A method for automatic facial rigging based on skinning decomposition

Abstract

The application relates to a kind of face automatic binding methods based on skin decomposition, comprising S1: joint initialization: input face 4D expression and template binding, and the joint position of character head mesh is calculated using offset scaling, S2: skin decomposition, S21: based on quaternion realizes the identity transformation of joint rotation matrix;S22: update joint transformation matrix;S23: update target function weight and staggered optimization with update joint transformation matrix, S3, face component migration: using radial basis function (RBF) to carry out the migration of these components, by selecting control points on the head mesh of template, the deformation of component from template to specific character is calculated by integrating Gaussian function into radial basis function;The application has the advantage of being suitable for high-fidelity face animation production.

Description

Technical Field

[0001] This invention belongs to the field of computer graphics technology, specifically relating to an automatic face binding method based on skin decomposition. Background Technology

[0002] A recent study proposed an automatic high-fidelity facial rigging method that combines skinning decomposition with 4D facial expressions to complete the rigging process. This method takes a predefined rigging template and the character's 4D facial expression as input. It initializes joint positions and transfers facial components using prior information from the template rigging, and optimizes the rigging weights and the joint transformation matrix for reproducing the 4D expression through alternating iterations. The method achieves skinning decomposition by minimizing the reconstruction error of vertex positions, while incorporating soft constraints on joint positions to limit their location. Hard constraints, such as a fixed sparse weight distribution, ensure that joints only affect a small neighborhood within the head mesh. Experimental results show that this method can automatically generate high-fidelity facial rigging and effectively guarantee the rationality of joint positions and weight distribution.

[0003] This study primarily designs the energy function based on the reconstruction error of the facial expression mesh vertex positions. It only considers the consistency of the binding in reproducing the vertex positions of the input facial expression, neglecting the impact of vertex normal transformation direction and weight distribution during deformation on the practical use of the model. For example, incorrect vertex normal transformation direction during deformation can cause the facial model mesh to flip, which is obviously detrimental to animation production. Uneven weight distribution can also lead to abrupt and unnatural deformation of model mesh points, significantly increasing the difficulty of using binding for animation production. Furthermore, this study does not pay special attention to the consistency of details at the corners of the eyes, which can easily result in a situation where the vertex positions at the corners of the eyes after model deformation, while numerically similar to the actual input facial expression, exhibit significant visual differences. For instance, the actual input facial expression has closed corners of the eyes, but although the numerical difference in vertex positions at the upper and lower eyelids in the calculated binding model is not significant, the failure to achieve eyelid closure creates a noticeable visual difference. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide an automatic face binding method based on skin decomposition suitable for high-fidelity facial animation production.

[0005] The technical solution of the present invention is as follows:

[0006] An automatic face binding method based on skin decomposition, characterized by the following steps:

[0007] S1: Joint initialization: Input facial 4D expressions and template binding, and use offset scaling to calculate the joint positions of the character's head mesh;

[0008] S2: Skin Decomposition:

[0009] S21: Implement the identity transformation of joint rotation matrices based on quaternions;

[0010] S22: Update the joint transformation matrix;

[0011] S221: The objective function E is updated by the transformation matrix as shown in Equation (1a). A Perform joint transformation matrix calculation for 4D facial expressions;

[0012] E A =E M +γE N +λE V +βE J (1a)

[0013] The E M The constraint designed to minimize vertex position reconstruction error, the E V For the vertex normal transformation direction constraint, γ, λ, and β are the regularization coefficients of each constraint, all greater than or equal to 0, and are also adjustable parameters. N As a surface normal constraint term, the E J For joint soft constraint;

[0014] S222: As shown in formula (1b), in E M In the process, the vertices of the key region are set as the set of vertices with the initial maximum influence, which is defined as I0. For other vertices in the head mesh of the 4D facial expression character, their influence is determined by the distance d. i It decays exponentially, at a distance of d i This represents the shortest path distance between the i-th vertex and the nearest vertex in the set of vertices in the critical region;

[0015] The attenuation formula is: Where τ>0 is a parameter controlling the decay rate, and e is a natural constant; Ensure that the minimum influence of a vertex is not lower than 1.0;

[0016]

[0017] s represents the total number of other arbitrary emojis in all inputs, and m represents the number of vertices for each emoji, where m is the number of vertices for the k-th emoji. k The position of the i-th vertex in the sequence k = 1...s is used This indicates that j is the j-th joint. The weights of the neutral character model are represented by u, where u is the position of the i-th vertex of the neutral expression u. iThis indicates that the neutral expression u transforms into the k-th expression v. k The transformation matrix of the j-th joint is

[0018] S223: As shown in formula (1d), in EV, It is the input k-th character expression grid {v k The unit normal vector of the i-th vertex in the sequence k = 1...s. This describes the normal vector of the i-th vertex in the neutral mesh u of the character, which is transformed into the normal vector of the i-th vertex of the k-th expression under the influence of all control joint rotation matrices {R}, where w j The weight coefficients of the corresponding joints are represented. To ensure that the final normal vector is still a unit normal vector, the above results are normalized.

[0019]

[0020] The The modulus of the above results is given, and E in the above formula (1a) is given. M E N E V and E J Limited by

[0021] S23: The objective function for updating weights based on the joint weight distribution is cyclically optimized with the updated joint transformation matrix;

[0022] S3: Facial Component Migration: This feature utilizes radial basis functions to migrate these components. By selecting control points on the head mesh of the template, Gaussian functions are integrated into the radial basis functions to calculate the deformation of the components from the template to a specific character.

[0023] Furthermore, in step S23, the weights are updated using the weight update objective function in formula (2a), and E in formula (2a) W The specific details are shown in formula (2e);

[0024] E B =E M +γE N +λE V +αE W (2a)

[0025]

[0026] And E in the above formula (2a) M E N E V and E W Limited by

[0027]

[0028] The weight of the j-th joint of the template model g relative to the i-th vertex is expressed as follows: The E W Weight distribution constraints

[0029] Furthermore, the E N The specific details are shown in formula (1c):

[0030]

[0031] in It is the input k-th character expression grid {v k The unit normal vector of the f-th face in the sequence k = 1...s. It is the character binding weight w u The function refers to the neutral mesh u of the character utilizing the character-bound weight w. u The unit normal vector of the f-th face of the k-th expression is reproduced by deforming the joint transformation matrix {R, T}.

[0032] Furthermore, the E J The specific details are shown in formula (1e):

[0033]

[0034] Where β is used to balance E M and E J The parameters, as β increases, correspond to the actual joint position of the k-th expression. Deviation from expected joint position The smaller the degree, the better.

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] 1. This invention effectively improves the rationality, naturalness, and accuracy of automatic facial binding by integrating vertex normal transformation direction constraints, weight distribution constraints, and key region attention constraints. Specifically, the vertex normal transformation direction constraint limits the joint transformation matrix, making joint deformation transitions more natural and avoiding face flipping; the weight distribution constraint optimizes the smooth deformation of vertices in the bound facial model, reducing abruptness; and the key region attention constraint applies a higher penalty for vertex position errors to key areas (such as the corners of the eyes), solving the problem of the significant impact of minor deformations in visually critical areas on visual effects.

[0037] In summary, this invention has the advantage of being suitable for high-fidelity facial animation production. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the algorithm framework in the comparison example;

[0039] Figure 2 This is a diagram illustrating the offset scaling.

[0040] Figure 3 This is a schematic diagram of the method framework of this application;

[0041] Figure 4 This image shows the black face phenomenon that occurs when the proportional binding solution result is used to reproduce a certain input expression.

[0042] Figure 5 A comparison diagram of vertex normal directions when the neutral expression in the proportional scheme and the modified scheme of this application are the same input expression;

[0043] Figure 6 A heatmap showing the error between the vertex normal direction and the vertex normal direction of the actual input expression when the neutral expression in the comparative scheme and the modified scheme of this application are the same input expression;

[0044] Figure 7 A comparison diagram of the weight distribution of the same joint in the proportional scheme and the scheme of this application;

[0045] Figure 8 This is a schematic diagram illustrating the effect of moving a certain joint to the same position on mesh deformation in both the proportional scheme and the scheme in this application.

[0046] Figure 9 A schematic diagram of the eye corner vertex region selected in this application as having the highest initial influence;

[0047] Figure 10 A comparison diagram of the corner of the eye area when reproducing an expression using the proportional scheme and the scheme in this application;

[0048] Figure 11 A heat map showing the error between the vertex position of the eye corner region when inputting an expression and the actual input expression, in order to compare the proportional scheme and the scheme of this application. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] Example 1

[0051] An automatic facial rigging method based on skin decomposition, taking a predefined rigging template and the actor's 4D facial expressions as input, including a neutral expression u and a set of arbitrary expressions {v}. k : k = 1...s}. "4D Expressions" refers not only to using the actor's static facial expressions, but also to the dynamic changes in expressions during the rendering process. Furthermore, it is necessary to ensure that the mesh topology and orientation of all character expressions are consistent with the head mesh of the rigging template. The output includes not only the initial joint positions of the actor's head mesh. and linear hybrid skin weights It also includes other facial components, such as teeth and eyes.

[0052] Includes the following steps:

[0053] S1: Joint initialization: as shown Figure 2 As shown, "offset scaling" is used to calculate the joint positions of the character's head mesh. Given a template neutral mesh g, iterates through the meshes to obtain the indices of the vertices closest to the joints and the offset between them. The initial positions b of all joints in the target neutral mesh are calculated by combining the scaling factor κ of the bounding boxes between the template neutral mesh g and the target neutral mesh u. u In addition, the expected joint positions of other input expressions. It can also be calculated using "offset scaling" to constrain the update of the joint transformation matrix in the skin decomposition step;

[0054] S2: Skin Decomposition:

[0055] S21: Implement the identity transformation of joint rotation matrices based on quaternions;

[0056] S22: Update the joint transformation matrix;

[0057] S221: The objective function E is updated by the transformation matrix as shown in Equation (1a). A Perform joint transformation matrix calculation for 4D facial expressions;

[0058] E A =E M +γE N +λE V +βE J (1a)

[0059] The E M The constraint designed to minimize vertex position reconstruction error, the E V For the vertex normal transformation direction constraint, γ, λ, and β are the regularization coefficients of each constraint, all greater than or equal to 0, and are also adjustable parameters. N As a surface normal constraint term, the E J For joint soft constraint;

[0060] S222: As shown in formula (1b), in E M In the process, the vertices of the key region are set as the set of vertices with the initial maximum influence, which is defined as I0. For other vertices in the character's head mesh, their influence is determined by the distance d. i It decays exponentially, at a distance of d i This represents the shortest path distance between the i-th vertex and the nearest vertex in the set of vertices in the critical region;

[0061] The attenuation formula is: Where τ>0 is a parameter controlling the decay rate, and e is a natural constant; Ensure that the minimum influence of a vertex is not lower than 1.0;

[0062]

[0063] s represents the total number of other arbitrary emojis in all inputs, and m represents the number of vertices for each emoji, where m is the number of vertices for the k-th emoji. k The position of the i-th vertex in the sequence k = 1...s is used Let j be the j-th joint, and let the weight of the j-th joint of the character's facial model u with respect to the i-th vertex be expressed as follows: (i.e., skinning weights), the position of the i-th vertex of the neutral expression u is represented by u. i This indicates that the neutral expression u transforms into the k-th expression v. k The transformation matrix of the j-th joint is

[0064] Wherein E N The specific details are shown in formula (1c):

[0065]

[0066] in It is the input k-th character expression grid {v k The unit normal vector of the f-th face in the sequence k = 1...s. It is the character binding weight w u The function refers to the neutral mesh u of the character utilizing the character-bound weight w. u The unit normal vector of the f-th face of the k-th expression is reproduced by deforming the joint transformation matrix {R, T}.

[0067] S223: As shown in formula (1d), in EV, It is the input k-th character expression grid {v k The unit normal vector of the i-th vertex in the sequence k = 1...s. This describes the normal vector of the i-th vertex in the neutral mesh u of the character, which is transformed into the normal vector of the i-th vertex of the k-th expression under the influence of all control joint rotation matrices {R}, where w j The weight coefficients of the corresponding joints are represented. To ensure that the final normal vector is still a unit normal vector, the above results are normalized.

[0068]

[0069] The The modulus of the above results;

[0070] The E J The specific details are shown in formula (1e):

[0071]

[0072] Where β is used to balance E M and E J The parameters, as β increases, correspond to the actual joint position of the k-th expression. Deviation from expected joint position The smaller the degree will be

[0073] In the above formula (1a), E M E N E V and E J Limited by

[0074] S23: The objective function for updating weights based on the joint weight distribution is cyclically optimized with the updated joint transformation matrix;

[0075] The weights are updated using the weight update objective function in formula (2a), and E in formula (2a) is... W As shown in formula (2e), the weight update and the joint transformation matrix update are performed alternately. This means that during the weight update process, the joint transformation matrix {R, T} remains fixed, and the character-bound weight w... u That is the only variable that needs optimization. Conversely, the same applies;

[0076] E B =E M +γE N +λE V +αE W (2a)

[0077] in,

[0078]

[0079] Limited by,

[0080]

[0081] The weight of the j-th joint of the template model g relative to the i-th vertex is expressed as follows:

[0082] S4: Facial Component Migration: These components are migrated using radial basis functions (RBF). By selecting control points on the head mesh of the template, Gaussian functions are integrated into the radial basis functions to calculate the deformation of the components from the template to the specific character.

[0083] Comparative Example

[0084] Existing automatic facial rigging schemes based on skin decomposition include the following: the input is a predefined rigging template and the actor's 4D facial expressions, including neutral expressions and a set of arbitrary expressions. "4D expressions" refers not only to using the actor's static facial expressions, but also to the dynamic changes of expressions during the rendering process. In addition, it is necessary to ensure that the mesh topology and orientation of all character expressions are consistent with the head mesh of the rigging template. The output includes not only the initial joint positions and linear blending skin weights of the actor's head mesh, but also other facial components such as teeth and eyes.

[0085] like Figure 1 As shown, the algorithm framework consists of three steps: joint initialization, skin decomposition, and facial component transfer. As shown in Equation (3a), the input 4D facial expressions include the character's neutral expression u and other arbitrary expressions {v}. k :k=1...s}, each expression has m vertices;

[0086] The position of the i-th vertex of the neutral expression u is represented by u. i This indicates that the k-th expression {v} k The position of the i-th vertex in the sequence k = 1...s is used Let s represent the total number of other arbitrary expressions in the input, and let g be the reference template mesh bound to n joints, which are indexed by j and whose initial positions are denoted by b. g This indicates that the initial position of the character joints, calculated based on offset scaling, is represented by b. u To indicate, w ij The weight of the j-th joint relative to the i-th vertex is represented by w. The skinning weights of the joints and the character's expression are respectively represented by w. g and w u It means, w u With w g Initial value;

[0087] The weight of the j-th joint with respect to the i-th vertex in the character's facial model is represented as follows: The weight of the j-th joint of the target facial model with respect to the i-th vertex is expressed as follows: Transform from the neutral emoji u to the k-th emoji v. k The transformation matrix of the j-th joint is in It is a rotation matrix. It is a translation vector;

[0088] The binding weights of the character's facial model w u The joint transformation matrix {R, T} will be updated alternately until the maximum number of iterations specified by the user or the model fitting term E is reached. M Convergence, E M For a detailed definition, see formula (3b), the facial component c of the neutral mesh in the template. g The facial model is deformed based on radial basis functions to fit a neutral mesh. The facial components of the deformed neutral mesh are then defined using c... u express.

[0089] Joint initialization: such as Figure 2 As shown, "offset scaling" is used to calculate the joint positions of the character's head mesh. Given the neutral mesh g of the character's face model, iterate through the meshes to obtain the vertex indices closest to the joints and the offset between them. The initial positions b of all joints in the neutral mesh u of the target face model are calculated by combining the scaling factor κ between the bounding boxes of the neutral mesh g of the character's face model and the neutral mesh u of the target face model. u In addition, the expected joint positions for other input expressions. It can also be calculated using "offset scaling" to constrain the update of the joint transformation matrix in the skin decomposition step.

[0090] Skin decomposition. The energy function is shown in equation (3a), and the reconstruction error E at the vertex position is... M Apply joint soft constraints E on the basis J To determine the update of the joint transformation matrix, β is used to balance E. M and E J The parameters, as β increases, correspond to the actual joint position of the k-th expression. Deviation from expected joint position The smaller the degree, the better. It is worth noting that the expected joint position has been calculated in the joint initialization step.

[0091] E = E M +βE J (3a)

[0092] in,

[0093]

[0094] Limited by,

[0095]

[0096] As shown in Equation (3f), in order to improve the calculation speed and ensure that each joint only controls the vertices of the local area of ​​the head mesh, the existing scheme designs a fixed sparse distribution constraint as shown in Equation (3f).

[0097] First, the weights of the template facial model are used as the initial weights of the character's facial model to accelerate convergence. Second, only when... When the weights are not equal to zero, the weights of the character's facial model Only then will it participate in the update process; otherwise, it will not participate in the entire iteration process. Keeping it at zero, this constraint can prevent the movement of a single joint from causing the vertices of multiple regions of the head mesh of the character's face model to move. When the weights are updated, the joint transformation matrix remains unchanged, so only equation (3b) and constraints (3d), (3e), and (3f) need to be considered for optimization.

[0098] Facial Component Migration: In addition to binding the head mesh of the character's facial model, the facial components also need to be adjusted when the character changes. Radial Basis Functions (RBFs) are used to migrate these components. By selecting control points on the head mesh of the template, Gaussian functions are integrated into the RBFs to calculate the deformation of the components from the template to the specific character.

[0099] Compared to the comparative example, this application has made optimizations in the following three aspects:

[0100] like Figure 3 As shown, the first aspect is to design the vertex normal transformation direction constraint E. V This avoids significant joint flipping and overturning during the deformation process, ensuring a natural deformation transition and improving the stability and rationality of the deformation of the bound model.

[0101] The second aspect is the introduction of weight distribution constraints E. W This makes the deformation of vertices smoother and more fluid, reduces abruptness, and enhances the naturalness of the animation effect.

[0102] The third aspect is to improve the vertex position reconstruction error for key visual areas such as the corner of the eye, which is manifested in E with attention constraints on key areas. M This avoids the significant visual impact caused by subtle differences in key visual areas, greatly improving the visual consistency of facial expression reproduction.

[0103] Compared with the comparative example, the technical solution of this application has the following advantages:

[0104] 1) Vertex normal transformation direction constraint

[0105] like Figure 4 As shown, existing solutions can achieve high-fidelity automatic face binding, but if the vertex normals of neutral expressions are not unlocked, the model may exhibit a black face phenomenon, or face flipping, when deformed into other input expressions. This is because the vertex normals do not point outwards from the model. Therefore, this invention adds a vertex normal transformation direction constraint E to the existing solution. V This enables a reasonable decomposition of the transformation matrix of the joints, thereby improving the usability of face rigging.

[0106] Vertex normal transformation direction constraint term E V The essence is to restrict the rotation of the joints {R} so that the vertex normal is... Transform from neutral u to target expression {v} k Vertex normals for k = 1...s and vertex normals for the input target facial expression Consistency. This prevents the problem of face normals being in the correct direction while vertex normals point inside the model.

[0107] Specifically, the surface normal constraint term E N The difference lies in the fact that the vertex normal transformation direction constraint considers the change in the vertex normal direction when the bound model is deformed into other expressions. The face normal constraint term E... N Because it is designed to be determined solely by the relative positions between the deformed vertices, it cannot account for unreasonable situations during the deformation process.

[0108] This invention experimentally verified the results of adding vertex normal transformation direction constraints and compared them with a scheme that only considers vertex position reconstruction errors and surface normal constraints. Figure 5 and 6 As shown, heatmaps of errors between the vertex normal directions when reproducing the input expression using different schemes and the vertex normal directions of the actual input expression are plotted.

[0109] 2) Weight distribution constraint term

[0110] While existing solutions for high-fidelity automatic facial rigging can reproduce input expressions, abrupt and inconsistent vertex deformations occur when artists adjust or move joints, severely impacting the usability of the rigging results. Therefore, this invention adds a weight distribution constraint term E to the original solution. W This ensures that the weight distribution of the vertices is as similar as possible to the weight distribution of the template, thereby improving the naturalness and stability of the animation effect.

[0111] This invention experimentally verifies the results of adding weight distribution constraints. Specifically, by randomly selecting a joint, the influence distribution of the bound joint calculated by this scheme and existing schemes on the character model was visualized. Figure 7 As shown, compared to the original solution which did not consider weight distribution constraints, the solution of this invention provides a more consistent, smoother, and more natural distribution of skin weights and template weights. Furthermore, for both solutions, the model binding selects one joint and performs the same movement. Figure 8 It is evident that the model deformation of the present invention is more natural, the stability is better, and the usability of binding is greatly improved. In contrast, the original solution has poor continuity between vertices, which clearly does not conform to the prior knowledge that should be followed in the process of human facial deformation.

[0112] 3) Focus on constraints in key areas

[0113] While existing automatic binding methods consider the accuracy of reproducing the vertex positions of input facial expressions, they fail to account for the significant visual impact that even minute differences can have in key facial regions, such as the degree of eye opening and closing. Therefore, this invention achieves better visual consistency in the reproduction of input facial expressions by imposing stricter constraints on areas such as the eyelids. Figure 9 As shown, the vertex with the highest initial influence I0 is selected. As shown in equations (1b) and (2b), in order to ensure a smooth transition in the importance of vertices in the peri-eye region, an exponential decay method is designed to gradually attenuate the influence of surrounding vertices.

[0114] This invention experimentally verified the solution of adding focus region constraints. Specifically, compared to the original solution that did not consider focus region constraints, the solution of this invention achieves a higher consistency between the reproduced facial expression and the ground truth of the input expression in the corner of the eye area. Figure 10 As shown, the input facial expression reproduced in this solution achieves eye closure consistent with the input expression, while existing solutions without focused area attention constraints exhibit slight eye opening. For example... Figure 11 As shown, the present invention visualizes the vertex position error in the region where additional influence is applied. It can also be clearly seen that the input expression reproduced by the present invention has a smaller vertex position error in this region compared to existing solutions.

[0115] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An automatic facial binding method based on skin decomposition, characterized in that: Includes the following steps S1: Joint initialization: Input facial 4D expressions and template binding, and use offset scaling to calculate the joint positions of the character's head mesh; S2: Skin Decomposition: S21: Implement the identity transformation of joint rotation matrices based on quaternions; S22: Update the joint transformation matrix; S221: The objective function E is updated by the transformation matrix as shown in Equation (1a). A Perform joint transformation matrix calculation for 4D facial expressions; E A =E M +γE N +λE V +βE J (1a) The E M The constraint designed to minimize vertex position reconstruction error, the E V For the vertex normal transformation direction constraint, γ, λ, and β are the regularization coefficients of each constraint, all greater than or equal to 0, and are also adjustable parameters. N For the surface normal constraint term, the E J For joint soft constraint; S222: As shown in formula (1b), in E M In the process, the vertices of the key region are set as the set of vertices with the initial maximum influence, which is defined as I0. For other vertices in the head mesh of the 4D facial expression character, their influence is determined by the distance d. i It decays exponentially, at a distance of d i This represents the shortest path distance between the i-th vertex and the nearest vertex in the set of vertices in the critical region; The attenuation formula is: Where τ>0 is a parameter controlling the decay rate, and e is a natural constant; Ensure that the minimum influence of a vertex is not lower than 1.0; s represents the total number of other arbitrary emojis in all inputs, and m represents the number of vertices for each emoji, where m is the number of vertices for the k-th emoji. k The position of the i-th vertex in the sequence k = 1...s is used This indicates that j is the j-th joint. The weights of the neutral character model are represented by u, where u is the position of the i-th vertex of the neutral expression u. i This indicates that the neutral expression u transforms into the k-th expression v. k The transformation matrix of the j-th joint is S223: As shown in formula (1d), in EV, It is the input k-th character expression grid {v k The unit normal vector of the i-th vertex in the sequence k = 1...s. This describes the normal vector of the i-th vertex in the neutral mesh u of the character, which is transformed into the normal vector of the i-th vertex of the k-th expression under the influence of all control joint rotation matrices {R}, where w j The weight coefficients of the corresponding joints are represented. To ensure that the final normal vector is still a unit normal vector, the above results are normalized. The The modulus of the above results is given, and E in the above formula (1a) is given. M E N E V and E J Limited by S23: The objective function for updating weights based on the joint weight distribution is cyclically optimized with the updated joint transformation matrix; S3: Facial Component Migration: This feature utilizes radial basis functions to migrate these components. By selecting control points on the head mesh of the template, Gaussian functions are integrated into the radial basis functions to calculate the deformation of the components from the template to a specific character.

2. The automatic facial binding method based on skin decomposition according to claim 1, characterized in that: In step S23, the weights are updated using the weight update objective function in formula (2a), and E in formula (2a) W The specific details are shown in formula (2e); E B =E M +γE N +λE V +αE W (2a) And E in the above formula (2a) M E N E V and E W Limited by The weight of the j-th joint of the template model g relative to the i-th vertex is expressed as follows: The E W For weight distribution constraints.

3. The automatic facial binding method based on skin decomposition according to claim 2, characterized in that: The specific content of EN is shown in formula (1c): in It is the input k-th character expression grid {v k The unit normal vector of the f-th face in the sequence k = 1...s. It is the character binding weight w u The function refers to the neutral mesh u of the character utilizing the character-bound weight w. u The unit normal vector of the f-th face of the k-th expression is reproduced by deforming the joint transformation matrix {R, T}.

4. The automatic facial binding method based on skin decomposition according to claim 1, characterized in that: The E J The specific details are shown in formula (1e): Where β is used to balance E M and E J The parameters, as β increases, correspond to the actual joint position of the k-th expression. Deviation from expected joint position The smaller the degree, the better.

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