A method and device for describing the human body structure relationship based on spatial transformation

Abstract

A method and device for describing the human body structure relationship based on spatial transformation, belonging to the field of medical information processing. It is set that each rigid component of the human body is represented by a spatial triangular surface formed by three adjacent bone feature points. Typical rigid components include the upper triangular plane of the shoulder, the left and right scapula planes, the thoracic vertebrae, the lumbar vertebrae, the pelvic plane, and the left and right lower limb planes. An independent local coordinate system of its own is established for each rigid component. The local coordinate system of its own of the rigid component pelvic plane is established as the base coordinate system, and the coordinate system where the upper camera is located is the global world coordinate system. The spatial rotation transformation matrix of each rigid component relative to the pelvic base coordinate system is obtained through the coordinate transformation under the local coordinate system of its own of each rigid component and the global world coordinate system. The singular value decomposition method is used to solve the relative spatial rotation transformation matrix, and a mathematical expression for describing the spatial position relationship between the bone parts of the human body with abnormal postures is constructed. The present invention is used to accurately detect the abnormal body postures and structures of the human body.

Description

Technical Field:

[0001] The present invention belongs to the field of medical information processing, and particularly relates to a method for establishing a mathematical model of the human body structure. Background Art:

[0002] The normal movement ability of the human body requires a balanced mechanical structure, and the formation of the bone structure can reflect certain mechanical laws. Overall, the abnormal structure of a certain part of the human body may cause abnormal stress on other related parts, gradually forming a vicious cycle, leading to postural structure imbalance and damage to the entire myofascial chain. The imbalance of structural mechanics can externally manifest as a series of diseases such as muscle pain and joint movement disorders. Research has found that there is a significant relationship between abnormal postures such as winged scapula, scoliosis, pelvic tilt, knee hyperextension, and genu varum and body pain.

[0003] In the field of computer vision, human pose estimation is an important research direction. Given a static image or a video sequence, it studies the description of human poses and predicts human behaviors, and is widely used in fields such as motion analysis, human-computer interaction, and film and television production. Currently, human pose estimation methods are mainly divided into model-based and model-free methods. The model-based method divides the human body into several components, and the edges connecting the graphical nodes represent the spatial position relationships between the components. The model-free method refers to learning a mapping relationship function from the input image feature space to the human pose space from a large number of training samples. However, this method requires a large-scale dataset to learn a better mapping relationship function and is not suitable for small-sample human pose estimation tasks. Therefore, the model-based method is the mainstream method for human pose estimation. This method regards the human body as an object composed of multiple body components connected in a certain way, and can improve the detection result by constructing a structural model that describes the constraint relationships between human body components.

[0004] Existing human pose estimation generally tracks the positions of 14 joint points, namely the head, neck, left shoulder, right shoulder, left elbow, right elbow, left hand, right hand, left hip, right hip, left knee, right knee, left foot, and right foot. The human pose is described by measuring the positions of these 14 joints. Microsoft's Kinect sensor tracks 20 joint points of the human body, adding the recognition of joint points of the left wrist, right wrist, spine, hip center, left ankle, and right ankle, making the skeleton model more refined.

[0005] Most existing human body structure models regard a certain body part as a whole component. Although they can detect and track human motion behaviors, since only key nodes of the human body are collected, they cannot accurately describe the detailed information of pathological structures. Generally, they can only evaluate gross movements of the human body and are not suitable for describing abnormal detailed postures. In particular, the existing methods only describe motion characteristics and cannot give the accurate relative analytical relationship between various parts of the body, which does not meet the clinical pathological diagnosis requirements for abnormal postures such as scoliosis. To address the above problems, the present invention proposes a mathematical model for describing the human body structure to accurately describe the spatial position relationship between the bone parts of the human body with abnormal postures. Summary of the Invention:

[0006] In view of the deficiencies in the prior art, the present invention proposes a device and method for describing the human body structure based on spatial transformation for accurately detecting the abnormal body posture structure of the human body. The present invention regards the relatively non-moving parts of the body as rigid body components, and each rigid body component is represented by a spatial triangular surface formed by three adjacent fixed points. Taking the pelvis as the base coordinate system, the spatial pose relationship of the spatial triangular surface of each rigid body component relative to the pelvis is calculated for describing the human body posture structure.

[0007] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the method and device include two parts: a data acquisition device and a description method. The data acquisition device includes a three-dimensional scanner 21, an acquisition and processing computer 22, and cooperative marking points 23.

[0008] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the three-dimensional scanner 21 in the data acquisition device is composed of an upper camera 24, a lower camera 25, a camera bracket 28, and a tripod 26. The upper camera 24 and the lower camera 25 are both installed on the camera bracket 28, and the camera bracket 28 is installed on the tripod 26. The common field of view of the upper camera 24 and the lower camera 25 covers all the cooperative marking points 23 pasted on the measured human body 20.

[0009] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the acquisition and processing computer 22 in the data acquisition device is used to control the upper camera 24 and the lower camera 25 to acquire the cooperative marking points 23 pasted on the measured human body 20 and calculate the three-dimensional spatial coordinates of all the cooperative marking points 23.

[0010] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the cooperative marking points 23 in the data acquisition device are a group of marking points with a circular black outer ring and a white center, and the material can be paper or plastic-based. The number and pasting positions of the cooperative marking points 23 are determined according to the human body parts to be analyzed.

[0011] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the connection relationship of each part of the data acquisition device is as follows: The cooperative marking points 23 are pasted on the designated parts of the measured human body 20 and face the three-dimensional scanner 21. The upper camera 24 and the lower camera 25 on the components of the three-dimensional scanner are both installed on the camera bracket 28, and the camera bracket 28 is installed on the tripod 26, and the lenses of the upper camera 24 and the lower camera 25 face the measured human body 20. The upper camera 24 and the lower camera 25 are connected to the acquisition and processing computer 22 through the data line 27, and are used to transmit the images collected by the two cameras into the acquisition and processing computer 22 for coordinate calculation.

[0012] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the data acquisition steps are as follows:

[0013] 1. The measured human body 20 stands in front of the three-dimensional scanner 21 and takes off the clothes on the detected part.

[0014] 2. The doctor pastes the cooperative marking points 23 on the key nodes of the bones of the measured human body 20. The number and positions of the cooperative marking points 23 can vary according to different detection purposes. The typical configuration is 19 bone key points, including the 7th cervical vertebra 1, left armpit 2, right armpit 3, left upper scapular angle 4, left lower scapular angle 5, right upper scapular angle 6, right lower scapular angle 7, 6th thoracic vertebra 8, 12th thoracic vertebra 9, 3rd lumbar vertebra 10, gluteal cleft endpoint 11, left lumbar fossa 12, right lumbar fossa 13, left iliac crest 14, right iliac crest 15, left popliteal fossa 16, right popliteal fossa 17, left ankle 18, and right ankle 19.

[0015] 3. The three-dimensional scanner 21 is started to perform three-dimensional scanning and imaging on the measured human body 20, and the image data enters the acquisition and processing computer 22 through the data line 27. The three-dimensional space coordinate data of the cooperative marking points 23 are calculated according to the binocular stereo vision calculation model.

[0016] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the method for describing the human body structure relationship is to set that the spatial triangular surfaces formed by adjacent three bone feature points represent the respective rigid components of the human body. The typical rigid components include the upper triangular plane A of the shoulder, the left and right scapular planes B, the thoracic vertebra C, the lumbar vertebra D, the pelvic plane E, and the left and right lower limb planes F, and an independent local coordinate system of its own is established for each rigid component.

[0017] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the calculation steps of the relative spatial positions of the respective rigid components in the method for describing the human body structure relationship are as follows:

[0018] 1. Establish the local coordinate system of its own of the rigid component pelvic plane E as the base coordinate system ∑ A, let the end point 29 of the natal cleft be the coordinate origin P1 of the coordinate system, the left lumbar fossa 30 be the left end point P2 of the pelvic rigid component, the right lumbar fossa 31 be the right end point P3 of the pelvic rigid component, the midpoint 32 of the line connecting P2 and P3 be P4, the line connecting P1 and P4 be the X-axis, and rotate 90 degrees counterclockwise in the plane of P1P2P3 around the X-axis to get the Y-axis, and determine the Z-axis direction according to the right-hand rule. Establish the coordinate system ∑ where the upper camera 24 is located. O , with the optical center of the upper camera 24 as the origin of the camera coordinate system, the optical axis direction as the Z-axis, vertically upward as the X-axis, and determine the Y-axis direction according to the right-hand rule. This coordinate system is called the global world coordinate system.

[0019] 2. Establish the local coordinate system ∑ of each other rigid component of the human body i relative to the global world coordinate system ∑ O there is a relative spatial rotation transformation matrix expressed by the formula as:

[0020]

[0021] where, θ represents the rotation angle of each rigid component around the X-axis of the global world coordinate system ∑ O , represents the rotation angle around the Y-axis of the global world coordinate system ∑ O , ω represents the rotation angle around the Z-axis of the global world coordinate system ∑ O .

[0022] If O P iO is the position offset vector of the local coordinate system of each rigid component relative to the global world coordinate system ∑ O , then the rotation and translation combined homogeneous transformation matrix is expressed as:

[0023]

[0024] 3. Calculate the spatial position transformation matrix A of each rigid component relative to the pelvic base coordinate system ∑ as:

[0025]

[0026] where, is the homogeneous transformation matrix of the pelvic base coordinate system ∑ A relative to the global world coordinate system ∑ O , is the rotation transformation matrix of ∑ A relative to ∑ O , represents the transpose matrix, O P AOis ∑ A The translation vector relative to ∑ O .

[0027] Construct the expression of each rigid part of the human body relative to the pelvic base coordinate system ∑ A as:

[0028]

[0029] A method and device for describing the human body structure relationship based on space transformation, characterized in that the transformation matrix in the above step 3 is calculated by the singular value decomposition method (SVD)

[0030] Denote the target point set in the global world coordinate system ∑ O as A = {a1, a2,..., a n}, and the set of points to be matched in the local coordinate system of a certain rigid part is B = {b1, b2,..., b n}, where a n and b n are respectively the three-dimensional coordinates of a point in the two point sets.

[0031] The target point set A can be obtained by transforming the set of points to be matched B through the rotation matrix R and the translation vector t, that is:

[0032] A = RB + t,

[0033] Find the least squares solutions of the rotation matrix R and the translation vector t by the singular value decomposition (SVD) method. Let the objective function be:

[0034]

[0035] where k represents the number of points in the point set, and the centroids of the target point set A and the set of points to be matched B are expressed as:

[0036]

[0037]

[0038] Let: where a i represents the three-dimensional spatial coordinate of a point in the target point set A, and b j represents the three-dimensional spatial coordinate of a point in the set of points to be matched B, and respectively represent the point coordinates in the target point set A and the set of points to be matched B minus their respective centroids, eliminating the position translation relationship between the target point set A and the set of points to be matched B. Then the objective function is:

[0039]

[0040] To minimize the objective function Y is equivalent to maximizing . Let:

[0041]

[0042]

[0043] where tr represents the trace of the matrix RH, that is, the sum of the diagonal elements of the matrix.

[0044] Use SVD to decompose the H matrix:

[0045] H = UΛV T

[0046] where U and V are orthogonal matrices, and Λ is a diagonal matrix with non - negative diagonal elements.

[0047] When R = VU T then RH = VU T UΛV T = VΛV T is a symmetric positive - definite matrix. For any orthogonal matrix B, there is:

[0048] tr(RH) ≥ tr(BRH)

[0049] Therefore, when R = VU T it satisfies the maximum of tr(RH), and the translation vector is expressed as:

[0050]

[0051] The homogeneous transformation matrix representing the combination of rotation and translation is expressed as:

[0052]

[0053] This matrix expression is the relative relationship expression of a rigid part of the body relative to the pelvic rigid part.

[0054] The detection results of the present invention are shown in Table 1, which shows the attitude angles of the pelvis relative to the X - axis, Y - axis, and Z - axis of the world coordinate system and the attitude angles of each part of the human body relative to the pelvic coordinate system. To verify the feasibility and effectiveness of the proposed method, relevant experiments were carried out using a human bone model with a height of 85 cm. The pelvis of the bone model was fixed, and the lumbar spine was rotated around the X - axis of the pelvic coordinate system at a certain angle to different states. Table 2 shows the measurement results of the method of the present invention and the actual rotation angles. Similar methods were used to verify the other parts. The mean square error (MSE) between the measured values and the actual rotation angles is 0.085, which can effectively detect the relative position changes of the body.

[0055] Table 1 Attitude Angles of Each Part Detected by the Present Invention

[0056]

[0057] Table 2 Experimental Verification Results of the Relative Position of the Lumbar Spine to the Pelvis

[0058]

[0059] Advantages of the present invention: Different from the current research that takes the large joint parts of the human body as a whole, the present invention finely decomposes specific parts and expresses each small joint of the target part as a key node. The present invention constructs a local coordinate system through adjacent key nodes and obtains the rotation and translation of each moving part of the human body relative to the pelvis base coordinate system through coordinate transformation. This index is the index of the relative position change of the body that clinicians are extremely concerned about, rather than the rough indexes such as joint angles and trajectories given by the current research. The present invention makes a refined and digital description of local deformation and provides a relatively effective method and tool for digital diagnosis and treatment in orthopedic clinics. Description of the Drawings:

[0060] Figure 1 For the data acquisition device, in the figure:

[0061] 20 is the human body to be measured

[0062] 21 is the 3D scanner

[0063] 22 is the acquisition and processing computer

[0064] 23 is the cooperative marking point

[0065] 24 is the upper camera

[0066] 25 is the lower camera

[0067] 26 is the tripod

[0068] 27 is the data cable

[0069] 28 is the camera bracket

[0070] Figure 2 For the rigid component structure model of the human body, in the figure:

[0071] 1 is the seventh cervical vertebra

[0072] 2 is the left armpit

[0073] 3 is the right armpit

[0074] 4 is the upper left scapular angle

[0075] 5 is the lower left scapular angle

[0076] 6 is the upper right scapular angle

[0077] 7 is the right inferior scapular angle

[0078] 8 is the 6th thoracic vertebra

[0079] 9 is the 12th thoracic vertebra

[0080] 10 is the 3rd lumbar vertebra

[0081] 11 is the end point of the natal cleft

[0082] 12 is the left lumbar fossa

[0083] 13 is the right lumbar fossa

[0084] 14 is the left iliac crest

[0085] 15 is the right iliac crest

[0086] 16 is the left popliteal fossa

[0087] 17 is the right popliteal fossa

[0088] 18 is the left ankle

[0089] 19 is the right ankle

[0090] A is the upper triangular plane of the shoulder

[0091] B is the plane of the left and right scapulas

[0092] C is the thoracic vertebra

[0093] D is the lumbar vertebra

[0094] E is the pelvic plane

[0095] F is the plane of the left and right lower limbs

[0096] Figure 3 is a schematic diagram of the base coordinate system of the pelvic rigid body component. In the figure:

[0097] 29 is the position of the origin of the base coordinate system of the pelvic rigid body component, which is the natal cleft

[0098] 30 is the position of the left end point of the base coordinate system of the pelvic rigid body component, which is the left lumbar fossa

[0099] 31 is the position of the right end point of the base coordinate system of the pelvic rigid body component, which is the right lumbar fossa

[0100] 32 is the midpoint of the line connecting the left end point of the base coordinate system of the pelvic rigid body component at the left lumbar fossa 30 and the right end point at the right lumbar fossa 31

[0101] X is the X-axis of the base coordinate system of the pelvic rigid body component

[0102] Y is the Y-axis of the base coordinate system of the pelvic rigid body component

[0103] Z is the Z-axis of the base coordinate system of the pelvic rigid body component

[0104] Figure 4 is the lumbar coordinate system of the rigid body component. In the figure:

[0105] 33 is the first lumbar vertebra

[0106] 34 is the third lumbar vertebra

[0107] 35 is the first sacral vertebra

[0108] X is the X-axis of the lumbar coordinate system of the rigid body component

[0109] Y is the Y-axis of the lumbar coordinate system of the rigid body component

[0110] Z is the Z-axis of the lumbar coordinate system of the rigid body component Specific implementation manner:

[0111] The technical solutions in the embodiments of the present invention will be described in detail below. The described embodiments are part of the embodiments of the present invention. Through these embodiments, the spatial position of the lumbar vertebra relative to the pelvis can be accurately measured according to the images collected by the data acquisition device.

[0112] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the method and device include two parts: a data acquisition device and a description method. The data acquisition device includes a three-dimensional scanner 21, a collection and processing computer 22, and cooperative marking points 23.

[0113] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the three-dimensional scanner 21 in the data acquisition device is composed of an upper camera 24, a lower camera 25, a camera bracket 28, and a tripod 26. The upper camera 24 and the lower camera 25 are both installed on the camera bracket 28, and the camera bracket 28 is installed on the tripod 26. The common field of view of the upper camera 24 and the lower camera 25 covers all the cooperative marking points 23 pasted on the measured human body 20.

[0114] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the collection and processing computer 22 in the data acquisition device is used to control the upper camera 24 and the lower camera 25 to collect the cooperative marking points 23 pasted on the measured human body 20, and calculate the three-dimensional spatial coordinates of all the cooperative marking points 23.

[0115] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the cooperative marker points 23 in the data acquisition device are a group of marker points with a circular black outer ring and a white center, and the material can be paper or plastic-based. The number and pasting positions of the cooperative marker points 23 are determined according to the human body parts to be analyzed. In this embodiment, the cooperative marker points 23 include three marker points at the positions of the pelvic rigid components and two landmark points on the thoracolumbar spine, which are respectively pasted at the gluteal cleft endpoints 29, the left lumbar fossa 30, the right lumbar fossa 31, the first lumbar vertebra 33, the third lumbar vertebra 34, and the first sacral vertebra 35.

[0116] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the connection relationship of each part of the data acquisition device is as follows: The cooperative marker points 23 are pasted on the specified parts of the measured human body 20 and face the three-dimensional scanner 21. The upper camera 24 and the lower camera 25 on the components of the three-dimensional scanner are both installed on the camera bracket 28, and the camera bracket 28 is installed on the tripod 26, and the lenses of the upper camera 24 and the lower camera 25 face the measured human body 20. The upper camera 24 and the lower camera 25 are connected to the acquisition and processing computer 22 through the data line 27, and are used to transmit the images collected by the two cameras into the acquisition and processing computer 22 for coordinate calculation.

[0117] A method and device for describing the human body structure relationship based on spatial transformation, characterized in that the data acquisition steps are as follows:

[0118] Obtain the global world coordinate system ∑ O The three-dimensional spatial coordinates of the positions P1 where the middle gluteal cleft endpoint 29 is located, P2 where the left lumbar fossa 30 is located, P3 where the right lumbar fossa 31 is located, Q1 where the first lumbar vertebra 33 is located, Q2 where the third lumbar vertebra 34 is located, and Q3 where the first sacral vertebra 35 is located are obtained, and the target point sets P (P1, P2, P3) of the pelvic rigid body components and Q (Q1, Q2, Q3) of the lumbar rigid body components in the global world coordinate system ∑ are formed. O

[0119] Establish the rigid body pelvic plane base coordinate system ∑ A and the lumbar joint rigid body component coordinate system ∑ B , the point sets P' to be matched in the rigid body pelvic component base coordinate system and Q' to be matched in the lumbar joint rigid body component coordinate system are expressed as:

[0120]

[0121] Q' = ((d1cosα, 0, d1sinα) T , (0, 0, 0) T , (d2cosβ, 0, -d2sinβ) T )

[0122] Let the line connecting the end points of the natal cleft 29 and the left lumbar fossa 30 be P1P2, the line connecting the end points of the natal cleft 29 and the right lumbar fossa 31 be P1P3, the line connecting the left lumbar fossa 30 and the right lumbar fossa 31 be P2P3, the line connecting the first lumbar vertebra 33 and the third lumbar vertebra 34 be Q1Q2, the line connecting the third lumbar vertebra 34 and the first sacral vertebra 35 be Q2Q3, the line connecting the first lumbar vertebra 33 and the first sacral vertebra 35 be Q1Q3, and the line connecting the third lumbar vertebra 34 and the midpoint of Q1Q3 be Q2Q4. Then l1 represents the length of P1P2, l2 represents the length of P1P3, θ represents the angle formed by P1P2 and P2P3, represents the angle formed by P1P3 and P2P3, d1 represents the length of Q1Q2, d2 represents the length of Q2Q3, α represents the angle between Q1Q2 and Q2Q4, and β represents the angle between Q2Q3 and Q2Q4.

[0123] The target point sets of the pelvic rigid body component and the lumbar vertebra rigid body component can be expressed as:

[0124]

[0125]

[0126] Among them, and O P AO respectively represent the rotation matrix and translation vector of the rigid body pelvic plane base coordinate system ∑ A relative to the global world coordinate system ∑ O , and O P BO respectively represent the rotation matrix and translation vector of the lumbar vertebra joint rigid body component coordinate system ∑ B relative to the global world coordinate system ∑ O .

[0127] Using SVD decomposition, the rotation matrix A of the rigid body pelvic plane base coordinate system ∑ O relative to the global world coordinate system ∑ and the translation vector O P AO can be expressed as:

[0128]

[0129] The rotation matrix B of the lumbar vertebra joint rigid body component coordinate system ∑ O relative to the global world coordinate system ∑ and the translation vector O P BO can be expressed as:

[0130]

[0131] Lumbar joint rigid component coordinate system ∑ B Spatial transformation matrix relative to the rigid component pelvic plane base coordinate system ∑ A can be expressed as: can be expressed as:

[0132]

[0133] This matrix is the expression of the rotational deformation relationship between the triangular surface formed by L1, L3, and S1 and the pelvic triangular surface.

Claims

1. A description method of the human body structure relationship based on spatial transformation, characterized in that: The calculation steps for the relative spatial positions of each rigid component in the method for describing the human body structure relationship are as follows: [1]Establish the local coordinate system of the rigid part of the pelvic plane E as the base coordinate system ∑ A , where the end point of the natal cleft is the origin P1 of the coordinate system, the left lumbar fossa is the left end point P2 of the pelvic rigid part, the right lumbar fossa is the right end point P3 of the pelvic rigid part, the midpoint of the line connecting P2 and P3 is P4, the line connecting P1 and P4 is the X-axis, the X-axis is rotated 90 degrees counterclockwise in the plane of P1P2P3 to obtain the Y-axis, and the direction of the Z-axis is determined according to the right-hand rule; establish the coordinate system ∑ O where the optical center of the upper camera is the origin of the camera coordinate system, the optical axis direction is the Z-axis, the vertical upward direction is the X-axis, and the direction of the Y-axis is determined by the right-hand rule. This coordinate system is called the global world coordinate system; [2]Establish the local coordinate system of each other rigid part of the human body and the global world coordinate system ∑ O The existing relative space rotation transformation matrix, expressed by the formula as: Among them, θ represents the rotation angle of each rigid component around the X-axis of the global world coordinate system ∑ O ; represents the rotation angle around the Y-axis of the global world coordinate system ∑ ; ω represents the rotation angle around the Z-axis of the global world coordinate system ∑ O ; O ​ If O P iO is the position offset matrix of the local coordinate system of each rigid component relative to the global world coordinate system ∑ O , then the combined rotation and translation homogeneous transformation matrix is expressed as: [3] Calculate the spatial position transformation matrix of each rigid component relative to the pelvic base coordinate system ∑ A as follows: For: Among them, is the homogeneous transformation matrix of the pelvic base coordinate system ∑ A relative to the global world coordinate system ∑ O ; is the rotation transformation matrix of ∑ A relative to ∑ O ; represents the transpose matrix; O P AO is the translation vector of ∑ A relative to ∑ O ; Construct the expressions of each rigid body of the human body relative to the pelvic base coordinate system ∑ A as follows:

2. The method according to claim 1, wherein: Calculate the transformation matrix in step 3 above using the Singular Value Decomposition (SVD) method Denote the global world coordinate system as ∑ O The set of target points under it is A = {a1, a2,..., a n}, and the set of points to be matched under the local coordinate system of a certain rigid component is B = {b1, b2,..., b n}, where a n and b n are respectively the three-dimensional coordinates of one point in the two point sets; The target point set A is obtained by transforming the point set B to be matched through the rotation matrix R and the translation vector t, that is: A = RB + t, The least squares solutions of the rotation matrix R and the translation vector t are obtained by the singular value decomposition (SVD) method. Let the objective function be: where k represents the number of points contained in the point set, and the centroids of the target point set A and the point set B to be matched are expressed as: Let: where a i represents the three-dimensional spatial coordinates of a point in the target point set A, and b j represents the three-dimensional spatial coordinates of a point in the point set B to be matched. and respectively represent the point coordinates in the target point set A and the point set B to be matched minus their respective centroids, eliminating the position translation relationship between the target point set A and the point set B to be matched. Then the objective function is: To minimize the objective function Y is equivalent to maximizing , let: where tr represents the trace of the matrix RH, that is, the sum of the diagonal elements of the matrix; Use SVD to decompose the H matrix: where U and V are orthogonal matrices, and Λ is a diagonal matrix with non-negative diagonal elements; When R = VU T then RH = VU T UΛV T = VΛV T is a symmetric positive definite matrix. For any orthogonal matrix B, there exists: tr(RH) ≥ tr(BRH) So R = VU T When, tr(RH) is maximized, the translation vector is expressed as: The homogeneous transformation matrix representing the rotation and translation combination is expressed as: This matrix expression is the relative relationship expression of a certain rigid component of the body relative to the pelvic rigid component.

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