsorption principle enhances the fit stability between the guide plate and the adjacent tooth. The geometric models of the guide plate body, guide channel, depth-marking ridges, fixation holes, and absorbent pads are merged using Boolean operations to generate a complete 3D guide plate template. This template is output in STL format or other 3D printing compatible formats. The file contains all the geometric details of the guide plate, including the outer surface triangular mesh, inner surface triangular mesh, guide channel inner wall mesh, ridge mesh, and the geometric boundaries of the fixation holes. The template file also includes material property annotation information, specifying that the guide plate body is printed using a light-cured resin material, and the absorbent pad is made of medical-grade silicone rubber material for later bonding or embedding.

[0124] After the three-dimensional guiding template is generated, it needs to be transformed into a practical guiding device through physical processing methods. The choice of processing method depends on the geometric complexity, precision requirements, and production cost of the guiding plate. First, evaluate the geometric features of the guiding plate and find that the guiding plate has a complex inner surface contour, precise guiding channels, and tiny depth marking ridges. These features are difficult to achieve through traditional CNC milling. Therefore, 3D printing technology can be used to manufacture the guiding plate. Import the STL file of the three-dimensional guiding template into the slicing software of the SLA printer, and set the layer thickness to 0.05 mm to ensure the precision of the inner wall of the guiding channel and the depth marking ridges. The software automatically adds grid-like or tree-like support structures that are easy to remove for the overhanging parts. The printing uses a standard-compliant medical-grade photo-curable resin. After curing, the elastic modulus of this resin is 2200 MPa, the flexural strength is 65 MPa, and the cytotoxicity level is level 0 or level 1. After printing, first use isopropyl alcohol for ultrasonic cleaning for 5 minutes to remove the residual resin, and then irradiate with 405-nm ultraviolet light for 15 minutes for post-curing to improve the mechanical strength and reduce the residual monomers. After removing the support structure and polishing, perform dimensional accuracy, functional performance, and biocompatibility tests. After passing the tests, perform low-temperature sterilization with ethylene oxide. During clinical use, the guiding plate achieves a unique positioning by precisely matching the inner surface with adjacent teeth. The guiding channel restricts the bur to cut along the preset track, and the depth marking ridges provide tactile feedback to ensure accurate reaching of the occluding material without damaging the implant or abutment. After completion, loosen the abutment screw to remove the crown.

[0125] This application embodiment also provides an apparatus for fabricating a guide plate for dental implant crown removal. The apparatus includes an acquisition unit, a processing unit, a calculation unit, and a planning unit. The acquisition unit acquires three-dimensional image data of the patient's oral and maxillofacial region where the dental implant crown to be removed is located, as well as oral scan data containing tooth tissue morphology. The processing unit registers and fuses the three-dimensional image data and oral scan data in a unified coordinate system to obtain a digital three-dimensional scene containing anatomical structures. The digital three-dimensional scene is voxelized to obtain a three-dimensional voxel mesh containing multiple voxels. Based on the spatial geometric distance from the target voxel to the anatomical structure, the conditional probability of triggering various preset failure events when the cutting tool passes through the target voxel is calculated, and a three-dimensional probability cloud map is constructed for the conditional probabilities corresponding to all voxels, where the target voxel is any voxel in the three-dimensional voxel mesh. The calculation unit acquires the clinical target of the dental implant crown to be removed, and based on the clinical target... The conditional probabilities of the target voxels in the 3D probability cloud map are calculated to obtain the local path cost value. Using the surface voxel of the implant crown to be removed as the starting point and the voxel corresponding to the top of the central screw hole of the implant as the ending point, guided by the local path cost value, an optimal set of path voxels with the minimum cumulative local path cost value is obtained. A planning unit is used to fit and smooth the optimal path voxel set to obtain the final safe crown removal path in 3D space. Based on the final safe crown removal path, a rigid cutting envelope analysis is performed to determine the rigid axial cutting trajectory of the cutting tool. Combined with the surface morphology of adjacent teeth in the digital 3D scene, a 3D guide plate template is generated for physical fabrication. The 3D guide plate template includes a main body for matching the surface of adjacent teeth and a guide channel. The geometric constraint boundary of the guide channel corresponds to the rigid axial cutting trajectory.

[0126] In one possible implementation, the processing unit is used to extract point clouds of the hard tissue surface of the crown from 3D image data and point clouds of the crown surface from oral scan data; using principal component analysis algorithm, it calculates the initial rotation matrix and translation vector of the point clouds of the hard tissue surface of the crown and the point clouds of the crown surface; iteratively optimizes the initial rotation matrix and translation vector until the root mean square error between the point clouds of the hard tissue surface of the crown and the point clouds of the crown surface is less than a preset threshold, thereby obtaining a spatial transformation matrix; based on the spatial transformation matrix, it transforms the 3D image data and the oral scan data to a unified coordinate system for 3D fusion to generate a fused data model; it performs semantic segmentation on the fused data model to obtain a digital 3D scene containing anatomical structures, wherein the anatomical structures include implants, abutments, crowns to be removed, adjacent teeth, important nerve canals of the inferior alveolar ridge, and gingival soft tissue.

[0127] In one possible implementation, the acquisition unit is used to acquire a preset set of failure events, which includes events of mechanical damage to the implant, mechanical damage to the abutment, damage to adjacent teeth or restorations, damage to the bone tissue around the implant due to heating, and events where the crown cannot be easily separated by instruments after cutting. The processing unit is used to calculate the Euclidean distance from the target voxel to each corresponding surface of the anatomical structure to obtain the spatial geometric distance. When the preset failure event is an event of mechanical damage to the implant, an event of mechanical damage to the abutment, or an event of damage to adjacent teeth or restorations, the spatial geometric distance is substituted into the first probability mapping function to calculate the distance the cutting tool has traveled. When the target voxel is reached, the conditional probability of triggering a preset failure event is calculated. When the preset failure event is damage to the bone tissue around the implant due to heating, the spatial geometric distance is substituted into the second probability mapping function to calculate the conditional probability of triggering the preset failure event when the cutting tool passes through the target voxel. When the preset failure event is that the crown cannot be easily separated by the instrument after cutting, the spatial geometric distance is substituted into the third probability mapping function to calculate the conditional probability of triggering the preset failure event when the cutting tool passes through the target voxel. All voxels in the three-dimensional voxel grid are traversed, and the conditional probabilities corresponding to each voxel are spatially arrayed and mapped to construct a three-dimensional probability cloud map containing multiple probability dimensions.

[0128] In one possible implementation, the acquisition unit acquires the clinical target of the dental implant crown to be removed, the processing unit determines the corresponding set of weight coefficients based on the clinical target, wherein the set of weight coefficients includes weight factors corresponding one-to-one with each preset failure event; the calculation unit uses the set of weight coefficients to perform a weighted summation calculation on the multi-channel conditional probabilities corresponding to the target voxel to obtain the corresponding local path cost value, the formula for calculating the local path cost value is as follows: ; Where x represents the target voxel, C(x) represents the local path cost at target voxel x, N represents the total number of preset failure events, and P(E) i |x) represents the conditional probability of triggering the i-th preset failure event when the cutting tool passes through the target voxel x, w i Let G(x) represent the weight factor corresponding to the i-th preset failure event, and let each weight factor in the set of weight coefficients satisfy the normalization mapping constraint. Let G(x) represent the geometric constraint penalty term of the guidance path, and let γ represent the geometric constraint adjustment coefficient.

[0129] In one possible implementation, the processing unit is used to construct a three-dimensional stress distribution field of the implant crown to be removed under a preset removal load, and to identify stress concentration areas based on the three-dimensional stress distribution field. The stress concentration areas are regions that reduce the stability of the crown structure. Based on the digital three-dimensional scene, the unit calculates the spatial geometric distance from each voxel to the corresponding surface of the anatomical structure and constructs a spatial distance sensitivity function. When the clinical goal is to preserve the crown, based on the spatial geometric distance sensitivity function, the weight factors corresponding to the preset failure events related to anatomical damage are determined as positive penalty functions that are negatively correlated with spatial geometric distance, and the weight factors corresponding to the event that the cut crown cannot be easily separated by instruments are determined to be zero. When the clinical goal is to discard the crown, the weight factors corresponding to the event that the cut crown cannot be easily separated by instruments are determined as negative reward functions that are positively correlated with the distance to the stress concentration area, and the weight factors corresponding to the preset failure events related to anatomical damage are kept as positive penalty functions. The determined weight factors are dynamically normalized and mapped, and the normalized weight factors are vectorized and combined to obtain a set of weight coefficients corresponding to the clinical goal.

[0130] In one possible implementation, the planning unit is used to push the exploration starting point into a dynamic priority queue and initialize the cumulative path cost of all voxels in the 3D voxel mesh, excluding the exploration starting point, to infinity, while initializing the cumulative path cost of the exploration starting point to zero; pop the voxel to be evaluated with the smallest current cumulative path cost from the dynamic priority queue, and traverse the neighboring voxels of the voxel to be evaluated in 3D space; calculate the temporary cumulative path cost from the exploration starting point through the voxel to be evaluated to the target neighboring voxel, where the temporary cumulative path cost is the sum of the cumulative path cost of the voxel to be evaluated, the local path cost at the neighboring voxel, and the spatial step cost between the two adjacent voxels. The target neighborhood voxel is any neighborhood voxel in 3D space. If the temporary cumulative path cost value is less than the historical cumulative path cost value recorded by the target neighborhood voxel, the historical cumulative path cost value of the target neighborhood voxel is updated using the temporary cumulative path cost value. The parent node pointer of the target neighborhood voxel is then pointed to the voxel to be evaluated, and the target neighborhood voxel is updated in the dynamic priority queue. The step of updating the cumulative path cost value is repeated until the exploration endpoint is popped. When the exploration endpoint is popped, the process starts from the exploration endpoint and backtracks along the parent node pointers corresponding to each voxel until the exploration starting point is reached. All voxels passed during the backtracking process are arranged in order to generate the optimal path voxel set.

[0131] In one possible implementation, the planning unit extracts the center 3D coordinates of each voxel in the optimal path voxel set to construct a discrete control point sequence; based on the discrete control point sequence, a fitting algorithm is used to perform continuous interpolation fitting to generate an initial continuous 3D path curve; in the 3D probability cloud map, the conditional probabilities corresponding to each voxel traversed by the initial continuous 3D path curve are retrieved; if the conditional probability corresponding to the current voxel is greater than a preset safety threshold, the current voxel is marked as a conflict voxel, and the current voxel is any voxel traversed by the initial 3D path curve; based on the spatial location of the conflict voxel, the initial continuous 3D path curve is... Apply a normal repulsive force to the opposing conflict voxel, iteratively adjust the control point positions of the initial continuous 3D path curve until all conditional probabilities of the regions traversed by the initial continuous 3D path curve are less than or equal to a preset safety threshold, thus obtaining the final safe crown removal path; calculate the overall geometric morphological features of the final safe crown removal path; based on the geometric morphological features, use a preset strategy classifier to perform topology strategy identification on the final safe crown removal path; based on the identified topology strategy, automatically configure the geometric configuration of the guide channel in the 3D guide plate template so that the geometric constraint boundary of the guide channel matches the motion envelope space of the rigid cutting tool when executing the corresponding topology strategy.

[0132] It should be noted that the above embodiments of the apparatus are only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the apparatus and method embodiments provided in the above embodiments belong to the same concept, and the specific implementation process can be found in the method embodiments, which will not be repeated here.

[0133] This application also discloses an electronic device. (See reference...) Figure 2 , Figure 2 This application provides a schematic diagram of the structure of an electronic device. The electronic device 200 may include: at least one processor 201, at least one network interface 204, a user interface 203, a memory 202, and at least one communication bus 205.

[0134] The communication bus 205 is used to enable communication between these components.

[0135] The user interface 203 may include a display screen and a camera. Optionally, the user interface 203 may also include a standard wired interface and a wireless interface.

[0136] The network interface 204 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0137] The processor 201 may include one or more processing cores. The processor 201 connects to various parts of the server using various interfaces and lines, and performs various server functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in memory 202, and by calling data stored in memory 202. Optionally, the processor 201 may be implemented using at least one hardware form of Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), or Programmable Logic Array (PLA). The processor 201 may integrate one or a combination of several of the following: Central Processing Unit (CPU), Graphics Processing Unit (GPU), and modem. The CPU primarily handles the operating system, user interface, and application requests; the GPU is responsible for rendering and drawing the content required for display; and the modem handles wireless communication. It is understood that the modem may also not be integrated into the processor 201 and may be implemented as a separate chip.

[0138] The memory 202 may include random access memory (RAM) or read-only memory. Optionally, the memory 202 may include a non-transitory computer-readable storage medium. The memory 202 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 202 may include a program storage area and a data storage area. The program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch functionality, sound playback functionality, image playback functionality, etc.), instructions for implementing the various method embodiments described above, etc.; the data storage area may store data involved in the various method embodiments described above, etc. Optionally, the memory 202 may also be at least one storage device located remotely from the aforementioned processor 201.

[0139] like Figure 2 As shown, the memory 202, which serves as a computer storage medium, may include an operating system, a network communication module, a user interface module, and an application program for making a guide plate for the removal of dental implant crowns.

[0140] exist Figure 2In the electronic device 200 shown, the user interface 203 is mainly used to provide an input interface for the user and to obtain the user input data; while the processor 201 can be used to call the application program stored in the memory 202 for making a guide plate for removing dental implant crowns. When executed by one or more processors, the electronic device performs one or more of the methods described in the above embodiments.

[0141] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0142] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0143] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some service interfaces; indirect couplings or communication connections between devices or units may be electrical or other forms.

[0144] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0145] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0146] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0147] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of other embodiments of this disclosure upon considering the specification and practical application disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure.

Claims

1. A method for fabricating a guide plate for dental implant crown removal, characterized in that, The method includes: Obtain three-dimensional imaging data of the patient's oral and maxillofacial region where the dental implant crown to be removed is located, as well as oral scan data including tooth tissue morphology; The three-dimensional image data and the oral cavity scan data are registered and fused in a unified coordinate system to obtain a digital three-dimensional scene containing anatomical structures. The digitized 3D scene is voxelized to obtain a 3D voxel mesh containing multiple voxels; Based on the spatial geometric distance from the target voxel to the anatomical structure, the conditional probability of triggering various preset failure events when the cutting tool passes through the target voxel is calculated, and a three-dimensional probability cloud map is constructed for the conditional probabilities corresponding to all voxels. The target voxel is any voxel in the three-dimensional voxel grid. Obtain the clinical target of the dental implant crown to be removed, and calculate the conditional probabilities of each item corresponding to the target voxel in the three-dimensional probability cloud map based on the clinical target to obtain the local path cost value; In the three-dimensional probability cloud map, the surface voxel of the implant crown to be removed is taken as the starting point of exploration, the voxel corresponding to the top of the central screw hole of the implant is taken as the ending point of exploration, and the local path cost value is used as a guide to solve for an optimal set of path voxels with the minimum cumulative local path cost value. The optimal path voxel set is fitted and smoothed to obtain the final safe crown removal path in three-dimensional space. Based on the final safe crown removal path, a rigid cutting envelope analysis is performed to determine the rigid axial cutting trajectory of the cutting tool. Combined with the surface morphology of adjacent teeth in the digital three-dimensional scene, a three-dimensional guide plate template is generated for physical processing and fabrication according to the three-dimensional guide plate template. The three-dimensional guide plate template includes a main body for matching the surface of the adjacent teeth and a guide channel. The geometric constraint boundary of the guide channel corresponds to the rigid axial cutting trajectory.

2. The method according to claim 1, characterized in that, The process of registering and fusing the three-dimensional image data and the oral cavity scan data in a unified coordinate system to obtain a digital three-dimensional scene containing anatomical structures specifically includes: Point clouds of hard tissue surface of the crown are extracted from the three-dimensional image data, and point clouds of crown surface are extracted from the oral cavity scan data; Using principal component analysis, the initial rotation matrix and translation vector of the point cloud on the hard tissue surface of the crown are calculated. The initial rotation matrix and the translation vector are iteratively optimized until the root mean square error between the point cloud of the hard tissue surface of the crown and the point cloud of the crown surface is less than a preset threshold, thus obtaining the spatial transformation matrix; Based on the spatial transformation matrix, the three-dimensional image data and the oral cavity scan data are transformed to a unified coordinate system for three-dimensional fusion to generate a fused data model. The fused data model is semantically segmented to obtain a digital three-dimensional scene containing the anatomical structure, wherein the anatomical structure includes the implant, abutment, crown to be removed, adjacent teeth, important nerve canal of the inferior alveolar bone, and gingival soft tissue.

3. The method according to claim 2, characterized in that, Based on the spatial geometric distance from the target voxel to the anatomical structure, the conditional probability of triggering various preset failure events when the cutting tool passes through the target voxel is calculated, and a three-dimensional probability cloud map is constructed for the conditional probabilities corresponding to all voxels, specifically including: Obtain a preset set of failure events, which includes mechanical damage events to the implant, mechanical damage events to the abutment, damage events to adjacent teeth or restorations, bone tissue damage around the implant due to heating, and events where the crown cannot be easily separated by instruments after cutting. The Euclidean distance from the target voxel to each corresponding structural surface in the anatomical structure is calculated to obtain the spatial geometric distance; When the preset failure event is the mechanical damage event to the implant, the mechanical damage event to the abutment, or the damage event to adjacent teeth or restorations, the spatial geometric distance is substituted into the first probability mapping function to calculate the conditional probability of triggering the preset failure event when the cutting tool passes through the target voxel. When the preset failure event is the bone tissue damage around the implant caused by heating, the spatial geometric distance is substituted into the second probability mapping function to calculate the conditional probability of triggering the preset failure event when the cutting tool passes the target voxel. When the preset failure event is that the cut crown cannot be easily separated by the instrument, the spatial geometric distance is substituted into the third probability mapping function to calculate the conditional probability of triggering the preset failure event when the cutting tool passes the target voxel. By traversing all voxels in the three-dimensional voxel grid, the conditional probabilities corresponding to each voxel are spatially arrayed and mapped to construct a three-dimensional probability cloud map containing multiple probability dimensions.

4. The method according to claim 1, characterized in that, The process of obtaining the clinical objective of the dental implant crown to be removed, and calculating the conditional probabilities of the target voxels in the three-dimensional probability cloud map based on the clinical objective to obtain the local path cost value, specifically includes: Obtain the clinical goal of the dental implant crown to be removed, and determine the corresponding set of weight coefficients based on the clinical goal, wherein the set of weight coefficients includes weight factors that correspond one-to-one with each of the preset failure events; The local path cost value is obtained by weighted summation of the multi-channel conditional probabilities corresponding to the target voxel using the set of weighting coefficients. The formula for calculating the local path cost value is as follows: ; Where x represents the target voxel, C(x) represents the local path cost at target voxel x, N represents the total number of preset failure events, and P(E) represents the total number of failure events. i |x) represents the conditional probability of triggering the i-th preset failure event when the cutting tool passes through the target voxel x, w i Let G(x) represent the weight factor corresponding to the i-th preset failure event, and let each weight factor in the set of weight coefficients satisfy the normalization mapping constraint. Let G(x) represent the geometric constraint penalty term of the guidance path, and let γ represent the geometric constraint adjustment coefficient.

5. The method according to claim 4, characterized in that, The clinical goals include goals for preserving or discarding crowns. A corresponding set of weighting coefficients is determined based on these clinical goals, specifically including: A three-dimensional stress distribution field is constructed for the dental implant crown to be removed under a preset removal load, and stress concentration areas are identified based on the three-dimensional stress distribution field. The stress concentration areas are areas that reduce the structural stability of the dental implant crown. Based on the digital 3D scene, the spatial geometric distance from each voxel to the corresponding surface of the anatomical structure is calculated, and a spatial distance sensitivity function is constructed. When the clinical goal is the goal of preserving the crown, based on the spatial geometric distance sensitivity function, the weight factors corresponding to each preset failure event related to the damage to the anatomical structure are determined as positive penalty functions that are negatively correlated with the spatial geometric distance, and the weight factor corresponding to the event that the cut crown cannot be easily separated by instruments is determined to be zero; When the clinical goal is the discarded crown goal, the weighting factor corresponding to the event that the cut crown cannot be easily separated by instruments is determined as a negative reward function that is positively correlated with the distance of the stress concentration area, and the weighting factors corresponding to the preset failure events related to the anatomical structure damage are kept as the positive penalty function; The determined weight factors are dynamically normalized and mapped, and the normalized weight factors are vectorized and combined to obtain the set of weight coefficients corresponding to the clinical goal.

6. The method according to claim 4, characterized in that, The process involves using the surface voxel of the implant crown to be removed as the starting point in the three-dimensional probability cloud map, the voxel corresponding to the top of the central screw hole of the implant as the ending point, and the local path cost value as the guide, to solve for an optimal set of path voxels with the minimum cumulative local path cost value. Specifically, this includes: Push the exploration starting point into the dynamic priority queue, and initialize the cumulative path cost of all voxels in the three-dimensional voxel mesh except the exploration starting point to infinity, and initialize the cumulative path cost of the exploration starting point to zero. Pop the voxel with the smallest current cumulative path cost value from the dynamic priority queue, and traverse the neighborhood voxels of the voxel to be evaluated in three-dimensional space. Calculate the temporary cumulative path cost value from the exploration starting point to the target neighboring voxel via the voxel to be evaluated. The temporary cumulative path cost value is the sum of the cumulative path cost value of the voxel to be evaluated, the local path cost value at the neighboring voxel, and the spatial step cost between the two adjacent voxels. The target neighboring voxel is any neighboring voxel in the three-dimensional space. If the temporary cumulative path cost value is less than the historical cumulative path cost value recorded by the target neighborhood voxel, then the historical cumulative path cost value of the target neighborhood voxel is updated using the temporary cumulative path cost value, the parent node pointer of the target neighborhood voxel is pointed to the voxel to be evaluated, and the target neighborhood voxel is updated in the dynamic priority queue. Repeat the step of updating the cumulative path cost value until the exploration endpoint is popped up; When the exploration endpoint is popped up, starting from the exploration endpoint, backtracking is performed along the parent node pointers corresponding to each voxel until the exploration starting point is reached. All voxels passed during the backtracking process are arranged in order to generate the optimal path voxel set.

7. The method according to claim 1, characterized in that, The fitting and smoothing of the optimal path voxel set to obtain the final safe crown removal path in three-dimensional space specifically includes: Extract the center three-dimensional coordinates of each voxel in the optimal path voxel set to construct a discrete control point sequence; Based on the discrete control point sequence, a fitting algorithm is used to perform continuous interpolation fitting to generate an initial continuous three-dimensional path curve; In the three-dimensional probability cloud map, the conditional probabilities corresponding to each voxel traversed by the initial continuous three-dimensional path curve are retrieved. If the conditional probability corresponding to the current voxel is greater than a preset safety threshold, the current voxel is marked as a conflict voxel. The current voxel is any voxel traversed by the initial three-dimensional path curve. Based on the spatial location of the conflicting voxel, a normal repulsive force away from the conflicting voxel is applied to the initial continuous three-dimensional path curve, and the control point position of the initial continuous three-dimensional path curve is iteratively adjusted until all conditional probabilities of the area traversed by the initial continuous three-dimensional path curve are less than or equal to the preset safety threshold, thus obtaining the final safe crown removal path. Calculate the overall geometric features of the final safe crown removal path; based on the geometric features, use a preset strategy classifier to perform topological strategy recognition on the final safe crown removal path; Based on the identified topology strategy, the geometric configuration of the guide channel in the 3D guide plate template is automatically configured so that the geometric constraint boundary of the guide channel matches the motion envelope space of the rigid cutting tool when executing the corresponding topology strategy.

8. An apparatus for fabricating a guide plate for the removal of dental implant crowns, characterized in that, The device includes an acquisition unit, a processing unit, a calculation unit, and a planning unit. The acquisition unit acquires three-dimensional image data of the patient's oral and maxillofacial region where the dental implant crown to be removed is located, as well as oral scan data including tooth tissue morphology. The processing unit registers and fuses the three-dimensional image data and the oral cavity scan data in a unified coordinate system to obtain a digital three-dimensional scene containing anatomical structures. The digitized 3D scene is voxelized to obtain a 3D voxel mesh containing multiple voxels; Based on the spatial geometric distance from the target voxel to the anatomical structure, the conditional probability of triggering various preset failure events when the cutting tool passes through the target voxel is calculated, and a three-dimensional probability cloud map is constructed for the conditional probabilities corresponding to all voxels. The target voxel is any voxel in the three-dimensional voxel grid. The calculation unit obtains the clinical target of the implant crown to be removed, calculates the conditional probabilities of the target voxels in the three-dimensional probability cloud map based on the clinical target, and obtains the local path cost value; in the three-dimensional probability cloud map, taking the surface voxel of the implant crown to be removed as the exploration starting point, the voxel corresponding to the top of the central screw hole of the implant as the exploration ending point, and the local path cost value as the guide, solves for an optimal set of path voxels with the minimum cumulative local path cost value. The planning unit fits and smooths the optimal path voxel set to obtain the final safe crown removal path in three-dimensional space. Based on the final safe crown removal path, a rigid cutting envelope analysis is performed to determine the rigid axial cutting trajectory of the cutting tool. Combined with the surface morphology of adjacent teeth in the digital three-dimensional scene, a three-dimensional guide plate template is generated for physical processing and fabrication according to the three-dimensional guide plate template. The three-dimensional guide plate template includes a main body for matching the surface of the adjacent teeth and a guide channel. The geometric constraint boundary of the guide channel corresponds to the rigid axial cutting trajectory.

9. An electronic device, characterized in that, The device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to cause the electronic device to perform the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed, perform the method as described in any one of claims 1-7.

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