Automatic workpiece 3D posture alignment system based on normal entropy-inertia axis coupling

Abstract

This invention provides an automatic 3D workpiece posture alignment system based on normal entropy-inertia axis coupling. It includes a data acquisition and preprocessing module for acquiring the 3D mesh model of the workpiece, performing data preprocessing, and translating the model's centroid to the origin of the coordinate system; a coarse registration module for calculating the inertia tensor matrix based on the vertex distribution of the 3D model, performing eigenvalue decomposition on the inertia tensor matrix to extract the three principal axes of inertia of the model, constructing a first rotation matrix, and performing rotation transformation on the model's vertex coordinates to complete the initial coarse registration; and a fine registration module for searching the optimal rotation angle based on the posture after coarse registration, with the optimization objective of minimizing the normal entropy value of the 3D model surface. This invention effectively avoids the local optima or alignment deviation problems that may arise from a single method by employing a two-stage strategy: first performing coarse registration based on the principal axes of inertia, and then combining it with normal entropy optimization for fine adjustment.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional computer vision and digital geometry processing technology, specifically to an automatic three-dimensional orientation alignment system for workpieces based on normal entropy-inertia axis coupling. Background Technology

[0002] In the fields of 3D vision and intelligent manufacturing, automatic workpiece positioning and orientation alignment is a critical preprocessing task that directly affects subsequent inspection accuracy, assembly quality, and processing efficiency. Traditional methods often rely on principal component analysis (PCA) or inertial principal axis alignment for initial orientation. However, when dealing with symmetrical or near-symmetrical structures, models with complex local features, or models with a lot of noise, these methods are prone to unstable alignment results or deviations from the visually semantic "natural posture" due to eigenvalue degradation or distribution ambiguity. On the other hand, while methods based on surface normal statistics can capture the consistency of geometric details and orientations, they are prone to getting trapped in local optima or becoming computationally inefficient without proper initialization and constraints.

[0003] Therefore, there is an urgent need for an automatic workpiece posture alignment method that can integrate multi-source information and perform hierarchical processing. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides an automatic workpiece three-dimensional posture alignment system based on normal entropy-inertia axis coupling, thereby solving the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: an automatic workpiece three-dimensional posture alignment system based on normal entropy-inertia axis coupling, comprising:

[0006] The data acquisition and preprocessing module is used to acquire the 3D mesh model of the workpiece, perform data preprocessing, and translate the centroid of the model to the origin of the coordinate system.

[0007] The three-dimensional mesh model consists of a set of vertices and a set of triangular faces.

[0008] The coarse registration module calculates the inertia tensor matrix based on the vertex distribution of the 3D mesh model, performs eigenvalue decomposition on the inertia tensor matrix, extracts the three principal axes of inertia of the model, constructs the first rotation matrix based on this, and performs rotation transformation on the vertex coordinates of the model to complete the initial coarse registration of the model.

[0009] The fine registration module is used to search for the optimal rotation angle based on the attitude after coarse registration, with the optimization objective of minimizing the surface normal entropy of the 3D mesh model;

[0010] The orientation correction output module is used to construct a second rotation matrix based on the optimal rotation angle, perform rotation transformation on the vertex coordinates of the model, and output the 3D mesh model after orientation correction.

[0011] As a further preferred embodiment, the specific process of preprocessing the input 3D mesh model and translating the model's centroid to the origin of the coordinate system includes:

[0012] After obtaining the 3D mesh model of the workpiece to be processed, traverse all vertices of the model and calculate the centroid of the 3D mesh model of the workpiece.

[0013] The formula for calculating the centroid is: ;

[0014] Where N represents the total number of vertices. Represents the coordinate vector of the i-th vertex;

[0015] Translate each vertex of the model so that the model's centroid coincides with the origin of the 3D coordinate system.

[0016] As a further preferred embodiment, the process of translating each vertex of the model so that the model's centroid coincides with the origin of the three-dimensional coordinate system specifically includes:

[0017] The model is centered by subtracting the coordinates of the geometric center point from the coordinates of all vertices of the workpiece, and finally the model is translated to the origin of the coordinate system.

[0018] The process of changing each vertex is as follows: ;

[0019] in, This represents the coordinate vector of the i-th vertex after the change.

[0020] As a further preferred embodiment, the specific process of performing eigenvalue decomposition on the inertia tensor matrix to extract the three principal axes of inertia of the model, and constructing the first rotation matrix accordingly, includes:

[0021] The inertia tensor matrix is ​​decomposed into eigenvalues ​​to obtain three eigenvalues ​​and three corresponding eigenvectors. The corresponding eigenvectors are then taken as the three principal inertial axes of the model.

[0022] Sort the three eigenvectors according to the size of their corresponding eigenvalues;

[0023] The three sorted, mutually orthogonal eigenvectors are sequentially mapped to the coordinate axes of the target coordinate system to construct the first rotation matrix.

[0024] As a further preferred embodiment, the initial coarse registration of the completed model specifically includes:

[0025] Eigendecomposition of the inertia tensor matrix: k=1, 2, 3;

[0026] We obtain three eigenvalues ​​λ1, λ2, λ3 and their corresponding eigenvectors u1, u2, u3;

[0027] Construct the first rotation matrix, whose column vectors are normalized eigenvectors;

[0028] Perform rotation transformations on all vertices of the model to complete coarse registration, so that the principal axes of the model are initially aligned with the axes of the world coordinate system;

[0029] The formula for calculating the rotation transformation is as follows: , Let R represent the coordinate vector of the i-th vertex after the rotation transformation, and let R represent the first rotation matrix.

[0030] As a further optimization, based on the attitude after coarse registration, and with the goal of minimizing the surface normal entropy of the 3D mesh model, the specific process of searching for the optimal rotation angle through an optimization algorithm includes:

[0031] For the coarsely registered 3D mesh model, calculate the unit normal vector for each triangular facet;

[0032] Divide the unit sphere into multiple regions, and define the number of regions as M;

[0033] Calculate the probability that the normals of all triangular facets fall into each spherical region:

[0034] j = 1, 2, ..., M;

[0035] Calculate the Shannon entropy of the normal distribution, construct an Euler angle rotation optimization problem around the X, Y, and Z axes of the current coordinate system, and use gradient descent to search for the optimal rotation angle in the angle space (-π, π].

[0036] As a further preferred embodiment, the formula for calculating the Shannon entropy of the normal distribution is: .

[0037] As a further preferred embodiment, the formula for constructing the Euler angle rotation optimization problem around the current coordinate system's X, Y, and Z axes is as follows:

[0038] ;

[0039] in, represents the rotation matrix around the X, Y, Z axes of the world coordinate system, and n represents the set of all facet normals.

[0040] As a further preferred embodiment, the detailed process of constructing a second rotation matrix based on the optimal rotation angle, performing rotation transformation on the model vertex coordinates, and outputting the 3D mesh model with the posture corrected includes:

[0041] Construct a fine rotation matrix based on the optimal rotation angle;

[0042] Perform a final rotation transformation on the vertices of the coarsely registered model:

[0043] , This represents the coordinate vector of the i-th vertex after the final rotation transformation. Represents a fine rotation matrix;

[0044] Output the 3D mesh model after the orientation is corrected.

[0045] This invention provides an automatic 3D orientation system for workpieces based on normal entropy-inertia axis coupling, which has the following advantages: By employing a two-stage strategy of first performing coarse registration based on the principal inertia axis and then combining it with normal entropy optimization for fine adjustment, the system effectively avoids the local optima or alignment deviation problems that may arise from a single method. Principal inertia axis alignment quickly aligns the model body roughly with the coordinate system, providing a good initial posture for subsequent optimization and significantly reducing the complexity and convergence time of the optimization process. The inertia tensor reflects the physical mass distribution of the model and is insensitive to noise and local geometric changes. Meanwhile, normal entropy, as an information theory indicator, can capture the directional consistency of surface details. The combination of the two enables the system to adapt to workpiece models with different complexities, different symmetries, and even irregular geometric features, exhibiting good generalization ability. At the same time, by minimizing the surface normal entropy, the model achieves the most stable and natural orientation state in both visual and geometric senses. This not only achieves the theoretical alignment of the principal axis and the coordinate axis but also provides a better posture reference in visual perception and subsequent processing (such as inspection, assembly, or machining). Attached Figure Description

[0046] Figure 1 This is a flowchart of the automatic workpiece three-dimensional posture alignment system based on normal entropy-inertia axis coupling of the present invention. Detailed Implementation

[0047] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0048] The following disclosure provides many different embodiments or examples for implementing various structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. These are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed. In addition, examples of various specific processes and materials are provided in this invention, but those skilled in the art will recognize the application of other processes and / or the use of other materials.

[0049] like Figure 1 As shown, this embodiment of the invention provides an automatic workpiece three-dimensional posture alignment system based on normal entropy-inertia axis coupling, comprising:

[0050] The data acquisition and preprocessing module is used to acquire the 3D mesh model of the workpiece, perform data preprocessing, and translate the centroid of the model to the origin of the coordinate system.

[0051] The three-dimensional mesh model consists of a set of vertices and a set of triangular faces.

[0052] The coarse registration module calculates the inertia tensor matrix based on the vertex distribution of the 3D mesh model, performs eigenvalue decomposition on the inertia tensor matrix, extracts the three principal axes of inertia of the model, constructs the first rotation matrix based on this, and performs rotation transformation on the vertex coordinates of the model to complete the initial coarse registration of the model.

[0053] The fine registration module is used to search for the optimal rotation angle based on the attitude after coarse registration, with the optimization objective of minimizing the surface normal entropy of the 3D mesh model;

[0054] The orientation correction output module is used to construct a second rotation matrix based on the optimal rotation angle, perform rotation transformation on the vertex coordinates of the model, and output the 3D mesh model after orientation correction.

[0055] Specifically, the process of preprocessing the input 3D mesh model and translating its centroid to the origin of the coordinate system includes:

[0056] After obtaining the 3D mesh model of the workpiece to be processed, traverse all vertices of the model and calculate the centroid of the 3D mesh model of the workpiece.

[0057] The formula for calculating the centroid is: ;

[0058] Where N represents the total number of vertices. This represents the coordinate vector of the i-th vertex.

[0059] Translate each vertex of the model so that the model's centroid coincides with the origin of the 3D coordinate system;

[0060] Specifically, the coordinates of all vertices of the workpiece are subtracted from the coordinates of the geometric center point to center the model, and finally the model is translated to the origin of the coordinate system.

[0061] The process of changing each vertex is as follows: ;

[0062] Understandable This represents the coordinate vector of the i-th vertex after the transformation. This step eliminates the translational deviation of the model in space, preparing for subsequent rotation and alignment.

[0063] It should be noted that the three-dimensional coordinate system is specifically the world coordinate system.

[0064] In this embodiment, the formula for calculating the inertia matrix tensor is:

[0065] ;

[0066] Understandably, the tensor matrix represents the mass distribution characteristics of the model vertices around the origin of the coordinate system.

[0067] The specific process of performing eigenvalue decomposition on the inertia tensor matrix to extract the three principal axes of inertia of the model, and constructing the first rotation matrix accordingly, includes:

[0068] The inertia tensor matrix is ​​decomposed into eigenvalues ​​to obtain three eigenvalues ​​and three corresponding eigenvectors. The corresponding eigenvectors are then taken as the three principal inertial axes of the model.

[0069] Sort the three eigenvectors according to the size of their corresponding eigenvalues;

[0070] The three sorted, mutually orthogonal eigenvectors are sequentially mapped to the coordinate axes of the target coordinate system to construct the first rotation matrix.

[0071] Specifically, the inertia tensor matrix is ​​decomposed into eigenvalues: k=1, 2, 3;

[0072] We obtain three eigenvalues ​​λ1, λ2, λ3 and their corresponding eigenvectors u1, u2, u3;

[0073] Construct the first rotation matrix, whose column vectors are normalized eigenvectors;

[0074] Perform rotation transformations on all vertices of the model to complete coarse registration, so that the principal axes of the model are initially aligned with the axes of the world coordinate system;

[0075] The formula for calculating the rotation transformation is as follows: , Let R represent the coordinate vector of the i-th vertex after the rotation transformation, and let R represent the first rotation matrix.

[0076] It should be noted that the first rotation matrix is ​​an orthogonal matrix, which rotates the point from the original coordinate system to a new coordinate system based on the principal inertial axis. The order of the eigenvectors determines the correspondence between the principal axes and the world coordinate system axes (X, Y, Z). Usually, the most significant principal axis is aligned with the X-axis, and after completing the coarse alignment of the 3D mesh model, its main orientation is basically aligned with the coordinate system.

[0077] In this embodiment, based on the coarsely registered pose, the optimization objective is to minimize the surface normal entropy of the 3D mesh model. The specific process of searching for the optimal rotation angle using an optimization algorithm includes:

[0078] For the coarsely registered 3D mesh model, calculate the unit normal vector for each triangular facet;

[0079] For a face composed of vertices, its normal is calculated by the cross product of vectors. The calculation method is a current technical means and will not be described in detail here.

[0080] Divide the unit sphere into multiple regions, and define the number of regions as M;

[0081] Calculate the probability that the normals of all triangular facets fall into each spherical region:

[0082] j = 1, 2, ..., M;

[0083] Calculate the Shannon entropy of the normal distribution, construct an Euler angle rotation optimization problem around the X, Y, and Z axes of the current coordinate system, and use gradient descent to search for the optimal rotation angle in the angle space (-π, π].

[0084] The formula for calculating Shannon entropy is: ;

[0085] Understandably, the entropy value H quantifies the uncertainty or dispersion of the normal direction. The smaller the entropy value, the more concentrated and orderly the normal direction is, corresponding to a better placement posture.

[0086] Construct an optimization problem for Euler angle rotations around the current coordinate system's X, Y, and Z axes:

[0087] ;

[0088] in, represents the rotation matrix around the X, Y, Z axes of the world coordinate system, and n represents the set of all facet normals.

[0089] It should be noted that the unit sphere is divided using latitude and longitude or a uniform division based on solid angles, and when searching for the optimal rotation angle, the initial angle of the gradient descent method is based on the attitude after coarse registration as the starting point.

[0090] In this embodiment, the detailed process of constructing a second rotation matrix based on the optimal rotation angle, performing rotation transformation on the model vertex coordinates, and outputting the 3D mesh model after posture correction includes:

[0091] Construct a fine rotation matrix based on the optimal rotation angle;

[0092] Perform a final rotation transformation on the vertices of the coarsely registered model:

[0093] , This represents the coordinate vector of the i-th vertex after the final rotation transformation. Represents a fine rotation matrix;

[0094] The output is a 3D mesh model after the orientation is corrected, with its principal inertial axis aligned with the coordinate system axis and the surface normal distribution reaching the most ordered state, thus completing the automatic orientation correction of the workpiece's 3D orientation.

[0095] The automatic workpiece 3D posture alignment system based on normal entropy-inertia axis coupling provided in this embodiment effectively avoids the local optima or alignment deviation problems that may arise from a single method by employing a two-stage strategy: first, coarse registration based on the principal inertia axis, and then fine adjustment combined with normal entropy optimization. Principal inertia axis alignment quickly aligns the model body roughly with the coordinate system, providing a good initial posture for subsequent optimization and significantly reducing the complexity and convergence time of the optimization process. The inertia tensor reflects the physical mass distribution of the model and is insensitive to noise and local geometric changes. Meanwhile, normal entropy, as an information theory indicator, can capture the directional consistency of surface details. The combination of these two aspects enables the system to adapt to workpiece models with different complexities, symmetries, and even irregular geometric features, exhibiting good generalization ability. Furthermore, by minimizing surface normal entropy, the model achieves the most stable and natural orientation state both visually and geometrically. This not only achieves the theoretical alignment of the principal axis and coordinate axes but also provides a better posture reference for visual perception and subsequent processing (such as inspection, assembly, or machining).

[0096] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A workpiece three-dimensional attitude automatic alignment system based on normal entropy-inertia axis coupling, characterized in that, include: The data acquisition and preprocessing module is used to acquire the 3D mesh model of the workpiece, perform data preprocessing, and translate the centroid of the model to the origin of the coordinate system. The three-dimensional mesh model consists of a set of vertices and a set of triangular faces. The coarse registration module calculates the inertia tensor matrix based on the vertex distribution of the 3D mesh model, performs eigenvalue decomposition on the inertia tensor matrix, extracts the three principal axes of inertia of the model, constructs the first rotation matrix based on this, and performs rotation transformation on the vertex coordinates of the model to complete the initial coarse registration of the model. The fine registration module is used to search for the optimal rotation angle based on the attitude after coarse registration, with the optimization objective of minimizing the surface normal entropy of the 3D mesh model; The orientation correction output module is used to construct a second rotation matrix based on the optimal rotation angle, perform rotation transformation on the model vertex coordinates, and output the 3D mesh model after orientation correction. The specific process of searching for the optimal rotation angle based on the attitude after coarse registration, with the optimization objective of minimizing the surface normal entropy of the 3D mesh model, includes the following: For the coarsely registered 3D mesh model, calculate the unit normal vector for each triangular facet; Divide the unit sphere into multiple regions, and define the number of regions as M; Calculate the probability that the normals of all triangular facets fall into each spherical region: ,j=1,2,...,M; Calculate the Shannon entropy of the normal distribution, construct an Euler angle rotation optimization problem around the X, Y, and Z axes of the current coordinate system, and use gradient descent to search for the optimal rotation angle in the angle space (-π, π].

2. The workpiece three-dimensional attitude automatic alignment system based on normal entropy-inertia axis coupling according to claim 1, characterized in that, The specific process of obtaining the 3D mesh model of the workpiece, performing data preprocessing, and translating the model's centroid to the origin of the coordinate system includes: After obtaining the 3D mesh model of the workpiece to be processed, traverse all vertices of the model and calculate the centroid of the 3D mesh model of the workpiece. The formula for calculating the centroid is: ; Where N represents the total number of vertices. Represents the coordinate vector of the i-th vertex; Translate each vertex of the model so that the model's centroid coincides with the origin of the 3D coordinate system.

3. The workpiece three-dimensional attitude automatic alignment system based on normal entropy-inertia axis coupling according to claim 2, characterized in that, The process of translating each vertex of the model so that the model's centroid coincides with the origin of the 3D coordinate system specifically includes: The model is centered by subtracting the coordinates of the geometric center point from the coordinates of all vertices of the workpiece, and finally the model is translated to the origin of the coordinate system. The process of changing each vertex is as follows: ; in, This represents the coordinate vector of the i-th vertex after the change.

4. The workpiece three-dimensional attitude automatic alignment system based on normal entropy-inertia axis coupling according to claim 1, characterized in that, The specific process of performing eigenvalue decomposition on the inertia tensor matrix to extract the three principal axes of inertia of the model, and constructing the first rotation matrix accordingly, includes: The inertia tensor matrix is ​​decomposed into eigenvalues ​​to obtain three eigenvalues ​​and three corresponding eigenvectors. The corresponding eigenvectors are then taken as the three principal inertial axes of the model. Sort the three eigenvectors according to the size of their corresponding eigenvalues; The three sorted, mutually orthogonal eigenvectors are sequentially mapped to the coordinate axes of the target coordinate system to construct the first rotation matrix.

5. A workpiece three-dimensional attitude automatic alignment system based on normal entropy-inertia axis coupling according to claim 3 or 4, characterized in that, The initial coarse registration of the completed model specifically includes: Eigendecomposition of the inertia tensor matrix: k=1, 2, 3; Where I represents the inertia tensor matrix; We obtain three eigenvalues ​​λ1, λ2, λ3 and their corresponding eigenvectors u1, u2, u3; Construct the first rotation matrix, whose column vectors are normalized eigenvectors; Perform rotation transformations on all vertices of the model to complete coarse registration, so that the principal axes of the model are initially aligned with the axes of the world coordinate system; The formula for calculating the rotation transformation is as follows: , Let R represent the coordinate vector of the i-th vertex after the rotation transformation, and let R represent the first rotation matrix.

6. The workpiece three-dimensional posture automatic alignment system based on normal entropy-inertia axis coupling according to claim 1, characterized in that, The formula for calculating the Shannon entropy of the normal distribution is: .

7. The workpiece three-dimensional posture automatic alignment system based on normal entropy-inertia axis coupling according to claim 6, characterized in that, The formula for constructing the Euler angle rotation optimization problem around the current coordinate system's X, Y, and Z axes is as follows: ； in, represents the rotation matrix around the X, Y, Z axes of the world coordinate system, and n represents the set of all facet normals.

8. The workpiece three-dimensional attitude automatic alignment system based on normal entropy-inertia axis coupling according to claim 5, characterized in that, The detailed process of constructing a second rotation matrix based on the optimal rotation angle, performing rotation transformation on the model vertex coordinates, and outputting the 3D mesh model with the posture corrected includes: Construct a fine rotation matrix based on the optimal rotation angle; Perform a final rotation transformation on the vertices of the coarsely registered model: , This represents the coordinate vector of the i-th vertex after the final rotation transformation. Represents a fine rotation matrix; Output the 3D mesh model after the orientation is corrected.

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