Maxillofacial image segmentation method based on voxel risk field construction

Abstract

This invention discloses a maxillofacial image segmentation method based on voxel risk field construction, belonging to the field of three-dimensional image segmentation technology. It constructs a voxel risk envelope using CBCT and intraoral scanning AI segmentation and uncertainty modeling, and solves for the incident cone and posture sequence in conjunction with mapping the intraoperative control upper limit. A bone-priority trace registration establishes the optical master channel, configures electromagnetic / inertial dark domain channels, switches according to quality score and occlusion duty cycle, and triggers two-point verification and trace re-registration. Multi-sensor fusion estimates bone quality and temperature rise risks and performs voxel write-back. Risk-driven shared control and strategy linkage are implemented, including amplitude limiting, step-by-step reaming, chip removal pause, irrigation, and speed-feed coupling and degradation backoff. Micro-registration and micro-substitution trajectories are performed at key nodes, and a priori library is accumulated postoperatively. This forms a closed-loop risk system throughout the entire process, reducing out-of-bounds risks and overheating, and improving stability and reusability.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional image segmentation technology, specifically to a method for segmenting maxillofacial images based on voxel risk fields. Background Technology

[0002] In maxillofacial implant procedures and minimally invasive surgeries involving adjacent maxillary sinuses / inferior alveolar nerves, preoperative 3D anatomy is typically reconstructed using cone-beam computed tomography (CBCT) and intraoral scans, with static guides or optical navigation used for traverse planning and tracking. Current procedures often construct restricted areas using a combination of discrete safety distances and isotropic morphological expansion, followed by segmented path and posture calculations. Intraoperatively, optical markers are relied upon, supplemented by electromagnetic / inertial fusion when necessary, and the control layer uses empirical thresholds to limit rotational speed and feed. In real-world scenarios, the narrow oral cavity, spray and bloodstains, flap traction, and operator obstruction cause rapid changes in soft tissue morphology and visibility. While guides / sleeves can stabilize the entry point, they significantly reduce irrigation coverage and heat exchange.

[0003] This leads to three common defects: First, image segmentation errors and uncertainties lack quantitative management, and noise and artifacts make risk boundary values ​​unstable; second, anisotropy induced by bone orientation and cortical thickness is not explicitly modeled, and isotropic expansion is prone to being overly conservative or aggressive; third, there is a lack of differentiable and interpretable mapping between preoperative risks and intraoperative amplitude limits, making it difficult to link tracking degradation caused by occlusion, pose drift, and irrigation attenuation at the control layer, resulting in path-pose decoupling, lagging thermal management, and escalating events. For next-generation intelligent surgical systems, the clinical and engineering communities urgently need a closed-loop link connecting image segmentation and uncertainty, anisotropic distance and voxel risk, multi-channel registration and consistency, thermal modeling, and shared control, which can be precipitated into a structured incremental learning postoperative knowledge base to support cross-case transfer and threshold self-calibration.

[0004] Therefore, it is urgent to couple the post-hoc uncertainty of 3D image segmentation based on CBCT / oral scanning with the anisotropic structure and thermal properties of bone tissue within a unified patient reference frame. This would construct a differentiable, monotonic, and directly callable voxel-level risk-mass integrated field, and establish a deterministic mapping between this field and the incident cone geometry, the instrument's six-DOF attitude, irrigation effectiveness, and guide plate reduction coefficient. Furthermore, dynamic control upper limits and shared control laws that are adaptive in both the time domain and mass domain would be generated on the arc-length parameterized path.

[0005] This problem arises at the blurred boundary between the base of the maxillary sinus and the wall of the inferior alveolar nerve.

[0006] CBCT noise, metal artifacts, and tissue heterogeneity increase segmentation uncertainty. Traditional methods using point-based safety distances or isotropic expansion approximations cannot reflect the propagation susceptibility of bone orientation and weak directions. Intraoperative soft tissue obstruction degrades optical channel quality, and the superposition of EM / IMU drift and robot kinematic errors causes geodesical inconsistencies in pose across multiple channels. Simultaneously, guide plate / sleeve obstruction weakens irrigation convection, and bone differences lead to significant variations in heat source intensity and diffusion anisotropy. Without the aforementioned self-consistent link of "image segmentation - anisotropic distance - heat source estimation - channel consistency - control upper limit," risks cannot be continuously and interpretably projected into upper limits and mode selection for propulsion speed, spindle speed, and angle stepping. The direct consequences are path and attitude decoupling, amplitude limiting and risk disconnection, and the inability to promptly downgrade and revert escalation events, thus significantly increasing the probability of nerve injury, sinus floor perforation, thermal necrosis, and drill jamming. Re-registration and alternative trajectories are difficult to trigger in a timely manner, and may even lead to intraoperative interruption and reoperation.

[0007] Therefore, the core issue addressed in this case is: within the scope of 3D image analysis and segmentation, to design a systematic method that transforms the segmentation posterior and uncertainty field into an optimizable risk metric through anisotropic distance and the Eikonal equation, and is driven by a dynamic control mapping based on multi-channel pose consistency, irrigation parameters, and thermodynamics. This method would ensure a closed-loop consistency between preoperative planning, intraoperative tracking, and strategy switching within a unified geometry-thermal-control domain. Simultaneously, the mapping should be guaranteed to monotonically tighten with respect to risk and uncertainty, maintain a one-to-one correspondence with arc length indices, and incorporate adjustable penalties and verifiable logs for hysteresis and mode switching to support threshold prior transfer and interpretable initialization across cases. Summary of the Invention

[0008] (a) Technical problems to be solved

[0009] To address the shortcomings of existing technologies, this invention provides a maxillofacial image segmentation method based on voxel risk field construction. It constructs a voxel risk envelope by using CBCT and intraoral scanning AI segmentation and uncertainty modeling, and solves for the incident cone and posture sequence in conjunction with mapping the intraoperative control upper limit. A bone-priority trace registration establishes the optical master channel, configures electromagnetic / inertial dark domain channels, switches according to quality score and occlusion duty cycle, and triggers two-point verification and trace re-registration. Multi-sensor fusion estimates bone quality and temperature rise risks and performs voxel write-back. Risk-driven shared control and strategy linkage are implemented, including amplitude limiting, step-by-step reaming, chip removal pause, irrigation, and speed-feed coupling and degradation backoff. Micro-re-registration and micro-substitution trajectories are used at key nodes, and a priori library is accumulated postoperatively. This reduces out-of-bounds and overheating issues, solving the technical problems described in the background art.

[0010] (II) Technical Solution

[0011] To achieve the above objectives, the present invention provides the following technical solution:

[0012] The maxillofacial image segmentation method based on the voxel risk field includes: acquiring CBCT voxels and oral scan mesh in the patient reference frame, performing AI segmentation and estimating uncertainty, solving the anisotropic Eikonal distance by combining symmetric positive definite tensors, and generating the voxel risk field and the upper limit curve of the arc length baseline.

[0013] Robust point-to-surface registration is performed using the bone surface trace point cloud and the risk field mask to establish the optical master channel and electromagnetic / inertial channel, construct the quality score and occlusion duty cycle, set hysteresis gating and use geometric interpolation to generate fused pose and consistency quantity;

[0014] The spindle torque, axial force, vibration, and feed are collected and combined with the fused pose extraction features. The bone type is updated with exponential posterior, contact gating is set, and the temperature rise is estimated according to energy, convection, and Arrhenius. The thermal risk is written back in anisotropy.

[0015] Based on the voxel risk and thermal risk, irrigation factor and visual score, the upper limit of the arc length baseline is exponentially scaled using a coupling matrix to obtain a dynamic upper limit. The operator input and path following are then fused together with risk weighting to generate control commands and a mode selector is set.

[0016] When a consistency alarm is triggered and the contact gating condition is met, two-point verification and trajectory re-registration update are performed. Based on risk and curvature / attitude optimization, the arc length baseline is corrected with small perturbations to generate an alternative trajectory, and the library is updated with Bregman regularization.

[0017] Furthermore, the AI ​​segmentation estimates uncertainty through ensemble learning or Monte Carlo dropout; the anisotropic tensor is inferred from the structural tensor and bone density gradient, and the Eikonal equation is solved using fast travel or semi-Lagrange method to generate the normalized voxel risk field, and the version identifier is stored in the patient voxel coordinates.

[0018] Furthermore, the arc-length baseline upper limit curve is parameterized using cubic splines or non-uniform rational splines and archived by binding it to the entrance configuration and guide cone geometry of the patient reference system; the baseline upper limit is subsequently mapped to the baseline factor of the control upper limit vector, and the node vector and control point index are recorded.

[0019] Furthermore, point cloud-bone surface registration is achieved by minimizing point-to-face residuals using Lie group optimization. The residual weighting is jointly determined by the voxel risk field sampling values ​​on the bone surface and the curvature confidence. The penalty function is robust and a priori regularization is applied to constrain the rigid body solution. A metric matrix is ​​set to balance the dimensions of translation and rotation.

[0020] Furthermore, the quality score is a linear combination of reprojection error, visible marker ratio, occlusion duty cycle and frame rate normalization, compressed to a closed interval of zero to one by a logic function; the occlusion duty cycle is obtained by integration according to a threshold indication within a fixed time window and participates in switching gating, and the linear combination weight is given by a calibration table.

[0021] Furthermore, the fused pose is geometrically interpolated on a special Euclidean group using an exponential mapping. The interpolation coefficients are jointly given by the quality score and the occlusion duty cycle, and generated by a hysteresis-based double-threshold saturation operator. The interpolation uses group logarithmic write-back of pose perturbation to output a unified pose for navigation and control.

[0022] Furthermore, the geodesic distance between the optical pose and the electromagnetic / inertial pose constitutes the consistency quantity and is linked with the timeout; when the threshold is exceeded, two-point verification and trace re-registration are performed, only the small perturbation increment rigid body is solved and the binding is written back, while the trigger timestamp and gating state are recorded.

[0023] Furthermore, a feature vector containing spindle torque, axial force, feed rate, and vibration spectrum centroid is constructed and aligned with the fused pose time; the bone category is updated recursively using exponential family posterior, and the update weight is gated using the contact consistency index; the feature mapping includes logarithmic and ratio transformations to suppress dimensional coupling.

[0024] Furthermore, bone temperature evolution is composed of friction and compression power, equivalent heat capacity and convection term, and the convection intensity is parameterized by the irrigation effective factor and the guide plate reduction coefficient; the temperature rise risk is obtained by Arrhenius integration and written back as the voxel thermal risk degree in the voxel domain with anisotropic kernel, and the kernel covariance is given by the posterior convex combination of bone category.

[0025] Furthermore, the dynamic upper limit is obtained by multiplying the baseline upper limit by a tightening factor with exponential scaling component by component; the elements of the coupling matrix are non-negative, and the tightening factor includes the temperature rise risk, the voxel risk, uncertainty, the irrigation effectiveness factor, and the guide plate reduction coefficient. The uncertainty originates from the AI ​​segmentation posterior and the ensemble variance estimate.

[0026] Furthermore, the fusion weight is obtained by linearly combining the temperature rise risk, the voxel risk, the contact consistency, the quality score, and the consistency quantity, and then compressing them using a logical function; the command torque is formed by weighting the surgeon torque and the path following torque according to the fusion weight, and is subject to the dynamic upper limit limit and gating.

[0027] Furthermore, the over-level triggering amount is obtained by summing the pairwise geodesic residuals of the optical pose, the electromagnetic / inertial pose, and the robot kinematic pose; the back-off arc length speed is calculated by weight mapping based on the over-level triggering amount, the temperature rise risk, the voxel risk, and the safety margin formed by the anisotropic distance, and then written into the execution queue.

[0028] Furthermore, the sample weights for incremental registration are a weighted sum of the voxel risk, the quality score, and the consistency quantity, and compressed by a logical function; the micro-displacement and micro-angle are optimized in the current arc-length neighborhood to form the alternative trajectory, and the knowledge base parameters are incrementally updated and the index is rearranged using Bregman divergence.

[0029] (III) Beneficial Effects

[0030] This invention provides a method for maxillofacial image segmentation based on voxel risk field construction, which has the following beneficial effects:

[0031] Before surgery, the risk envelope composed of voxel risk degree and uncertainty heat map is integrated with the incident cone-attitude sequence and rigidly mapped to the upper limit of intraoperative control. Furthermore, the accessibility and occlusion cost are superimposed to form a prior that monotonically tightens with arc length. As a result, the path and control are consistent from the source, reducing geometric out-of-bounds and unreachable segments, and the planning results can be directly transmitted to the execution layer.

[0032] The optical master channel is established by tracing registration with bone priority, while electromagnetic and inertial dark domain channels are configured. The state machine with hysteresis gating and geodesic consistency error constraint is used for seamless switching. It can maintain continuous and stable pose output even when spray, bloodstains and occlusion occur, and can trigger two-point verification and tracing re-registration in time to suppress drift accumulation and attitude jump.

[0033] Multi-sensor synchronous fusion outputs bone type and contact consistency, and thermodynamics explicitly incorporates irrigation effectiveness and guide plate reduction, and writes back the temperature rise risk as a spatial voxel thermal risk degree; thus, heat sources accumulate only on stable occlusal cutting samples, expose bone hot zones in advance, avoid systematic underestimation of thermal risk caused by guide plate obstruction, and improve the reliability of intraoperative early warning.

[0034] The shared control adaptively allocates human and machine tasks with integrated weights. The dynamic upper limit tightens in tandem with temperature rise risk, voxel risk, contact consistency, quality score and voxel thermal risk. The mode selector is linked to the step-by-step hole enlargement, chip removal pause, irrigation mode and speed feed coupling. Therefore, the risk upward segment can be smoothly taken over and the advance and angle step can be limited simultaneously to reduce drill jamming and heat peak. Moreover, the control process is interpretable and can be rolled back.

[0035] When the consistency of the three channels deteriorates or the quality deteriorates, the system quickly retreats to a safe posture along the centerline according to the backoff law, and is linked with the registration and error verification closed loop. In this way, it can escape danger in the event of unexpected occlusion or drift, limit the spread of risk to a local area, ensure that the operation is restarted in an orderly manner according to the established strategy after stabilization, and reduce interruption and secondary damage.

[0036] Two-point verification and trajectory re-registration are performed at critical drill diameter nodes or when triggered by adjacent risk envelopes, outputting only micro-reregistration increments and micro-displacement and micro-angle replacement trajectories; postoperatively, the state sequence and outcome are precipitated into a structured prior library and similar case initialization suggestions are generated; thus, the binding and trajectory are refreshed with minimal perturbation, shortening the parameter optimization time for the next case, forming cross-step synergistic gains and continuous evolution capabilities. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the maxillofacial image segmentation method based on voxel risk field construction according to the present invention. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Please see Figure 1 This invention provides a method for maxillofacial image segmentation based on voxel risk field construction, including:

[0040] Step 1: Taking AI segmentation, uncertainty and anisotropic risk measurement as the main line, the anatomical risk is transformed from image probability into a calculable control limit, and the integrated linkage planning of the incident cone and instrument posture sequence is completed under this limit.

[0041] Clinically, the proximity of the maxillary sinus and inferior alveolar nerve determines the hard constraints of the implant path. However, point-based safety distances alone are insufficient to cover the impact of image noise, metal artifacts, and bone anisotropy on the actual risk. Therefore, a continuous voxel field composed of a posteriori segmentation-uncertainty-anisotropic distance is needed to transform the discrete judgment of whether a risk is present into an optimizable function whose degree of risk changes monotonically with space. This provides a differentiable and superimposed metric basis for subsequent posture planning and intraoperative amplitude limiting.

[0042] Within the patient reference domain, using cone-beam CT voxel fields Based on this, and supplemented by the geometric priors of the gingiva and occlusal surfaces obtained from the surface mesh of the oral scan, the posterior probability of the anatomical category is first obtained. Then, the risk-sensitive structural voxels are amplified by integrating uncertainty, so that the fuzzy boundaries of the neural canal wall and the maxillary sinus floor are numerically highlighted, so as to form a more robust safety envelope. To this end, the coupling relationship between the anatomical saliency field and uncertainty is defined as follows:

[0043]

[0044] Where: voxel position vector The domain is defined as the patient voxel space. Used for locating voxels, bearing probability, and risk values, in mm; anatomical saliency field. : No. Significance of anatomical structures (such as the maxillary sinus, inferior alveolar nerve, and alveolar bone). This is used to drive subsequent anisotropy measurements and risk weighting;

[0045] Posterior segmentation probability : The posterior class derived from AI segmentation Used to measure the voxel's affiliation to the first voxel. Class credibility; Uncertainty intensity Uncertainty in segmented integration Used to increase saliency weights in areas of ambiguity; uncertainty weighting factor : This is used to adjust the amplifying effect of uncertainty on significance. The larger the value, the stronger the emphasis on the blurred boundaries; Category Index : Anatomical category set index .

[0046] To avoid measuring uncertainty by variance, power-entropy aggregation is used to obtain the uncertainty intensity:

[0047]

[0048] Where: average probability of categories Number of categories Sampling rounds : The number of samplings for model randomization (such as Monte Carlo dropout or multi-model ensemble). , used to stably estimate the class distribution;

[0049] No. Round Class probability : No. The class probabilities obtained from the forward prediction. Used to construct empirical mean distributions; power exponent Power entropy order, ; The smaller the value, the more sensitive it is to multimodal distributions, and it is used to sensitize the uncertainty of overlapping boundaries.

[0050] When using it, the saliency field is dissected. In high uncertainty intensity The magnification of the region numerically elevates the thin layer at the sinus floor and the wall of the neural canal, thus naturally expanding its scope in the subsequent risk envelope; simultaneously, it avoids excessive smoothing caused by approximating uncertainty with variance, making the risk boundary more closely match the true ambiguous region; and it ensures that the instrument is close to areas with high uncertainty intensity. When the area is controlled, the upper limit of control will be tightened accordingly, and the consistency from preoperative to intraoperative period will be enhanced.

[0051] In obtaining the anatomical saliency field Subsequently, anatomical saliency needs to be mapped to anisotropic distances to the risk sources to reflect the propagation susceptibility of trabecular bone orientation and weak directions. This is constructed using a symmetric positive definite tensor field. The induced anisotropic distance is used to obtain the directed distance field of the risk source using the Eikonal equation, which is then weighted with thermal and geometric vulnerability to synthesize a voxel-level risk field. First, the anisotropic Eikonal equation is solved:

[0052]

[0053] Wherein: anisotropic distance Anisotropic distance to the boundary of the risk source Used to measure the penetration cost of a voxel relative to the risk source; gradient operator Spatial gradient, used to calculate the directional derivative of the range field; anisotropic norm. : By symmetric positive definite tensor The induced norm is used to reduce distance growth in the longitudinal direction of cancellous bone and increase distance growth in the transverse direction.

[0054] Anisotropic tensor : ,Depend on Bone density gradient and cortical bone thickness inference are used to encode local propagation anisotropy, with a range of eigenvalues. Risk source boundary : Generated from the isosurface of the sinus floor and the neural canal, used to set the zero-distance boundary condition.

[0055] Furthermore, synthetic voxel-level risk fields:

[0056]

[0057] Among them: voxel risk level : Hard trigger values ​​used for subsequent pose planning and intraoperative amplitude limiting; distance weights Thermal weight Geometric weights :all ,and Used to balance contributions among spatial, thermal, and geometric fragility; normalized scale : Upper bound of distance normalization , used to Zoom to Power exponent : This is used to control the nonlinear sensitivity of distance to risk.

[0058] Thermal susceptibility weight field It is obtained by prior mapping of bone mineral density and cortical thickness. Used to enhance risk in areas with thin cortex or low irrigation accessibility; geometric vulnerability field : Obtained from a priori inference of morphological thickness and curvature It is used to increase risk at ridges and sharp turns.

[0059] When in use, anisotropic distance This allows the risk envelope to expand faster along the fracture-prone direction of the trabeculae, thus better reflecting the actual biomechanical weak direction than isotropic expansion; the synthesized voxel risk level Taking into account the three factors of space, heat, and geometry, and avoiding overly conservative or overly aggressive approaches caused by relying on a single distance threshold; when subsequent planning and control involve voxel risk assessment. At the same time, strategies can be tightened simultaneously in different dimensions, reflecting cross-modal collaboration.

[0060] Risk of obtaining voxels Subsequently, the clinical expectation is that the entry configuration, guide cone, and drilling posture will tighten monotonically with risk; at the same time, occlusion and accessibility must be explicitly taken into account, otherwise even if the risk is safe, it may be mechanically unenforceable.

[0061] Therefore, it is necessary to integrate and optimize the incident cone geometry with the instrument's six-DOF attitude sequence, and output the upper limit curve of the control index with arc length, so that it can be directly used for intraoperative shared control.

[0062] The path is expressed as the change of trajectory centerline and attitude with arc length, and voxel risk, occlusion cost, and reachability cost are unified into an integrated objective functional. Geometric regularization is used to prevent excessive bending, and the optimization objective is defined as follows:

[0063]

[0064] Among them: centerline curve : The arc length normalized parameterized centerline is used to define the spatial location of the drill duct; Cubic B-splines (or NURBS) are preferred for their differentiability, adjustability, and numerical optimization.

[0065]

[0066] in This is the control point (located in the patient reference frame). The basis functions are cubic b-spline (using uniform or quasi-uniform node vectors with endpoint emphasis to ensure controllable endpoint interpolation and tangential direction). This is the normalized arc length parameter; Here are the indices of the current basis functions and control points; attitude sequence The instrument's attitude parameters as a function of arc length (such as yaw-pitch-roll or quaternion parameterization) are used to define the incident direction at each position; attitude sequence The pose is as follows: , This is the position of the center line.

[0067] Risk weight Occlusion weight Accessibility weight Smoothing weights :all Used to balance four types of costs; voxel risk : on the centerline curve Sampling is used to drive the path away from the risk envelope; occlusion cost : Obtained by determining the visual volume intersection of the incident cone and the geometry of the oral soft tissue / guide plate, normalized to It is used to punish situations where the visible area is unreachable or the irrigation nozzle is blocked.

[0068]

[0069] Among them: visibility ; number of rays Indicator functions ;

[0070] Accessibility Cost : Obtained by normalizing the joint margin and operability of the robotic arm Used to penalize near-singular configurations or joint limitations;

[0071]

[0072] Where: Sigmoid Operability Joint margin:

[0073]

[0074] Weight .

[0075] Curve derivative The first derivative of the centerline is used to construct bending regularity and suppress unnecessary attitude swaying.

[0076] Constraints and Incident Cone Linkage: The entrance point and incident cone are determined by the entrance pose and guide sleeve geometry, and the incident half-angle is... Internal adaptive contraction;

[0077] Feasible domain based on voxel risk The threshold surface definition requires the centerline curve Within this feasible region, the minimum anisotropic distance to the boundary is maintained at a preset margin; the occlusion duty cycle and the tracking frustum overlap rate are used as hard constraints for embedding and solving. Hierarchical optimization (coarse-to-fine) or alternating minimization (fixed pose sequence) is employed. Optimize centerline curve Conversely, while ensuring accessibility and visibility, the path's risk to voxels can be reduced. First-order sensitivity enables a coordinated response of increased risk, narrowing of the incident cone, and attitude shift to a low-risk channel.

[0078] In practice, the objective functional integrates risk, occlusion, and accessibility within a single integral framework, avoiding the fragmented process of prioritizing path selection and then shape verification; curvature regularization ensures the stability of the instrument's propulsion, reducing flutter and guide plate wear; the incident cone parameters vary with the voxel risk during optimization. Automatic tightening creates a causally consistent geometric-risk closed loop between the entry point and the deep attitude.

[0079] To enable preoperative results to directly guide intraoperative shared control, voxel risk and uncertainty are projected onto a control upper limit curve on the arc length parameter. This allows the advance speed, spindle speed, and angle step to automatically tighten in high-risk or high-uncertainty segments, while ensuring the monotonicity and interpretability of the mapping. A vectorized upper limit mapping is defined as follows:

[0080]

[0081] Where: control upper limit vector : ; These correspond to the upper limits of propulsion speed, spindle speed, and angle step, respectively; baseline control vector : Each component represents the baseline recommended by the doctor / device, with units of mm / s, rpm, and deg / step, respectively; Hadamard product Component-wise multiplication is used to control the upper limit of scaling by component.

[0082] Coupling matrix : The elements are non-negative; the first column is used for risk coupling, and the second column is used for uncertainty coupling, ensuring monotonically tightening; Risk-Uncertainty Vector : Due to the voxel field Upsampling was used to obtain the sample.

[0083] Exponential mapping Component-wise exponent, used to guarantee right It is monotonically decreasing and has a bounded positive value.

[0084] In practice, the mapping ensures consistency in the exponential tightening of the control ceiling as risk / uncertainty increases, avoiding discrete jumps caused by linear clipping, and coupling matrices. The parameters of each column can be adjusted individually to achieve differentiated and sensitive control of speed, rotational speed, and angle step; the output control upper limit vector The natural and posture sequences are synchronized to facilitate synchronous amplitude limiting and degraded triggering according to arc length during surgery.

[0085] Step 2: Complete a highly reliable registration prioritizing bone within the patient reference frame and construct the optical master channel. Simultaneously, configure an electromagnetic / inertial dark domain channel and a switching state machine to ensure that attitude estimation remains continuous, traceable, and re-registerable under occlusion and dynamic disturbances.

[0086] In clinical settings, flap traction, saliva reflection, and bloodstains can cause rapid changes in soft tissue morphology, making registration based solely on gingival or dentition features prone to drift; while the voxel risk level obtained from step one... Anisotropic magnification of the boundary between the maxillary sinus floor and the inferior alveolar nerve was performed, which can be used as a mask and weighted source for bone-preferred mapping. Therefore, by relying primarily on the rigid geometric prior formed by bone surface tracing, supplemented by visual quality assessment of the optical master channel, registration and tracking are coupled in a closed loop within the same patient reference frame, thus providing a stable anchor point for subsequent channel switching and re-registration.

[0087] Clinical tracing involves continuously sliding a sterilized probe along the alveolar ridge and exposed bone surface to create a point cloud sequence. The point cloud is then aligned point-to-face with the bone surface model output from step one within the patient reference frame. To suppress the influence of weak boundaries near high-risk envelopes, voxel risk levels are... As an optimization objective on the Lie group using spatial weighting and robust penalty unified construction eigenvalues, we obtain a rigid body solution as the initial binding.

[0088]

[0089] Where: rigid body transformation : Map the trace coordinates to the patient reference frame, output the registered pose, and take values ​​from elements of a special Euclidean group; trace points : ; Three-dimensional points obtained from bone surface tracing; unit: mm; corresponding bone surface points : The nearest point from the preoperative bone surface mesh, in mm; local normal. : ,exist The unit normal at the point is used for point-to-surface residuals; robust function Set to Geman-McClure format Used to suppress isolated outliers. ;

[0090] Weight Trajectory matching weights Regularity coefficient : Constrained solutions do not deviate from the prior; prior transformation : ; Obtained from preoperative positioning and initial binding of the dental tray / guide; Lie algebra measurement : , Dimensions of equilibrium translation and rotation; scale parameters : Robust function scale; given by the upper bound of the trace noise; number of samples : ; Track point count; Ensure over-constraint;

[0091] To assess voxel risk Explicitly inject registration weights, using exponential decay superimposed curvature confidence. Method:

[0092]

[0093] Among them: voxel risk level : Output from step one and at the corresponding bone surface point Sampling at the location, ;

[0094] Risk attenuation coefficient : Curvature credibility : The contribution of smoothed high-curvature outliers is estimated by the principal curvature and normal stability of the bone surface.

[0095] In practice, through risk-curvature coupling weights, fuzzy points near the thin layer of the maxillary sinus floor and the nerve canal wall are adaptively deweighted, so that the rigid body solution is dominated by the principal components of the stable bone surface; robust penalty combined with Lie algebra regularization ensures that the solution is not sensitive to a small number of occlusions or accidental touches; finally, the registration forms a single optimized link with the geometric prior of step one and the intraoperative trace data, which can establish a reliable starting point for subsequent tracking.

[0096] To ensure the effectiveness of the optical master channel under strong light, spray, and operator occlusion, a measurable tracking quality score needs to be established, and the occlusion duty cycle needs to be incorporated into the same scale. This allows it to serve as both a switching gating input and a consistency score. A normalized score with logical compression should be constructed, unifying the dimensions of reprojection error, marker coverage, occlusion duty cycle, and frame rate to a single standard. Interval:

[0097]

[0098] Error normalization : The smaller the error, the closer it is to 1; reprojection error : Robust aggregation, threshold : px; calibration.

[0099] Optical quality rating : A higher Sigmoid value indicates greater reliability; Sigmoid compression. : Used to compress linear combinations to Weighting coefficients : Balanced four contributions; robust reprojection error : Image point error using quantile or Huber aggregation; number of visible markers : The number of reflective markers observed by the camera at the current moment;

[0100] Maximum number of tags Nominal visible total, used for normalization; Occlusion duty cycle : ; see the following definition for frame rate : Current camera processing frame rate; Reference frame rate System nominal frame rate; unit: Hz;

[0101] The occlusion duty cycle is defined by a binary indicator of the time window integral to avoid misjudgment due to instantaneous jitter.

[0102]

[0103] Among them: occlusion duty cycle : indicates near The occlusion ratio within the time window; the length of the time window : Typical values ​​are 1–3 seconds; Indicator function : 1 is set if the condition is true, 0 is set otherwise, used for duty cycle statistics;

[0104] Error threshold : Alarm threshold for reprojection error; minimum marker threshold : If the value is below a certain level, it is considered occlusion; time variable. : Independent variable for integration.

[0105] When used, a single rating Multi-source quality characteristics are expressed on the same scale and correlated with occlusion duty cycle. Embedded coupling provides coherent gating signals for subsequent state machines; occlusion duty cycle is achieved through time-windowed occlusion. Suppressing false triggers due to brief occlusion improves handover stability; this quality modeling shares a reference frame with the registration in the previous section, ensuring a consistent coordinate benchmark for good / bad evaluation and pose estimation.

[0106] The optical main channel will temporarily fail when severely obstructed or when the field of view is limited, while electromagnetic and inertial sensors can continuously output attitude in the dark domain (without line of sight); however, both have their own shortcomings in terms of drift and transient noise.

[0107] Therefore, it is necessary to design a seamless switching and fusion mechanism between optical and electromagnetic / inertial systems, and to trigger minimal perturbation micro-repetition registration when timeout or consistency anomalies occur, so as to ensure end-to-end consistency after the switchback.

[0108] To achieve continuous switching between pose estimation based on monocular / binocular optical estimation and electromagnetic / inertial fusion estimation, geometric interpolation using exponential mappings on Lie groups is employed; the interpolation coefficients are determined by optical quality scoring. Compared with the duty cycle of occlusion A joint decision was made, and a delay was set to prevent the door from shaking when it is knocked:

[0109]

[0110] Among them: fused pose : Real-time output of unified pose for navigation and control; electromagnetic / inertial pose. : Optical pose obtained by tightly coupled filtering of electromagnetic coil and IMU. : ; Calculated from the optical main channel;

[0111] Logarithmic mapping Exponential mapping : The bijection is used for linearization in Lie algebras and for writing back on groups; interpolation coefficients : Given by the gate function, it increases monotonically as the quality decreases, indicating a transition to the dark domain channel;

[0112] Gating function : It is a double threshold saturation operator (lower threshold 0, upper threshold 1, with hysteresis band). .

[0113]

[0114] Among them: hysteresis lower threshold Upper threshold :satisfy .

[0115] In practice, geometric interpolation avoids the path-dependent distortion introduced by Euler angles or independent linear interpolation, ensuring that the switching trajectory... Maintain geodesic continuity; interpolation coefficients Monotonic coupling with mass-duty cycle ensures a shift towards the darker region as darkness deepens, and hysteresis bands suppress back-and-forth jitter; during optical restoration, the interpolation coefficients... The smooth descent and seamless pose output ensure the continuity of subsequent shared control.

[0116] To monitor inter-channel drift and trigger micro-repetitive registration when necessary, a Lie group geodesic error for channel consistency is defined and linked to a timeout mechanism. If the threshold is exceeded or a timeout occurs continuously, a two-point check / tracing re-registration is forcibly performed, the reference binding bit is reset, and the optical channel is switched back for error verification and log storage.

[0117]

[0118] Among them: geodetic consistency error : As the trigger quantity and the number of records; metric matrix : Adjust translation / rotation weights; degree pose Electromagnetic / Inertial Pose Same as above. Lie algebra norm : The six-dimensional disturbance is compressed into a scalar error.

[0119]

[0120] Among them: consistency score : Gating, sharing, and degradation. Weighting. : .

[0121] Triggering Mechanism and Re-registration Process: When Geodetic Consistency Errors Continuously exceeding the upper limit of the threshold (e.g.) And the timeout timer reaches the window. At that time, two steps are performed: (1) Two-point verification: Select two anatomical points with long spatial baselines and high separation within the bony priority mask, collect their stylus click coordinates in real time, and calculate the deviation from the model prediction; (2) Tracing re-registration: Use the same robust point-surface constraint as technical point A, but restrict the optimization variable to small perturbation increment. and based on a priori rigid body transformation Based on this, convergence is achieved through one or two Gaussian-Newton iterations; after reversing the optical channel, convergence is achieved with a new... Update the binding. Then calculate the review error, refresh the logs, and calculate the consistency score. (Depend on and (Obtained through Sigmoid mapping) and fed back to the gating in step four.

[0122] When used, geodesic consistency error unifies attitude differences to Lie group metric, avoiding scale confusion of Euclidean difference; two-point verification quickly verifies drift direction with minimal interaction, and trace re-registration ensures no abrupt jumps in back-cut with small perturbation solution; error verification-log accumulation makes it possible for subsequent case scenario-based participation and threshold self-calibration.

[0123] Step 3: Based on multi-sensor synchronous fusion, estimate bone type and temperature rise risk online, and correlate the risk information with voxel risk levels in the voxel domain. Forming a closed-loop coupling, outputting the temperature rise risk level. With anomaly probability Two types of hard triggers.

[0124] Bone type directly affects drilling load and heat generation by orders of magnitude. Relying solely on a single-channel signal (e.g., using only spindle torque) will result in high sensitivity to wetting, contact state, and guide plate friction. Therefore, spindle torque, axial force, and vibration spectrum are constructed into temporal features and fused with the pose from step two. Alignment is performed, and then the bone class posterior is updated through exponential family posterior. Contact consistency gating is then used to suppress aberrant transients to ensure the physical consistency of subsequent temperature rise estimation.

[0125] Construct time on the established unified time base. The feature vectors are updated online using exponential family posteriors, thus stably outputting the bone class posterior under a small sample size and fast convergence setting. For this purpose, we define:

[0126]

[0127] Among them: bone category post-test : And for Satisfying normalization, used as an adaptive index for thermal parameters and mechanical thresholds; bone category set. : ; Corresponding to commonly used clinical bone grading; Post-hoc test at the previous time step : ; Category parameter vector : Offline estimation from a case database and intraoperative fine-tuning are used to measure the discriminative power of features on categories.

[0128] Feature mapping : It includes piecewise affine transformations and logarithmic / ratio transformations; the publicly available form is [not specified]. ; Eigenvector : Data are collected synchronously by the sensing system; the units are N·mm, rad / s, N, mm / s, and Hz, respectively.

[0129] Spindle torque : ; Estimated by the spindle drive or measured by the torque sensor; Spindle angular velocity : ; Obtained by encoder; Axial force : Feed rate is measured by a six-axis force sensor or a strain gauge embedded in the spindle. : The centroid of the vibration spectrum is obtained by converting the robot's joint velocities using geometric Jacobian. : It is calculated from the normalized power spectrum of the acceleration signal within the analysis window.

[0130] In practice, this posterior update compresses the coupling relationship between category, mechanics, and kinematics into a single differentiable expression, allowing for stable category estimates with a small number of samples. The log / ratio feature suppresses the collinear amplification effect of rotational speed and feed, avoiding bias from a single load index. The output bone category posterior... This will produce an adaptive effect on the temperature rise parameter and kernel function anisotropy, forming a tight coupling with the subsequent thermal model.

[0131] In actual drilling processes, brief slippage, air cutting, or guide plate friction can cause a mismatch between energy input and chip removal. If not properly managed, this can contaminate the posterior category and heat source estimation. Therefore, a contact consistency index is constructed. By combining the power-feed ratio and vibration envelope amplitude, a gating signal is generated to suppress the contribution of anomalous transients to model updates.

[0132]

[0133] Among them: contact consistency index : A higher value indicates a higher probability of stable biting and cutting, used for gating updates and heat source acquisition; Sigmoid compression function. : This is used to normalize and enhance sensitivity before and after the threshold (consistent with step two); weights : , Vibration envelope amplitude is set through calibration. : ; Acceleration amplitude obtained from Hilbert transform or envelope detection; Main shaft torque angular velocity of the main shaft Feed rate : The definition is the same as above.

[0134] When using, contact consistency indicators Symmetrical suppression of air cutting and stuck drill bit effects can reduce model update weights in cases of energy-vibration mismatch, ensuring that both category and heat source estimations are based on real cutting samples; and it is compatible with optical quality scoring. The conjunction gating further avoids erroneous updates during the shading period, ensuring the physical interpretability of subsequent temperature rise predictions; the gating output is also fed back to step four as one of the additional triggering conditions of the limiting function family.

[0135] The risk of bone temperature rise and tissue damage is determined by the instantaneous heat source, convective heat dissipation, and duration of action. The presence of guide plates / sleeves significantly reduces irrigation coverage and heat exchange capacity; if these factors are not explicitly parameterized, the risk of temperature rise will be systematically underestimated. Therefore, temperature evolution is modeled under the approximation of local equivalent heat capacity, and the irrigation effectiveness factor and guide plate reduction coefficient are introduced. Subsequently, the risk of temperature rise is obtained according to the histological reversible-irreversible Arrhenius mechanism, and then the risk is anisotropically written back along the orientation sequence in the voxel domain to form a bone hot zone / temperature rise warning.

[0136] Treating cutting friction and normal extrusion work as heat sources, and convective heat dissipation as linear terms, and using local equivalent heat capacity to concentrate thermal inertia in the vicinity of the drill tip, we obtain the bone temperature evolution dynamics. Simultaneously, we use the irrigation effectiveness factor... Together with the guide plate reduction factor, they characterize the convection intensity:

[0137]

[0138] Among them: bone temperature : Local equivalent temperature in the vicinity of the drill tip, in °C, used for subsequent risk integration; time derivative. Temperature change rate, in °C / s; friction efficiency : The efficiency coefficient of the conversion of cutting work into heat;

[0139] Normal dissipation efficiency : Efficiency of axial extrusion work-to-heat conversion; spindle torque angular velocity of the main shaft Axial force Feed rate Definition as above. Equivalent heat capacity. : Heat capacity of the contact area between the burr and the drill bit; unit: J / ℃; baseline heat transfer coefficient. : Convective heat transfer coefficient without irrigation reduction, unit W / (℃·m²); Irrigation effective factor : This indicates the irrigation flow rate, nozzle configuration, and effective intensity of the sprinkler coverage;

[0140]

[0141] Among them: traffic Reference flow ;index Sprinkler coverage (Estimated by visual / acoustic feedback);

[0142] Guide plate reduction factor : The smaller the value of the convection reduction caused by the guide plate / sleeve obstruction, the stronger the reduction.

[0143]

[0144] Where: Opening area Total circumferential area Alignment coefficient (Nose-sleeve axis alignment). Ambient temperature. : Reference temperature for irrigation fluid / oral environment.

[0145] In the criterion for tissue damage, the Arrhenius integral based on irreversible reaction kinetics is introduced to obtain the temperature rise risk (compressed to...). ):

[0146]

[0147] Among them: risk of temperature rise : Used to trigger the limiting / degradation in step four; Integral window : The risk accumulation time window can be clinically taken as a nominal scale consistent with 47℃·1min; pre-exponential factor. : Temperature independence coefficient of histological reaction rate; unit ;activation energy : Activation energy of an irreversible reaction in an organism; unit: J / mol;

[0148] gas constant : Ideal gas constant; unit: J / (mol·K); bone temperature trajectory Same as above; but with the integral independent variable For time index; constant Celsius-Kelvin conversion term Used for temperature scale conversion, dimensionless.

[0149] In practice, the kinetic equations bridge mechanics and thermodynamics into a single identifiable model, with the guide plate reduction coefficient... The clinical fact of reduced irrigation due to sleeve occlusion is transformed into an adjustable parameter; the Arrhenius integral is more sensitive to the nonlinear coupling of temperature and duration, and can give a consistent risk increase in both short-term high temperature and long-term medium temperature scenarios, which is more consistent with histological evidence than a simple thresholding strategy.

[0150] To make the time domain Transforming the early warning system into a spatial domain requires following the centerline curve of step one. Risk is diffused in voxel space; diffusion should not be isotropic, but rather anisotropic, dominated by the posterior influence of bone class, to reflect the differences in trabecular orientation's sensitivity to thermal diffusion and injury. Therefore, voxel-level thermal risk write-back is defined:

[0151]

[0152] The specific form of the anisotropic kernel function is disclosed:

[0153]

[0154] Among them: Voxel thermal risk level : Used in relation to voxel risk Fusion generates bone hot zones; Integral kernel : Projecting time-domain risk into the spatial domain; anisotropy measurement : By symmetric positive definite matrix The induced norm; its principal axis is determined by the posterior of bone class. Weighted determination to reflect trabecular bone orientation;

[0155] Category covariance : Different bone types are assigned different anisotropy ratios; the time-varying covariance is obtained using the posterior convex combination of bone types.

[0156]

[0157] Among them, category posterior : ; Category covariance SPD; .

[0158] bandwidth : Spatial influence range of the control nucleus; unit: mm; voxel position : Patient voxel coordinates; centerline curve Define the same as in step one; position parameters With time Obtained by advancing arc length / time calibration Temperature rise risk : Defined as above; with the independent variable as the integral. sampling.

[0159] When in use, the anisotropic core unifies the temperature rise risk, bone orientation, and spatial propagation within a differentiable framework, making the thermal risk spread faster toward the vulnerable direction of the bone and slower in the thick cortex, thus avoiding the excessive conservatism of isotropic expansion. and The coupling enables category recognition and thermal warning to form a self-consistent closed loop, directly producing bone hot zones and temperature rise warning voxels, which can be immediately invoked by the limiting function family and strategy switching in step four.

[0160] Step 4: Under the patient reference system, rigidly map the risk level, quality score, and consistency error into executable shared control commands and strategy switching logic, which tighten monotonically with risk and rapidly downgrade and roll back abnormalities.

[0161] The operator aims to maintain subjective control over propulsion and direction, but in cases of sudden increases in risk or deterioration in tracking quality, the system must predictably take over and tighten the upper limit to prevent thermal damage and geometric overruns. Therefore, a shared control law needs to be constructed, centered on risk and smoothly integrated with the operator's input, and the upper control vector of step one needs to be... Elevate to a dynamic upper limit that adapts to both the time domain and the quality domain. This enables seamless transfer from the preoperative approach to the intraoperative amplitude limit.

[0162] A risk-weighted fusion is established between continuous input from the main control handle and autonomous suggestions from the path-following domain, with the fusion weight being related to the temperature rise risk level. Voxel risk level Contact consistency index Optical quality rating and geodetic consistency error To achieve monotonic coupling and maintain interpretability and reversibility of the operator's actions, the fusion weights and command torques are constructed as follows:

[0163]

[0164]

[0165] Among them: fusion weight : Used to weight human control and self-control, with the proportion of self-control monotonically increasing with risk and inconsistency; Sigmoid compression function. Standard logic functions map real numbers to... Used to establish smooth gating; weighting coefficients : The system calibrates and controls the impact of various indicators on the gating and the baseline bias; temperature rise risk level. From step three, Voxel risk level :exist The sample is taken from the risk field in step one, and the value is taken as follows. Contact consistency index From step three, ;

[0166] Optical quality rating From step two, Geodetic consistency error From step two, Command torque : ; These correspond to the propulsion speed, spindle angular velocity, and angle step commands, respectively; Operator torque. : The desired torque mapped from the handle input to the patient reference frame; autonomous torque : Twist generated by the path following domain (based on , The error field is obtained from impedance / sliding mode shaping, which is used to provide a pullback trend when the surgeon's intention conflicts with the safety domain;

[0167]

[0168] Wherein: position error Rotation error is represented by the logarithm of the Lie group. Vectorization of antisymmetric matrices; gain Dynamic upper limit : An upper bound vector that adapts to risk and quality, used to limit the amplitude of each component;

[0169]

[0170] in: ; Limiting operator : Cut off component by component Ensure that commands do not exceed the limit.

[0171]

[0172] Where: Input Dynamic upper limit Arc length index :Depend on and The nearest point projection is used to locate the current control slice along the path.

[0173]

[0174] Nearest point projection The current instrument tip is located at the patient's reference point; numerical implementation: arc length parameter discretization + 1D line search.

[0175] When using it, if the risk or inconsistency increases, The smooth increase in torque, rather than abrupt takeover, significantly reduces the perceived control failure by the operator; at the same time, the limiting operator ensures that commands are bound to a safe upper limit that is updated over time, making the control layer's response to risk changes continuous and interpretable.

[0176] To achieve upper limit control that tightens monotonically with risk and can be linked across modalities, step one... As the arc length baseline, and by introducing four types of factors—temperature rise, contact, visual perception, and irrigation—to an exponentially tightening mapping, a unified dynamic upper limit for the three components is obtained:

[0177]

[0178] Among them: dynamic upper limit : ; Upper limits for propulsion, rotational speed, and angular stepping, respectively; Baseline upper limit : From step one, the preoperative upper limit with arc length; Hadamard product Component-wise multiplication is used to scale different upper bound components separately; coupling matrix : The columns correspond to different tightening factors, and the non-negative nature of the elements ensures monotonic tightening.

[0179] Tightening factor vector : It covers five categories of information: heat, contact, visual, irrigation, and voxel-based heat risk; irrigation effectiveness factors. From step three, Guide plate reduction factor From step three, ; The smaller the size, the stronger the tightening. (Vollogram thermal risk level) :exist Spatial early warning sampled from step three. Interval.

[0180] In practice, exponential scaling multiplicatively integrates the upper limit with multi-source risks, tightening rapidly when any one factor deteriorates and moderately relaxing when multiple factors are favorable; this is achieved through the use of a coupling matrix. The parameters of each column can be adjusted independently, and the sensitivity of propulsion, speed and angle steps to different risks can be configured differently, realizing the engineering adjustability of coaxial different strategies.

[0181] Simple amplitude limiting is insufficient to cover the multi-dimensional coordination of irrigation, orifice reaming rhythm, and chip management. Furthermore, when channel consistency or quality is extremely poor, it is necessary to degrade and revert to the pre-planned safe posture. Therefore, a mode selector with cost energy as its core is needed to weave four strategies—stepped orifice reaming, chip removal pause, irrigation method and nozzle configuration, and speed-feed coupling—into a switchable discrete mode. When a catastrophic event occurs, the three-channel consistency is used as a trigger signal to perform reversion and stabilization.

[0182] A finite set of modes is defined, and time-varying costs are formed by integrating factors such as temperature rise, bone density, thermal risk, contact, and vision. Penalties are introduced for mode switching to achieve hysteresis and steady-state maintenance. The selector outputs the current mode in a manner that minimizes the cost.

[0183]

[0184]

[0185] Among them: pattern set Weight ;feature (including) ); Switch penalty ; length of stay Current mode : The determination of the orifice enlargement step, pause time interval, irrigation method / nozzle configuration, and rotational speed-feed coupling curve;

[0186] Pattern set : Pattern weights : Sensitivity vectors for different patterns are calibrated using a case database and offline trials.

[0187] Feature vector : ; representing temperature rise, bone hardness index (weighted) in sequence. Voxel thermal risk, contact consistency, irrigation effectiveness and shading duty cycle; switching penalty : Used to suppress frequent mode transitions; indicator function : 1 if the condition is true, 0 otherwise, used to implement hysteresis; Previous mode The discrete mode output at the previous time step. Occlusion duty cycle. From step two, .

[0188] In use, this selector incorporates discrete strategies into a unified cost domain, avoiding the uninterpretability of rule concatenation; the hysteresis term suppresses frequent switching, and is combined with feature vectors. The bone and irrigation information in the hole allows the reaming step distance, pause ratio and irrigation configuration to adapt to the bone type and thermal state, significantly reducing the peak temperature rise and the probability of stuck drill bit.

[0189] When vision is obstructed or multi-channel drift increases, the system must be rapidly degraded and backtracked along the pre-planned path to a safe posture, only to be restored after re-registration is complete. Based on the consistency of the three-channel pose (optical, electromagnetic / inertial, and robot forward kinematics), the system defines the over-level triggering quantity and provides the backtracking law:

[0190]

[0191]

[0192] Among them: three-channel consistency error : This represents the sum of two geodetic residuals; the larger the sum, the worse the consistency.

[0193] optical attitude Electromagnetic / Inertial Pose Sports posture :all The logarithm of the Lie group is obtained from the fusion link and the robot solution in step two, respectively. With metric matrix Mapping the group difference to a Lie algebra and measuring it using six-dimensional weights; ; Retreat arc length speed : Negative values ​​indicate along Reverse backoff; unit is normalized arc length / s; gain : ; Upper bound of control rollback speed; Weight : The contribution of balancing heat, contact, consistency, and spatial risk to regression; voxel risk level. Voxel heat risk risk of temperature rise Contact consistency : Definition as above. Safety margin : Anisotropic distance With margin From step one; The smaller it is, the closer it is to the risk boundary; ,in Determined by preoperative risk budget (e.g., equal to the minimum safe distance between the implant and the neural canal) (and can adaptively update according to bone type in the learning library. Sigmoid function) Same as before, used for smooth trigger-back-off gain modulation.

[0194] In use, the three-channel consistency error unifies the visual-electromagnetic-kinematic drift onto a geodesic scale, and the trigger signal is insensitive to local occlusion and short-term jitter; the backoff law incorporates thermal and spatial risks into the same gating, and uses a safety margin. Develop preventative behaviors such as accelerating retreat before exceeding the limit, ensuring the device is pulled back before re-fitting or strategy adjustment. The safety segment reduces the risk of secondary damage.

[0195] Step 5: Under strict risk and quality gating, refresh the reference binding with minimal perturbation and generate an executable alternative trajectory. Then, perform structured incremental learning on the postoperative data so that the next case has interpretable transfer priors on the initial values ​​and thresholds.

[0196] Under the three triggering conditions of critical drilling circumference nodes, adjacent risk envelopes, and deterioration in tracking quality, if the predetermined attitude sequence continues... Propulsion may introduce systematic deviations when local thermal or geometric constraints are weakened. Therefore, under the assumption of minimum perturbation, fine-grained corrections need to be made only to the local reference binding and trajectory, ensuring that the corrected position-attitude remains consistent with the centerline curve from step one. With voxel risk Maintain consistency with the dynamic upper limit in step four. This ensures compatibility, thereby avoiding the overhead and disruption of global replanning.

[0197] Three triggers are effective and contact consistency indicators To ensure stable cutting, a sequence of two-point verification followed by trace re-registration is employed, with reference binding refreshed using small-increment rigid body transformation. The solution is obtained using small perturbation optimization on a Lie group. Construct a local point-to-surface robust target and apply a priori regularization to the solution so that the registration changes only to the necessary extent, where:

[0198]

[0199] Where: Incremental rigid body transformation : ; Map the trace coordinates to a small perturbation in the current patient reference frame; Solve for the objective, taking values ​​from elements of a special Euclidean group; Trace points : Points acquired in real-time within the bony priority region; unit: mm; corresponding model points. : ; The closest point given by the preoperative bone surface mesh in the patient's reference frame; unit: mm; normal direction : ;exist Unit normal, used for point-to-surface residuals; robust function Take the Geman–McClure form ,scale Weighting coefficients Trajectory sample weights Regularity coefficient : Control the perturbation amplitude of the solution to avoid excessive modification; Lie algebra and logarithm : The logarithmic mapping is used to linearize the group elements; the metric matrix : ; Dimensions and weights of balancing translation / rotation angles; Sample size : The number of trace points is guaranteed to meet certain constraints.

[0200] To combine risk, quality, and consistency in gating and weighting, a trigger coupling mapping for sample weights is defined:

[0201]

[0202] Where: Sample weight Same as above; simultaneously affected by spatial risk and temporal quality modulation; voxel risk degree :exist Voxel risk level at the sampling site; From step one; risk attenuation coefficient : Control the weighting intensity near the risk envelope; Sigmoid function : Map the weighted sum to Weighting coefficients : , The impact of balancing quality and consistency on weighting; optical quality scoring : From step two. Three-channel consistency error. : From step four. Contact consistency index : From step three.

[0203] In practice, the above incremental solution only takes effect when the trigger is valid and the quality is acceptable, weights Automatic reduction at high-risk and low-quality locations ensures that micro-registration is insensitive to fuzzy boundaries; regularization terms suppress over-correction, keeping the reference binding consistent with the existing trajectory, thus providing a stable base for subsequent micro-registration planning.

[0204] After micro-registration, to avoid continuing along the original posture through newly formed bone hot zones, the local trajectory needs to be corrected with minimal perturbation. This is based on voxel risk. With voxel heat risk Non-negative weighted sums constitute a composite field At the current arc length index Within the neighborhood of the variable, the micro-displacement-micro-angle update is obtained by combining curvature and attitude deviation penalties:

[0205]

[0206] Where: Optimal update amount : The output micro-displacements and micro-angles are used to generate alternative trajectories; micro-displacements : Local spatial translation update; unit: mm; micro-angle : Small-angle axis-angle vector; unit: rad; composite risk field :Depend on and The non-negative weighted sum, with a weighted sum of 1, is used to drive the trajectory away from high-risk voxels; centerline curve Current arc length position; from step one; curvature penalty operator : Take the diagonal of the unit block to equivalently restrict the bending of micro-segments; the disclosure is as follows Curvature penalty weight : Suppressing excessive bending; Posture penalty weights : Limit deviations from the original attitude sequence The range.

[0207] and A one- to two-step Gaussian-Newton backtracking search is employed, with the termination condition being the first-order residual reduction rate. or step size (The dimensions are normalized to the displacement (mm) / angle (rad) component) to ensure small perturbation solutions and avoid overfitting.

[0208] In practice, this optimization, dominated by the composite risk gradient, makes only the minimum necessary offset, ensuring that the alternative trajectory remains geometrically compatible with the original centerline; curvature and attitude penalties prevent sharp turns or abrupt rolls; the output is the optimal update amount. With the dynamic upper limit of step four It is directly compatible and can be immediately deployed to the execution layer, reducing downtime and operator cognitive burden.

[0209] The risk evolution and strategy switching patterns of a single case exhibit significant individual differences. If the intraoperative state sequence and outcome indicators are not converted into searchable priors, the next case will still need to start from a cold start. To address this, we structured the data from the perspective of bone type-strategy-outcome and used incremental updates with Bregman regularization to ensure stable convergence. For new cases, we provided interpretable initial parameters and warning threshold suggestions by measuring anisotropic similarity with the prior database, enabling cross-case transfer.

[0210] The time series data of a single case is compressed into event graph entries of state-action-risk-outcome, and then used as a parameter vector. The mapping from case description vectors to strategy effectiveness is represented; incremental correction is performed item by item post-surgery, and robust updates are achieved using convex loss and Bregman divergence.

[0211]

[0212] Where: parameter vector : ; Encoding a bone type-strategy-outcome mapping to generate recommendations for the next case; Sample index : ; Traverse entries in chronological or event order; Case description vector : Statistical analysis based on bone type posterior Risk envelope morphology characteristics, statistics of effective irrigation factors Guide plate reduction factor It is composed of dynamic upper limit trajectory statistics, etc.; target vector : Includes final stability score, imaging review results, and postoperative complication markers;

[0213] loss function Convex and differentiable, such as log-likelihood or smooth hinge, used to measure the deviation between prediction and outcome;

[0214]

[0215] Where: Classification label vector Unique hot or soft label; Regression target vector , Input description vector (Compiled from statistics on bone density, risk, irrigation, and control). Parameter vector. Classification probability , quantity And the sum is 1. Regression prediction Huber punishment , Weight Used to balance the three terms. Regular weights : Balance fit and stability. Bregman divergence. : By potential function Induced divergence. To provide sufficient disclosure, a specific class of potential functions and divergences are given: .

[0216] In practice, incremental correction allows the knowledge base to converge stably as cases are continuously updated; Bregman regularization ensures that new information is absorbed while preserving the historical stable structure, avoiding parameter oscillations; structured entries will... , , , Aligning with the final outcome within a unified symbolic system provides an interpretable dimension for retrieving similar cases.

[0217] For new cases, first construct a case description vector. (Including post-hoc statistics of bone type) Risk envelope tightness, guide plate reduction coefficient (Irrigation plans, expected drilling diameter sequences, etc.), then similar entries are retrieved from the prior library using anisotropy metrics, and initial control and early warning thresholds are generated using the kernel-weighted centroid method:

[0218]

[0219] Where: Initialize control vector : ; Initial recommendations for propulsion speed, spindle speed, and angle stepping; and the baseline from step one. Consistent; Case description vector Library vectors : Derived from bone structure, risk, and strategy features; kernel function : Reuse the anisotropic kernel function form disclosed in step three, the parameter matrix is ​​formed by replace ; metric matrix : Higher weights are given to risk and bone type dimensions to improve retrieval and discrimination capabilities; sample size : ; Number of similar entries participating in the aggregation; History initialization : From the library Verified initial values ​​for similar entries.

[0220] In practice, this aggregation naturally incorporates the empirical strength of similar cases into the recommendations through kernel weights, enabling the initialization and warning thresholds to adapt to bone type and risk morphology; it is integrated with the parameters in steps one and four, ensuring that the recommendations can be directly injected with dynamic upper limits. With mode selector In this way, the cold start time is reduced and the risk exposure of the first cut is lowered.

[0221] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0222] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0223] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods 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 coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0224] 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.

[0225] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for segmenting maxillofacial images based on voxel risk field construction, characterized in that: include, Within the patient reference frame, CBCT voxels and oral scan meshes are acquired, AI segmentation is performed, and uncertainty is estimated. An anisotropic tensor is constructed, and the Eikonal equation is solved to obtain the anisotropic distance. Voxel risk field and arc length baseline upper limit curve are generated. Robust point-to-surface registration is performed using the bone surface trace point cloud and the risk field mask. Rigid body solutions are solved to complete reference binding. An optical master channel and an electromagnetic / inertial channel are established. A quality score and occlusion duty cycle are constructed. Hysteresis gating is set and geometric interpolation is used to generate fused pose and consistency quantities. Data such as spindle torque, axial force, vibration, and feed are collected. Combined with the fused pose extraction features, bone type is updated with exponential posterior. A contact consistency index is constructed and contact gating is set. Temperature rise is estimated based on energy, convection, and Arrhenius. Thermal risk is written back anisotropically. Based on the voxel risk and thermal risk, irrigation effectiveness factor, guide plate reduction coefficient and visual score, the upper limit curve of the arc length baseline is exponentially scaled using a coupling matrix to obtain a dynamic upper limit. The dynamic upper limit is used as the control upper limit vector, the fusion weight is calculated, and the operator input and path following are fused according to the fusion weight to generate control commands and set a mode selector. When a consistency alarm is triggered and the contact gating condition is met, two-point verification and trajectory re-registration update are performed. Based on risk and curvature / attitude optimization, the arc length baseline is corrected with small perturbations to generate an alternative trajectory, and the library is updated with Bregman regularization.

2. The maxillofacial image segmentation method as described in claim 1, characterized in that: The AI ​​segmentation estimates uncertainty through ensemble learning or Monte Carlo dropout estimation; the anisotropic tensor is inferred from the structural tensor and bone density gradient, and the Eikonal equation is solved using fast travel or semi-Lagrange method to generate the normalized voxel risk field, and the version identifier is stored in the patient voxel coordinates.

3. The maxillofacial image segmentation method as described in claim 2, characterized in that: The upper limit curve of the arc length baseline is parameterized with cubic splines or non-uniform rational splines and archived with the entrance configuration and guide cone geometry of the patient reference system; the upper limit of the baseline is subsequently mapped to the baseline factor of the upper limit vector of the control, and the node vector and control point index are recorded.

4. The maxillofacial image segmentation method as described in claim 3, characterized in that: Point cloud-bone surface registration is achieved by minimizing point-to-face residuals using Lie group optimization. The residual weighting is determined by the voxel risk field sampling values ​​on the bone surface and the curvature confidence. The penalty function is robust and a priori regularization is applied to constrain the rigid body solution. A metric matrix is ​​set to balance the dimensions of translation and rotation.

5. The maxillofacial image segmentation method as described in claim 4, characterized in that: The quality score is a linear combination of reprojection error, visible marker ratio, occlusion duty cycle and frame rate normalization, compressed to a closed interval of zero to one by a logic function; the occlusion duty cycle is obtained by integration according to a threshold indication within a fixed time window and participates in switching gating, and the linear combination weight is given by a calibration table.

6. The maxillofacial image segmentation method as described in claim 5, characterized in that: The fused pose is geometrically interpolated using an exponential mapping on a special Euclidean group. The interpolation coefficients are jointly given by the quality score and the occlusion duty cycle and generated by a hysteresis-based double-threshold saturation operator. The interpolation uses group logarithmic write-back of pose perturbation to output a unified pose for navigation and control.

7. The maxillofacial image segmentation method as described in claim 6, characterized in that: The geodesic distance between the optical pose and the electromagnetic / inertial pose constitutes the consistency quantity and is linked with the timeout. When the threshold is exceeded, two-point verification and trace re-registration are performed. Only the rigid body with small perturbation increment is solved and the binding is written back. At the same time, the trigger timestamp and gating state are recorded.

8. The maxillofacial image segmentation method as described in claim 7, characterized in that: A feature vector containing spindle torque, axial force, feed rate, and vibration spectrum centroid is constructed and aligned with the fused pose time. The bone category is updated recursively using an exponential family posterior, and the update weights are gated using the contact consistency index. The feature mapping includes logarithmic and ratio transformations to suppress dimensional coupling.

9. The maxillofacial image segmentation method as described in claim 8, characterized in that: Bone temperature evolution is composed of friction and compression power, equivalent heat capacity and convection term. Convection intensity is parameterized by the irrigation effective factor and the guide plate reduction coefficient. Temperature rise risk is obtained by Arrhenius integration and written back as the voxel thermal risk degree in the voxel domain with anisotropic kernel. The kernel covariance is given by the posterior convex combination of bone category.

10. The maxillofacial image segmentation method as described in claim 9, characterized in that: The dynamic upper limit is obtained by multiplying the baseline upper limit by the component-wise tightening factor of exponential scaling; the elements of the coupling matrix are non-negative, and the tightening factor includes the temperature rise risk, the voxel risk, uncertainty, the irrigation effectiveness factor and the guide plate reduction coefficient, and the uncertainty comes from the AI ​​segmentation posterior and the ensemble variance estimation.

11. The maxillofacial image segmentation method as described in claim 10, characterized in that: The fusion weight is obtained by linearly combining the temperature rise risk, the voxel risk, the contact consistency index, the quality score, and the consistency quantity, and then compressing them using a logical function. The command torque is formed by weighting the operator torque and the path-following torque according to the fusion weight, and is subject to the dynamic upper limit limit and gating.

12. The maxillofacial image segmentation method as described in claim 11, characterized in that: The over-level triggering amount is obtained by summing the pairwise geodesic residuals of the optical pose, the electromagnetic / inertial pose, and the robot kinematic pose; the back-off arc length speed is calculated by weight mapping based on the over-level triggering amount, the temperature rise risk, the voxel risk, and the safety margin formed by the anisotropic distance, and written into the execution queue.

13. The maxillofacial image segmentation method as described in claim 12, characterized in that: The sample weights for incremental registration are a weighted sum of the voxel risk, the quality score, and the consistency quantity, and compressed by a logical function; the micro-displacement and micro-angle are optimized in the current arc-length neighborhood to form the alternative trajectory, and the knowledge base parameters are incrementally updated and the index is rearranged using Bregman divergence.

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