Bone registration method for joint replacement surgery and surgical navigation system

Abstract

A bone registration method and system for joint replacement surgery, based on a VSF surface in a preoperative coordinate system generated from preoperative bone image data and a source point set SPS in an intraoperative coordinate system generated from point data collected from the patient's actual bone surface during surgery, determines the transformation relationship between the preoperative and intraoperative coordinate systems through initial and precise registration. The method includes: a first step: selecting multiple corresponding point pairs from the source point set SPS and the VSF surface, performing initial registration based on Singular Value Decomposition (SVD), and obtaining the initial transformation matrix; and a second step: performing precise registration based on the initial transformation matrix using the ICP method. Each ICP iteration employs a least-squares optimization method that minimizes the sum of squared distances between each point in the transformed source point set SPS and the corresponding projection points in the projection point set PSPS. The algorithm stops when the error is less than a set value or the number of iterations reaches a set value.

Description

Technical Field

[0001] This invention relates to a bone registration method and system for joint replacement surgery, and more particularly to a bone registration method and surgical navigation system for knee and hip replacement surgery. Background Technology

[0002] Computer-aided surgical navigation systems are widely used in various surgeries to improve accuracy and precision. Navigation surgery exists in all areas of medicine, and this technology requires an optical tracking system to complete intraoperative registration (also known as registration). Registration is a crucial process that helps find the transformation matrix between the preoperative planned coordinate system in the software and the actual coordinate system in the operating room, thereby visualizing the position and orientation of surgical instruments in a three-dimensional model near the surgical area. Summary of the Invention

[0003] To address the aforementioned problems, this invention aims to provide a bone registration method and system. The proposed algorithm allows for the registration between the coordinate system of the preoperative plan in the software and the coordinate system of the patient's actual bones.

[0004] According to one aspect of the present invention, a bone registration method for joint replacement surgery is provided. Based on a VSF surface (a three-dimensional virtual surface) in a preoperative coordinate system generated using preoperative bone image data, and a source point set SPS in an intraoperative coordinate system generated using point data collected from the patient's actual bone surface during surgery, the transformation relationship between the preoperative coordinate system and the intraoperative coordinate system is determined through initial and precise registration between the source point set SPS and the VSF surface. The method is characterized by the following steps: First step: Selecting four corresponding point pairs from the source point set SPS and the VSF surface, performing initial registration based on singular value decomposition (SVD), and obtaining an initial transformation matrix; Second step: Based on the initial transformation matrix, performing basic... For precise registration using the ICP method, the corresponding transformed projection point set PSPS on the VSF surface is determined by projecting multiple points in the transformed source point set SPS onto the VSF surface. A least-squares optimization method is then performed to minimize the sum of squared distances between each point in the transformed source point set SPS and its corresponding projection point in the projection point set PSPS. This is used as the evaluation criterion for determining whether the ICP method iteration has terminated. The four sets of corresponding point pairs are applicable to knee replacement surgery and consist of four points in the femoral source point set SPS and four corresponding points in the femoral VSF surface, or four points in the tibial source point set SPS and four corresponding points in the tibial VSF surface. The number of points is more than 30.

[0005] Alternatively, the four sets of corresponding point pairs can be three sets of corresponding point pairs applicable to hip replacement surgery, namely, three points in the source point set SPS of the acetabulum and three corresponding points in the VSF surface of the acetabulum, or three points in the source point set SPS of the femur and three corresponding points in the VSF surface of the femur.

[0006] Preferably, the plurality of points is 30 points.

[0007] Preferably, the four points in the femoral origin point set SPS refer to: the femoral head center HC, the femoral knee joint center FKC, the lateral epicondyle LE, and the medial epicondyle ME. The four points in the tibial origin point set SPS refer to: the tibial knee joint center TKC, the tibial tuberosity TT, the lateral malleolus LM, and the medial malleolus MM.

[0008] Preferably, the input is: a source point set SPS, a VSF surface, and four points PM selected from the VSF surface. n PB, corresponding to four points selected from the actual femur. n Maximum number of iterations m, error threshold Let the target output of the algorithm be: the second transformation T2.

[0009] The first step further includes a third step: obtaining a vector to represent the initial matrix T1. (Equation 1), where, It's the rotation angle. It is a translation vector.

[0010] The second step also includes a fourth step: performing rigid alignment based on ICP iterations for precise registration, expressed as: (Equation 2), where, It's the rotation angle. It is a translation vector. The point to be transformed, where, through a predetermined iteration of m times, the transformation is first based on the vector saved in the third step. The SPS points in the transformed source point set SPS are projected onto the VSF surface to obtain the corresponding PSPS points. Then, using the least squares optimization method described above, the registration error E that minimizes the sum of squared distances between the transformed SPS points and the PSPS points is obtained. The estimated vector of the optimal rigid transformation T2 is then solved using the Gauss-Newton method and the Jacobian matrix formula. Then it is compared with the preset initial error. When the error is less than the preset error threshold, Then, the second step is complete.

[0011] According to another aspect of the present invention, a computer-aided surgical navigation system is provided, comprising an optical tracking system and a computer, wherein the computer performs the steps of the above-described bone registration method to register the intraoperative coordinate system with the preoperative coordinate system.

[0012] According to another aspect of the present invention, a bone registration system for intraoperative navigation is provided, used to determine the transformation relationship between a preoperative coordinate system and an intraoperative coordinate system, comprising: a VSF surface generation unit, which uses preoperative bone image data to establish a 3D virtual model in the preoperative coordinate system and generates a VSF surface as the surface of the 3D virtual model; a source point set acquisition unit, which uses point data collected from the actual bone surface of the patient during surgery to generate a source point set SPS in the intraoperative coordinate system; and an initial registration unit, which selects multiple corresponding point pairs from the source point set SPS and the VSF surface, performs initial registration between the source point set SPS and the VSF surface based on singular value decomposition (SVD), and obtains the initial transformation relationship. The transformation matrix is ​​used to perform precise registration between the source point set SPS and the VSF surface using the ICP method based on the initial transformation matrix. This precise registration unit further includes: a multi-point acquisition unit that acquires multiple points in the transformed source point set SPS; and a projection registration unit that determines the transformed projection point set PSPS corresponding to the transformed source point set SPS from the VSF surface by projecting the multiple points onto the VSF surface. The evaluation criterion for determining whether the ICP method iteration terminates is based on a least-squares optimization method that minimizes the sum of squared distances between each point in the transformed source point set SPS and the corresponding projection point in the projection point set PSPS.

[0013] The present invention also provides a computer-readable storage medium storing a computer program for performing the above-described bone registration method.

[0014] The present invention also provides an electronic device, comprising: a processor and a memory for storing processor-executable instructions, the processor being configured to read the executable instructions from the memory and execute the instructions to implement the above-described skeleton registration method.

[0015] The present invention also provides a computer program product, comprising a computer program that is executed by a computer to implement the above-described skeletal registration method.

[0016] According to the present invention, it can be used, for example, for computer-assisted knee or hip replacement surgery. Attached Figure Description

[0017] Figure 1 A flowchart illustrating the registration process according to an embodiment of the present invention is shown schematically. Detailed Implementation

[0018] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. The exemplary embodiments described below and illustrated in the drawings are intended to teach the principles of the invention, enabling those skilled in the art to implement and use the invention in several different environments and for several different applications. Therefore, the scope of protection of the present invention is defined by the appended claims, and the exemplary embodiments are not intended, and should not be considered, a limiting description of the scope of protection of the present invention.

[0019] Through research, the inventors have proposed a novel bone registration method for performing the registration process in surgical navigation systems, such as in knee replacement surgery and hip replacement surgery.

[0020] <Preoperative coordinate system and intraoperative coordinate system>

[0021] In intraoperative navigation, surgical instruments tracked by positioning devices, such as optical tracking systems, must be displayed in real time on the preoperatively reconstructed three-dimensional anatomical structure. Therefore, it is necessary to register the patient with the image-reconstructed three-dimensional anatomical structure to ensure mutual matching. By calculating and determining the transformation relationship between the positioning system coordinate system (intraoperative coordinate system) and the preoperative three-dimensional medical image coordinate system (preoperative coordinate system), the patient's actual intraoperative position and the preoperative three-dimensional anatomical structure are precisely registered, ensuring that the three-dimensional model seen by the surgeon on the display device accurately reflects the distance and positional relationship of the surgical instruments relative to the target bone, such as the lesion.

[0022] The methods and equipment for establishing the coordinate system are not the focus of this invention and will not be elaborated here; they can be achieved using existing means.

[0023] The algorithms used to achieve registration between two point sets are described in detail below through examples.

[0024] <First Example: Bone Registration for Knee Replacement>

[0025] Specifically, the registration method described in this embodiment further includes the following steps:

[0026] <Step S01: Construction of the 3D Virtual Surface and Acquisition of the Source Point Set>

[0027] On the one hand, three-dimensional medical images of the patient's bones are input before the operation to construct a three-dimensional virtual surface.

[0028] Using preoperative image data such as CT or MRI, X-ray, etc. as anatomical structure input data, the bone model is reconstructed in three dimensions to obtain a three-dimensional virtual surface (VSF).

[0029] On the other hand, the point set information of the patient's bone surface is output during the operation.

[0030] During the operation, data information of anatomical points on the bone surface of interest can be obtained through 3D scanning equipment such as probes, and the source point set (SPS) can be obtained.

[0031] Therefore, multiple points can be extracted from the femoral surface (preferably more than 30 points, more preferably 30 points) and multiple points can be extracted from the tibial surface during the operation (preferably more than 30 points, more preferably 30 points).

[0032] Preferably, the SPS should be sparsely collected to cover as much of the skeletal area as possible.

[0033] In this embodiment, bone registration is advantageously achieved by executing the following algorithm, namely, the registration between the source point set SPS obtained from the patient's actual bone surface and the three-dimensional virtual surface VSF of the bone.

[0034] <Step S02: Registration module or step>

[0035] Skeleton registration is divided into two steps: initial registration and precise registration. Initial registration is used to make the first approximation between two small point sets, while precise registration is used to find the optimal alignment between the source point set SPS and the surface VSF.

[0036] According to this embodiment, the first step is to find the initial transformation matrix T1 using SVD. More specifically, the surgeon finds four sets of corresponding points on the bone and the virtual 3D model, and performs coarse registration using the SVD method on these four sets of corresponding points to obtain the initial transformation matrix. The second step is to perform registration using the ICP (Iterative Closest Point) method with multiple sets of corresponding points based on the initial transformation matrix obtained by SVD. By iterating over the initial matrix, errors are reduced, and registration is completed.

[0037] <Step S021: Initial Registration>

[0038] To perform initial registration, several corresponding point pairs need to be selected from the source point set SPS and the surface VSF. Each corresponding point pair is selected from the same position on the corresponding bone surface of the two.

[0039] According to this embodiment, four anatomical points are preferably selected.

[0040] More specifically, the surgeon must locate the four anatomical points previously selected in the surface VSF on the patient's bones. This step is crucial because there is always an error in selecting points in the bones, and if the error is large, the algorithm may not be able to converge to the optimal solution in the precise registration in the second step.

[0041] In this embodiment, the initial registration is based on four points in the femoral source point set SPS and their corresponding four points in the curved surface VSF, as well as four points in the tibial source point set SPS and their corresponding four points in the curved surface VSF. The selection of these four point pairs is sufficient to support rigid transformations in three-dimensional space.

[0042] According to this embodiment, the anatomical points collected on the femur are as follows: femoral head center (HC, Hip Center), femoral knee joint center (FKC, Femur Knee Center), lateral epicondyle (LE, Lateral Epicondyle), and medial epicondyle (ME, Medial Epicondyle); the anatomical points collected on the tibia are as follows: tibia knee joint center (TKC, Tibia Knee Center), tibial tuberosity (TT, Tibia Tubercle), lateral malleolus (LM, Lateral Malleolus), and medial malleolus (MM, Medial Malleolus).

[0043] These anatomical points are easily located by surgeons using tools such as probes, which helps to ensure precision and operability.

[0044] In the estimation of the first transformation (matrix T1) used for initial registration, alignment is performed using a method based on singular value decomposition (SVD). The resulting first transformation matrix T1 will be used as an initial approximation for the second step of precise registration.

[0045] The first transformation matrix T1 can be represented as a vector:

[0046] (Equation 1)

[0047] in, It's the rotation angle. It is a translation vector.

[0048] <Step S022: Precise Registration>

[0049] To further improve the overall registration accuracy and reduce errors, a second step of precise registration, namely precise registration, is needed based on the results of the initial registration.

[0050] Registration will be performed between multiple points (i.e., data corresponding to more than 30 points) in the SPS point set extracted by the surgeon from the patient's bones (femur or tibia) and the VSF surface of the 3D virtual model. In the following embodiment, 30 points will be used as an example for illustration.

[0051] That is, the problem of registration between several points and a grid surface needs to be solved.

[0052] Therefore, the process includes the following two sub-steps:

[0053] Step S0221: Obtain multiple points (e.g., 30 points) from the SPS point set.

[0054] Step S0222: Based on the initial transformation matrix T1 found by SVD, the matching position of the multi-point is further searched using the ICP method (with the least squares optimization method described later as the evaluation criterion).

[0055] Using the initial transformation matrix T1 obtained by SVD, the ICP method is used to iteratively register the mesh surfaces of 30 points and the VSF surface.

[0056] Thus, the ICP algorithm, by finding a rigid transformation parameter R and translation parameter T from the preoperative coordinate system to the intraoperative coordinate system, enables point sets from different coordinate systems to be merged into the same coordinate system. The algorithm repeatedly selects corresponding point pairs and calculates the optimal rigid transformation T2 until the registration convergence accuracy requirement is met, ensuring optimal matching between SPS and VSF data.

[0057] In the ICP algorithm, the SPS and VSF are aligned using a least-squares optimization method. This alignment process is a rigid alignment, which can be expressed as:

[0058] (Equation 2)

[0059] in,

[0060] (Equation 3)

[0061] in, It is a rotation matrix relative to each coordinate axis. It's the rotation angle. It is a translation vector. The point to be transformed.

[0062] The least squares optimization method used, as described later, is a method for calculating the minimum sum of squared distances between corresponding point pairs between SPS and VSF.

[0063] Specifically, the transformed SPS points are passed through (See Equation 1) Project onto the VSF surface and define two sets of points in this way: the transformed SPS point set and the PSPS point set (projected source pointset).

[0064] Once the SPS point set is projected onto the VSF surface and the transformed PSPS point set corresponding to the transformed SPS point set is determined from the VSF surface, the least squares optimization method according to the present invention can be implemented, that is, minimizing the sum of squared distances between each point in the transformed SPS point set (also referred to as SPS points above) and the corresponding projected points in the PSPS point set (also referred to as PSPS points above).

[0065] (Equation 4)

[0066] Where i represents the i-th point in the point set, and i is a natural number whose maximum value is the number of projected points (SPS). i Let (PSPS) represent the i-th point in the SPS point set. i This represents the i-th point in the PSPS point set.

[0067] Representing the variables used in the evaluation as vectors, we get:

[0068] (Equation 5)

[0069] Therefore, let and Therefore, we can obtain:

[0070] (Equation 6)

[0071] Because the function contains a rotation matrix The function to be minimized It is a nonlinear function. To solve this problem, in this embodiment, the Gauss-Newton method is used to redefine the problem as follows:

[0072] (Equation 7)

[0073] in, yes The Jacobian matrix is ​​defined as follows:

[0074] (Equation 8)

[0075] (Equation 9)

[0076] (Equation 10)

[0077] (Equation 11)

[0078] (Equation 12)

[0079] The final solution is shown below:

[0080] (Equation 13).

[0081] This solution combines the principles of ICP (Iterative Closest Point) method, employing least squares optimization in each ICP iteration. The algorithm stops when the error falls below a set value or the number of iterations reaches a set value.

[0082] Figure 1 The diagram shows a registration flowchart according to this embodiment.

[0083] The inputs are: Source Point Set (SPS), 3D Virtual Surface (VSF), and four points in the model. Point data corresponding to four points on the skeleton Maximum number of iterations m, error threshold Accordingly, the output is the second transformation T2 and its corresponding vector to be solved: .

[0084] When the process begins (step S03), the initial matrix T1 used for the first step of initial registration is estimated and saved, that is, the initial vector is obtained by SVD method. 0 (S04). Then, ICP iterations (S05-S09) are performed for the second step of precise registration. Through a predetermined number of iterations m, the process is first based on the saved vectors. Projecting the SPS points onto the VSF surface yields the corresponding PSPS points (S06). Then, using the least squares optimization method described above, the registration error E (S07) that minimizes the sum of squared distances between the transformed SPS points and the PSPS points is obtained. The estimated vector for the optimal rigid transformation T2 is then solved using the Gauss-Newton method and the Jacobian matrix formula. (S08). Then, in step S09, the error is compared with a preset initial error. If the error is less than a preset error threshold, the result is considered valid. Then, the algorithm ends (S10).

[0085] <Second Embodiment: Bone Registration for Hip Replacement>

[0086] The steps in this embodiment are basically the same as those in the first embodiment, and the descriptions are omitted here. The following mainly focuses on the different individual details.

[0087] <Step S01': Construction of the 3D Virtual Surface and Acquisition of the Source Point Set>

[0088] During the procedure, multiple points can be extracted from the surface of the acetabulum (preferably more than 30 points, more preferably 30 points) and multiple points can be extracted from the surface of the femur (preferably more than 30 points, more preferably 30 points).

[0089] <Step S021': Registration module or initial registration in step S02'>

[0090] According to this embodiment, during initial registration, three points of the femur and their corresponding three points in the three-dimensional model, as well as three points of the acetabulum and their corresponding three points in the three-dimensional model, will be taken.

[0091] Preferably, the three anatomical points collected on the femur are as follows: one point on the anterior side of the femoral neck region; one point on the anterior side of the femoral region distal to the greater trochanter; and one point on the lateral side of the greater trochanter region.

[0092] Preferably, the three anatomical points collected on the acetabulum are as follows: a point in the posterior region of the acetabulum; a point in the anterior region of the acetabulum; and a point at the upper edge of the acetabulum region.

[0093] It is important to match these registration points as closely as possible to their corresponding points in the virtual model, as these initial points are used for the first alignment between the patient's skeleton and the patient's virtual model.

[0094] Initial registration includes finding the real skeleton point set. Point set of virtual model The correspondence between them is equivalent to finding a transformation T(R,t) that minimizes the sum of squared errors, where t is a translation vector, R is a rotation matrix, and i and j are natural numbers:

[0095] (Equation 14).

[0096] By considering the two point sets in the origin, we can derive:

[0097] (Equation 15)

[0098] (Equation 16)

[0099] in, and It is the average value of each set (each point set), and minimizing E(R,t) is equivalent to minimizing:

[0100] (Equation 17)

[0101] This new problem is called the orthogonal Procrustes problem, which can be solved by singular value decomposition (SVD).

[0102] Calculate the covariance matrix of the data W and obtain the SVD decomposition, yielding the following results:

[0103] (Equation 18)

[0104] SVD(W)=UDV T (Equation 19)

[0105] Where U and V are 3x3 rotation matrices, D is a diagonal matrix, and W represents the cross covariance matrix.

[0106] If rank(W) = 3, the parameter minimization E(R,t) is unique, given by the following equation:

[0107] R=UV T (Equation 20)

[0108] t= (Equation 21)

[0109] This solution represents the initial transformation (T1) and can be represented as a vector:

[0110] (Equation 22)

[0111] in, It is the rotation angle from R. It is the translation vector component from t.

[0112] This transformation matrix (T1) will be used as an initial approximation for the second registration step, i.e., precise registration.

[0113] <Step S022': Precise Registration>

[0114] Registration will be performed between multiple points (i.e., data corresponding to more than 30 points) in the SPS point set extracted by the surgeon from the patient's femur or hip bone and the VSF surface of the 3D virtual model. In the following embodiment, 30 points will be used as an example for illustration.

[0115] That is, the problem of registration between several points and a grid surface needs to be solved.

[0116] Similarly, this involves two sub-steps as follows:

[0117] Step S0221: Obtain multiple points (e.g., 30 points) from the SPS point set.

[0118] Step S0222: Based on the initial transformation matrix T1 found by SVD, the matching position of the multi-point is further searched using the ICP method (with the least squares optimization method described later as the evaluation criterion).

[0119] That is, the least squares optimization method is used to reduce the squared distance between SPS and VSF, and the transformed SPS points are then processed through... (See Equation 1) Project onto the VSF surface and define two sets of points in this way: the transformed SPS point set and the PSPS point set (projected source point set on the VSF surface).

[0120] Thus, the final solution is shown in Equation 13 above.

[0121] This solution combines the principles of ICP (Iterative Closest Point) method, using the proposed least-squares optimization solution in each ICP iteration. The algorithm terminates when the desired error is reached or the preset number of iterations is reached.

[0122] Accordingly, in execution Figure 1 In the flowchart shown, the points used as input replace the four points in the first embodiment, and here are three points (PM) in the model. n ), and point data corresponding to three points on the skeleton (PB) n ).

[0123] <Technical Effects>

[0124] According to this invention, SVD and ICP are used together to obtain an initial matrix in the initial registration of orthopedic surgery using several feature points and the SVD method, or using the SVD method for the orthogonal Procrustes problem. Then, based on the initial matrix, the ICP method (iterating over the rotation and translation parameters in the matrix) is used, and the least squares optimization method is used as the evaluation criterion to complete the accurate registration.

[0125] In precise registration, traditional ICP generally uses the average distance between corresponding points as the evaluation criterion. In contrast, this invention uses the least squares optimization method of the distance from several points (preferably more than 30) to the CT bone surface grid as the evaluation criterion. This effectively removes the interference of individual special points with large errors, solves the registration problem between several points (preferably more than 30) and a grid surface, and thus improves the accuracy of the judgment.

[0126] For example, the original 30 points of the SPS are transformed to obtain the corresponding PSPS points. That is, the SPS is projected onto the VSF to obtain the points. Thus, each of the 30 points of the SPS is matched to the virtual mesh plane to obtain the PSPS. The distance between the corresponding points of the projected PSPS and the original SPS is optimized by least squares and used to determine whether the iteration terminates.

[0127] According to one embodiment of the present invention, a computer-aided surgical navigation system is also provided, comprising an optical tracking system and a computer, wherein the computer executes the steps of the above-described bone registration method to perform intraoperative coordinate system and preoperative coordinate system registration.

[0128] According to one embodiment of the present invention, a computer-readable storage medium is also provided, storing a computer program for performing any of the methods described above.

[0129] The present invention also provides an electronic device, comprising: a processor and a memory for storing processor-executable instructions, the processor being configured to read executable instructions from the memory and execute the instructions to implement any of the methods described above.

[0130] The present invention also provides a computer program product, including a computer program that, when executed by a computer, implements the steps of the above-described method.

[0131] Although the invention has been described with reference to various specific embodiments, it should be understood that modifications can be made within the spirit and scope of the described inventive concept. Therefore, it is intended that the invention be limited to the described embodiments but will have the full scope defined by the language of the appended claims.

Claims

1. A bone registration method for joint replacement surgery, based on a VSF surface as a three-dimensional virtual surface generated under a preoperative coordinate system using preoperative bone image data, and a source point set SPS under an intraoperative coordinate system generated using point data collected from the actual bone surface of a patient in real time by a scanner during surgery, a transformation relationship between the preoperative coordinate system and the intraoperative coordinate system is determined through initial registration and accurate registration between the source point set SPS and the VSF surface, characterized in that, Includes the following steps: First step: Select multiple pairs of corresponding points from the source point set SPS and the VSF surface, perform initial registration based on singular value decomposition (SVD), and obtain the initial transformation matrix; and The second step: Based on the initial transformation matrix, perform precise registration using the ICP method. This involves projecting multiple points from the transformed source point set SPS onto the VSF surface to determine the corresponding transformed projection point set PSPS on the VSF surface. A least-squares optimization method is then used to minimize the sum of squared distances between each point in the transformed source point set SPS and its corresponding projection point in the projection point set PSPS. This optimization serves as the evaluation criterion for determining whether the ICP method iteration has terminated. In the first step, the multiple sets of corresponding point pairs are four sets of corresponding point pairs, namely, four points in the femoral source point set SPS and four corresponding points in the femoral VSF surface, or four points in the tibia source point set SPS and four corresponding points in the tibia VSF surface. The four points in the femoral origin point set SPS refer to: the femoral head center HC, the femoral knee joint center FKC, the lateral epicondyle LE, and the medial epicondyle ME; the four points in the tibial origin point set SPS refer to: the tibial knee joint center TKC, the tibial tuberosity TT, the lateral malleolus LM, and the medial malleolus MM. Let the input be: source point set SPS, VSF surface, and four points PM selected from the VSF surface. n PB, corresponding to four points selected from the actual femur. n Maximum number of iterations m, error threshold Let the target output of the algorithm be: the second transformation T2. The first step further includes a third step: obtaining a vector to represent the initial matrix T1. (Equation 1) in, It is the rotation angle. It is a translation vector. The second step also includes a fourth step: performing rigid alignment based on ICP iterations for precise registration, expressed as: (Equation 2) (Equation 3) in, It is a rotation matrix relative to each coordinate axis. It is the rotation angle. It is a translation vector. The point to be transformed. Specifically, through a predetermined iteration of m times, the vector saved in the third step is first... The SPS points in the transformed source point set SPS are projected onto the VSF surface to obtain the corresponding PSPS points. Then, using the least squares optimization method described above, the registration error E that minimizes the sum of squared distances between the transformed SPS points and the PSPS points is obtained. The estimated vector of the optimal rigid transformation T2 is then solved using the Gauss-Newton method and the Jacobian matrix formula. : (Equation 13) in, yes Jacobian matrix form Then it is compared with the preset initial error. When the error is less than the preset error threshold... Then, the second step ends.

2. The bone registration method according to claim 1, characterized in that, In the second step, the plurality of points is more than 30 points.

3. A bone registration method for joint replacement surgery, based on a VSF surface (a three-dimensional virtual surface) in a preoperative coordinate system generated using preoperative bone image data, and a source point set SPS in an intraoperative coordinate system generated using point data collected in real time from the patient's actual bone surface by a scanner during surgery, determines the transformation relationship between the preoperative coordinate system and the intraoperative coordinate system through initial and precise registration between the source point set SPS and the VSF surface, characterized in that... Includes the following steps: First step: Select multiple pairs of corresponding points from the source point set SPS and the VSF surface, perform initial registration based on singular value decomposition (SVD), and obtain the initial transformation matrix; and The second step: Based on the initial transformation matrix, perform precise registration using the ICP method. This involves projecting multiple points from the transformed source point set SPS onto the VSF surface to determine the corresponding transformed projection point set PSPS on the VSF surface. A least-squares optimization method is then used to minimize the sum of squared distances between each point in the transformed source point set SPS and its corresponding projection point in the projection point set PSPS. This optimization serves as the evaluation criterion for determining whether the ICP method iteration has terminated. In the first step, the multiple sets of corresponding point pairs are three sets of corresponding point pairs, namely, three points in the source point set SPS of the acetabulum and three corresponding points in the VSF surface of the acetabulum, or three points in the source point set SPS of the femur and three corresponding points in the VSF surface of the femur. The three points in the SPS (Source Point Set) of the acetabulum refer to: one point in the posterior region of the acetabulum; one point in the anterior region of the acetabulum; and one point at the upper edge of the acetabular region. The three points in the SPS of the femur refer to: one point on the anterior side of the femoral neck region; one point on the anterior side of the femoral region distal to the greater trochanter; and one point on the lateral side of the greater trochanter region. Let the input be: source point set SPS, VSF surface, and 3 points PM selected from the VSF surface. n PB, corresponding to the point data of 3 points selected from the actual femur. n Maximum number of iterations m, error threshold Let the target output of the algorithm be: the second transformation T2. The first step further includes a fifth step: obtaining a vector to represent the initial matrix T1 based on the initial transformation T(R,t). (Equation 22) Where t is a translation vector and R is a rotation matrix. It is the rotation angle. It is a translation vector, and R = UV T , (formula 20), t= (Equation 21) Where U and V are 3x3 rotation matrices. and It is the average value of each point set. The second step further includes a sixth step: performing rigid alignment based on ICP iterations for precise registration, expressed as: (Equation 2) (Equation 3) in, It is a rotation matrix relative to each coordinate axis. It is the rotation angle. It is a translation vector. The point to be transformed. Specifically, through a predetermined iteration of m times, the vector saved in the fifth step is first... The SPS points in the transformed source point set SPS are projected onto the VSF surface to obtain the corresponding PSPS points. Then, using the least squares optimization method described above, the registration error E that minimizes the sum of squared distances between the transformed SPS points and the PSPS points is obtained. The estimated vector of the optimal rigid transformation T2 is then solved using the Gauss-Newton method and the Jacobian matrix formula. : (Equation 13) in, yes Jacobian matrix form Then it is compared with the preset initial error. When the error is less than the preset error threshold... Then, the second step ends.

4. The bone registration method according to claim 1, characterized in that, In the second step, the plurality of points is more than 30 points.

5. A computer-aided surgical navigation system comprising an optical tracking system and a computer, wherein the computer executes the steps of the bone registration method according to any one of claims 1 to 4, and performs registration of the intraoperative coordinate system with the preoperative coordinate system.

6. A skeleton registration system for intraoperative navigation, used to determine the transformation relationship between a preoperative coordinate system and an intraoperative coordinate system using the skeleton registration method according to any one of claims 1 to 4, comprising: The VSF surface generation unit uses preoperative bone image data to establish a 3D virtual model in the preoperative coordinate system and generates the VSF surface of the surface of the 3D virtual model. The source point set acquisition unit uses point data collected in real time from the patient's actual bone surface by a scanner during the operation to generate the source point set SPS in the intraoperative coordinate system. The initial registration unit selects multiple pairs of corresponding points from the source point set SPS and the VSF surface, performs initial registration between the source point set SPS and the VSF surface based on singular value decomposition (SVD), and obtains the initial transformation matrix. The precise registration unit performs precise registration between the source point set SPS and the VSF surface using the ICP method based on the initial transformation matrix. This precise registration unit also includes: The multi-point acquisition unit acquires multiple points from the transformed source point set SPS. The projection registration unit determines the transformed projection point set PSPS corresponding to the transformed source point set SPS from the VSF surface by projecting the plurality of points onto the VSF surface. The evaluation criterion for determining whether the ICP method iteration has terminated is based on the least squares optimization method that minimizes the sum of squared distances between each point in the transformed source point set SPS and the corresponding projection point in the projection point set PSPS.

7. A computer-readable storage medium storing a computer program for performing the steps of the bone registration method according to any one of claims 1 to 4.

8. An electronic device, comprising: A processor and a memory for storing processor-executable instructions, the processor being configured to read the executable instructions from the memory and execute the instructions to implement the steps of the bone registration method according to any one of claims 1 to 4.

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