Face automatic binding method based on skin decomposition

Abstract

The invention relates to an automatic face binding method based on skin decomposition, which comprises the steps of S1, joint initialization: inputting a face 4D expression and template binding, and calculating a joint position of a role head grid by using offset scaling, S2, skin decomposition, S21, realizing equal transformation of a joint rotation matrix based on quaternion; s22, updating a joint transformation matrix; s3, face component migration: migration of the components is carried out by using a radial basis function (RBF), control points are selected on a head grid of a template, and a Gaussian function is integrated into the radial basis function to calculate deformation of the components from the template to a specific role; the method has the advantage of being suitable for high-fidelity facial animation production.

Description

Technical Field

[0001] The present invention belongs to the technical field of computer graphics, and particularly relates to a facial automatic binding method based on skin decomposition. Background Art

[0002] Currently, a research has proposed an automatic high-fidelity facial binding method, which can complete the binding process by combining skin decomposition from 4D expressions. This method takes a predefined binding template and the 4D expression of a character as inputs, initializes the joint positions using the prior information of template binding and migrates facial components, and optimizes the binding weights and reproduces the joint transformation matrix of the 4D expression in an alternating iterative manner. This method realizes skin decomposition by minimizing the reconstruction error of vertex positions, adds soft constraints on joint positions to limit the joint positions, and ensures that the joints only affect a small neighborhood range in the head mesh through hard constraints of fixed-weight sparse distribution. Experimental results show that this method can automatically generate high-fidelity facial bindings and effectively ensure the rationality of joint positions and weight distributions.

[0003] This research mainly designs the energy function based on the reconstruction error of the vertex positions of the expression mesh, only considering the consistency of the binding in reproducing the vertex positions of the input expression, without considering that the vertex normal transformation direction and weight distribution during the deformation process of the binding model will both affect the actual use of the model binding. For example, an incorrect vertex normal transformation direction during deformation will cause the mesh faces of the facial model to flip, which is obviously not conducive to animation production; uneven weight distribution will also cause the deformation of the model mesh points to be abrupt and unnatural, greatly increasing the difficulty of using the binding for animation production. Moreover, this research does not pay special attention to the detail consistency at the corners of the eyes, easily resulting in the problem that although the vertex positions at the corners of the eyes after model deformation are numerically less different from the real input expression, there is a relatively obvious visual difference. For example, the corners of the eyes of the actual input expression are closed, but although the vertex positions of the expression mesh reproduced by the solved binding model at the upper and lower eyelids are not much different numerically from the real input expression mesh, there is a relatively obvious visual difference due to the failure to achieve the closure of the upper and lower eyelids. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a facial automatic binding method based on skin decomposition applicable to high-fidelity facial animation production.

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

[0006] A facial automatic binding method based on skin decomposition includes the following steps

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

[0008] S2: Skin Decomposition:

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

[0010] S22: Update the joint transformation matrix;

[0011] S221: Solve the joint transformation matrix for the 4D facial expression through the objective function E updated by the transformation matrix in formula (1a) A for the joint transformation matrix of the 4D facial expression;

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

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

[0014] S222: As shown in formula (1b), in E M , the vertices in the key area are set as the vertex set with the initial maximum influence, and its initial influence is defined as I 0 . For the other vertices in the character's head mesh, their influence gradually decays exponentially according to the distance d i . The distance d i represents the shortest path distance between the i th vertex and the nearest vertex in the key area vertex set;

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

[0016]

[0017] The s represents the total number of all other arbitrary expressions of the input. The m represents that each expression has m vertices. The position of the i-th vertex of the {v k : k = 1... s} of the k-th expression is represented by , j is the j-th joint, is the weight of the character neutral model. The position of the i-th vertex of the neutral expression u is represented by ui Denote the transformation matrix of the j-th joint from the neutral expression u to the k-th expression v as k

[0018] S223: As shown in formula (1d), in E V , is the unit normal vector of the i-th vertex of the input k-th character expression mesh {v k : k = 1... s}, which describes that the normal vector of the i-th vertex in the character neutral mesh u is deformed 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 represents the weight coefficient of the corresponding joint. To ensure that the finally obtained normal vector is still a unit normal vector, the above result is normalized; j

[0019]

[0020] The said is the modulus length of the above result, and E in the above formula (1a) M , E N , E V and E J are restricted by

[0021] S23: Update the weights based on the weight update objective function of the joint weight distribution and cyclically optimize with the updated joint transformation matrix;

[0022] S3: Facial component migration: Use the radial basis function (RBF) to perform the migration of these components. By selecting control points on the head mesh of the template and integrating the Gaussian function into the radial basis function, calculate the deformation of the components from the template to a specific character.

[0023] Furthermore, in the step S23, the weights are updated through the weight update objective function in formula (2a), and the specific content of E in formula (2a) W is as 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]

[0029] The weight of the j-th joint of the template model g on the i-th vertex is expressed as

[0030] Furthermore, the specific content of the said E N is shown in formula (1c) as follows:

[0031]

[0032] Where is the unit normal vector of the f-th face of the k-th character expression mesh {v k : k = 1... s} of the input, is a function of the character binding weight w u , which means that the unit normal vector of the f-th face of the k-th expression reproduced by deforming the character neutral mesh u using the character binding weight w u and the joint transformation matrix {R, T}.

[0033] Furthermore, the specific content of the said E J is shown in formula (1e) as follows:

[0034]

[0035] Where β is a parameter used to balance E M and E J . As β increases, the degree of deviation of the actual joint position corresponding to the k-th expression from the expected joint position will be smaller.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] 1. By comprehensively considering the vertex normal transformation direction constraint, weight distribution constraint, and key area attention constraint, the present invention effectively improves the rationality, naturalness, and accuracy of automatic face binding. Among them, the vertex normal transformation direction constraint restricts the joint transformation matrix, making the joint deformation transition more natural and avoiding face flipping; the weight distribution constraint optimizes the smooth deformation of the vertices of the bound face model, reducing the sense of abruptness; the key area attention constraint imposes a higher vertex position error penalty on key parts (such as the corners of the eyes), solving the problem of the significant impact of small deformations in visually critical areas on the visual effect.

[0038] In summary, the present invention has the advantage of being applicable to high-fidelity facial animation production. Brief Description of the Drawings

[0039] Figure 1 It is a schematic diagram of the algorithm framework in the comparative example;

[0040] Figure 2 It is a schematic diagram of offset scaling;

[0041] Figure 3 It is a schematic diagram of the method framework of the present application;

[0042] Figure 4 It is a diagram of the black face phenomenon that appears when the binding solution result in the comparative example reproduces a certain input expression;

[0043] Figure 5 It is a comparison diagram of the vertex normal directions when the neutral expression is the same input expression in the comparative example solution and the solution of the present application;

[0044] Figure 6 It is a heat map of the error between the vertex normal direction when the neutral expression is the same input expression in the comparative example solution and the solution of the present application and the vertex normal direction of the real input expression;

[0045] Figure 7 It is a comparison diagram of the weight distribution of the same joint in the binding solution of the comparative example solution and the solution of the present application;

[0046] Figure 8 It is a schematic diagram of the influence of moving a certain joint to the same position on the mesh deformation in the comparative example solution and the solution of the present application;

[0047] Figure 9 It is a schematic diagram of the selected corner vertex region with the highest initial influence in the present application;

[0048] Figure 10 It is a comparison diagram of the corner region when the comparative example solution and the solution of the present application reproduce the input expression;

[0049] Figure 11 It is a heat map of the vertex position error between the corner region when the comparative example solution and the solution of the present application reproduce the input expression and the corner region of the real input expression. Detailed Description of the Preferred Embodiments

[0050] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0051] Embodiment 1

[0052] A facial automatic rigging method based on skin decomposition, with the input being a predefined rigging template and the 4D facial expressions of an actor, including the neutral expression u and a set of arbitrary expressions {v k : k = 1... s}. "4D expression" means not only using the static facial expressions of the actor, but also including the dynamic changes of the expressions during presentation. 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 positions of the joints of the actor's head mesh and the linear blend skin weights but also other facial components such as teeth and eyes.

[0053] The method includes the following steps:

[0054] S1: Joint initialization: As Figure 2 shown, use "offset scaling" to calculate the joint positions of the character's head mesh. Given the template neutral mesh g, traverse to obtain the vertex indices closest to the joints and the offsets between them. Combine the scale factor κ of the bounding box between the template neutral mesh g and the target neutral mesh u to calculate the initial positions b of all joints of the target neutral mesh u . In addition, the expected joint positions of other input expressions can also be calculated by the method of "offset scaling", thereby constraining the update of the joint transformation matrix in the skin decomposition step;

[0055] S2: Skin decomposition:

[0056] S21: Implement the identity transformation of the joint rotation matrix based on quaternions;

[0057] S22: Update the joint transformation matrix;

[0058] S221: Solve the joint transformation matrix of the facial 4D expression through the objective function E for updating the transformation matrix in formula (1a) A ;

[0059] E A = E M + γE N + λE V + βE J (1a)

[0060] The described E M is a constraint designed to minimize the vertex position reconstruction error, the E V is the vertex normal transformation direction constraint, the γ, λ, and β are the regularization coefficients of each constraint, all of which are greater than or equal to 0 and are also adjustable parameters, E N is the face normal constraint term, the E J is the joint soft constraint;

[0061] S222: As shown in formula (1b), in E M , the vertices of the key area are set as the set of vertices with the initial maximum influence, and its initial influence is defined as I0 . For other vertices in the character's head mesh, their influence gradually decays exponentially according to the distance d i . The distance d i represents the shortest path distance between the i -th vertex and the nearest vertex in the set of vertices of the key area;

[0062] The attenuation formula is: where τ＞0 is a parameter to control the attenuation rate, e is the natural constant; Ensure that the minimum influence of the vertex is not lower than 1.0;

[0063]

[0064] The s represents the total number of any other expressions of all inputs. The m represents that each expression has m vertices. The position of the i-th vertex of the {v k : k = 1... s} of the k-th expression is represented by . The j is the j-th joint. The weight of the j-th joint of the character's facial model u on the i-th vertex is represented by (i.e., skinning weight). The position of the i-th vertex of the neutral expression u is represented by ui. The transformation matrix of the j-th joint from the neutral expression u to the k-th expression v k is

[0065] where the specific content of the E N is shown in formula (1c):

[0066]

[0067] where is the unit normal vector of the f-th face of the k-th character expression mesh {v k : k = 1... s} of the input, is a function of the character binding weight w u , which refers to the unit normal vector of the f-th face of the k-th expression reproduced by deforming the character neutral mesh u using the character binding weight w u and the joint transformation matrix {R, T}.

[0068] S223: As shown in formula (1d), in E V is the k-th character expression mesh {v k: the unit normal vector of the i-th vertex of {k = 1... s}, describes the normal vector of the i-th vertex in the character-neutral mesh u, which is deformed 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 represents the weight coefficient of the corresponding joint. To ensure that the finally obtained normal vector is still a unit normal vector, the above result is normalized;

[0069]

[0070] the is the modulus length of the above result;

[0071] the E J is specifically shown in formula (1e):

[0072]

[0073] where β is a parameter used to balance E M and E J As β increases, the actual joint position corresponding to the k-th expression deviates from the expected joint position to a smaller extent

[0074] the E in the above formula (1a) M 、E N 、E V and E J are restricted by

[0075] S23: Update the weights based on the weight update objective function of the joint weight distribution and cycle-optimize with the updated joint transformation matrix;

[0076] Update the weights through the weight update objective function in formula (2a), and the E in formula (2a) W is specifically shown in formula (2e). The update of the weights and the update of the joint transformation matrix are staggered, which means that in the weight update step, the joint transformation matrix {R, T} remains fixed, and the character-binding weight w u is the only variable that needs to be optimized. Vice versa;

[0077] E B = E M + γE N + λE V + αE W (2a)

[0078] where,

[0079]

[0080] Limited by

[0081]

[0082] The weight of the j-th joint of the template model g on the i-th vertex is denoted as

[0083] S4: Facial component migration: Use the Radial Basis Function (RBF) to perform the migration of these components. By selecting control points on the head mesh of the template and integrating the Gaussian function into the radial basis function, calculate the deformation of the components from the template to a specific character.

[0084] Comparative example

[0085] Existing facial automatic rigging schemes based on skin decomposition include the following: The input is a predefined rigging template and the actor's 4D facial expressions, including the neutral expression and a set of arbitrary expressions. "4D expression" means not only using the actor's static facial expressions but also including the dynamic changes of the expressions during presentation. 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 positions of the joints and the linear blend skin weights of the actor's head mesh but also other facial components such as teeth and eyes.

[0086] As Figure 1 As shown, the algorithm framework consists of three steps: joint initialization, skin decomposition, and facial component migration. As shown in Equation (3a), the input facial 4D expressions include the character's neutral expression u and the character's other arbitrary expressions {v k : k = 1... s}, and each expression has m vertices;

[0087] The position of the i-th vertex of the neutral expression u is denoted as u i denoted, and the position of the i-th vertex of the k-th expression {v k : k = 1... s} is denoted as denoted, s represents the total number of all input other arbitrary expressions, the reference template mesh g is bound by n joints, these joints are indexed by j, the initial position of the joint is denoted as b g denoted, the initial position of the character joint calculated based on offset scaling is denoted as b u to represent, w ij represents the weight of the j-th joint on the i-th vertex, and the skin weights of the joint and the character expression are denoted as w g and w u respectively, w u takes w g as the initial value;

[0088] The weight of the j-th joint of the character facial model on the i-th vertex is denoted as The weight of the j-th joint of the target facial model on the i-th vertex is denoted as Deforming from the neutral expression u to the k-th expression v k The transformation matrix of the j-th joint is where is the rotation matrix, is the translation vector;

[0089] The binding weight w of the character facial model u and the joint transformation matrix {R, T} will be alternately updated until the maximum number of iterations specified by the user or the model fitting term E M converges. The detailed definition of E M is shown in formula (3b). The facial component c of the template neutral mesh g will be deformed based on the radial basis function to fit the neutral mesh of the character facial model. After deformation, the facial component of the neutral mesh of the character facial model is denoted by c u for representation.

[0090] Joint initialization: As Figure 2 shown, "offset scaling" is used to calculate the joint positions of the character head mesh. Given the neutral mesh g of the character facial model, traverse to obtain the vertex index closest to the joint and the offset between the two. Combine the scale factor κ of the bounding box between the neutral mesh g of the character facial model and the neutral mesh u of the target facial model to calculate the initial positions b of all joints of the neutral mesh of the target facial model u . In addition, the expected joint positions of other input expressions can also be calculated by the method of "offset scaling", thereby constraining the update of the joint transformation matrix in the skinning decomposition step.

[0091] Skinning decomposition. The energy function is shown in equation (3a). A joint soft constraint E M is imposed on the basis of the vertex position reconstruction error E J to determine the update of the joint transformation matrix. β is a parameter used to balance E M and E J . As β increases, the deviation of the actual joint position corresponding to the k-th expression from the expected joint position will be smaller. It should be noted that the expected joint position has been calculated in the joint initialization step.

[0092] E = E M + βE J (3a)

[0093] where

[0094]

[0095] Limited by

[0096]

[0097] 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 solution designs a fixed sparse distribution constraint as shown in Equation (3f);

[0098] First, use the weights of the template face model as the initial weights of the character face model to accelerate convergence. Second, only when is not equal to zero, the weights of the character face model will participate in the update process; otherwise, during the entire iteration process will remain zero. This constraint can avoid the error that the movement of a single joint causes the vertices of multiple regions of the head mesh of the character face model to move. When updating the weights, the joint transformation matrix remains unchanged, so only Equations (3b) and constraints (3d), (3e), (3f) need to be considered for optimization.

[0099] Facial component migration: In addition to the binding of the head mesh of the character face model, when the character changes, the facial components also need to be adjusted. Use radial basis functions (RBFs) to perform the migration of these components. By selecting control points on the head mesh of the template and integrating the Gaussian function into the radial basis function, the deformation of the components from the template to a specific character is calculated.

[0100] Compared with the comparative example, the present application has been optimized in the following three aspects:

[0101] As Figure 3 shown, the first aspect is to design the vertex normal transformation direction constraint E V , to avoid large flips and face-turning phenomena of the joints during the deformation process, ensure natural deformation transition, and improve the stability and rationality of the bound model deformation.

[0102] The second aspect is to introduce the weight distribution constraint E W , to make the deformation of the vertices smoother and more fluent, reduce the sense of abruptness, and enhance the naturalness of the animation effect.

[0103] The third aspect is to improve the vertex position reconstruction error for key visual areas such as the corners of the eyes, manifested as E with the focus area attention constraint M , to avoid the significant visual impact caused by the subtle differences in the key visual areas, and greatly improve the visual consistency of the expression reproduction.

[0104] Compared with the content of the comparative example, the technical solution of the present application has the following advantages:

[0105] 1) Vertex normal transformation direction constraint

[0106] As Figure 4 shown, the existing solution can achieve automatic binding of high-fidelity faces. However, if the vertex normals of the neutral expression are not unlocked, the model may exhibit black face phenomenon, that is, face flipping phenomenon when deformed into other input expressions. This is because the vertex normals do not point to the outside of the model. Therefore, based on the existing solution, the present invention adds a vertex normal transformation direction constraint E V to achieve a reasonable solution of the transformation matrix of the joint, so as to improve the usability of face binding.

[0107] The vertex normal transformation direction constraint term E V essentially restricts the rotation {R} of the joint so that the vertex normal transforms from the neutral u to the vertex normal of the target expression {v k : k = 1... s} and the vertex normal of the input target expression is consistent. This prevents the problem that the face normal direction is correct while the vertex normal points to the inside of the model.

[0108] Specifically, the difference from the face normal constraint term E N is that the vertex normal transformation direction constraint takes into account the change of the vertex normal direction when the bound model is deformed into other expressions. And the face normal constraint term E N since it is only designed to be determined by the relative positions between the deformed vertices, it cannot consider unreasonable situations during the deformation process.

[0109] The present invention has experimentally verified the result of whether to add the vertex normal transformation direction constraint and compared it with the scheme that only considers the vertex position reconstruction error and the face normal constraint. As Figure 5 and 6 shown, the error heat maps between the vertex normal directions of different schemes when reproducing the input expression and the vertex normal direction of the real input expression are respectively plotted.

[0110] 2) Weight distribution constraint term

[0111] Although the existing solution for calculating the automatic binding of high-fidelity faces can reproduce the input expression, there will be abrupt and discontinuous vertex deformations when the artist adjusts or moves the joints, which seriously affects the usability of the binding result. Therefore, based on the original solution, the present invention adds a weight distribution constraint term E W to ensure that the weight distribution of the vertices is as close as possible to the template weight distribution, improving the naturalness and stability of the animation effect.

[0112] The present invention has experimentally verified the results of whether to add weight distribution constraints. Specifically, by randomly selecting a joint and visualizing the influence distribution of the bound joint pairs solved by the present solution and the existing solution on the character model. As Figure 7 shown, compared with the original solution that does not consider weight distribution constraints, the skinning weights solved by the solution of the present invention are more consistent with the weight distribution of the template, and are smoother and more natural. Moreover, for the model bindings solved by both solutions, a joint is selected for the same movement. From Figure 8 it can be clearly seen that the model deformation of the solution of the present invention is more natural and has better stability, greatly improving the usability of the binding. On the contrary, the coherence between the vertices of the original solution is poor, which obviously does not conform to the prior knowledge that should be followed in the human face deformation process.

[0113] 3) Focus area attention constraint

[0114] Although the automatic binding solved by the existing solution considers the accuracy of reproducing the input expression vertex positions, it does not consider that in some key facial areas, even a small difference will cause a significant visual impact. For example, the opening and closing degree of the eyes. Therefore, the present invention achieves better visual consistency in reproducing the input expression by imposing stricter constraints on areas such as the eyelids. As Figure 9 shown, the vertex with the highest initial influence I 0 is selected. As shown in Equations (1b) and (2b), in order to ensure the smooth transition of the vertex importance in the eye area, an exponentially decaying method is designed to gradually decay the influence of the surrounding vertices.

[0115] The present invention has experimentally verified the solution of whether to add focus area attention constraints. Specifically, compared with the original solution that does not consider focus area attention constraints, the expression reproduced by the binding solved by the solution of the present invention is more consistent with the input expression truth value in the corner of the eye area. As Figure 10 shown, the eyes of the input expression reproduced by the present solution are closed in the same way as the input expression, while the existing solution without focus area attention constraints has a slightly open situation. As Figure 11 shown, the present invention has visualized the vertex position error of the vertices in the additional influence area, and it can also be clearly seen that the input expression reproduced by the solution of the present invention has a smaller vertex position error in this area compared with the existing solution.

[0116] Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A facial automatic binding method based on skin decomposition, characterized by: The following steps are included S1: Joint initialization: input facial 4D expression and template binding, and use offset scaling to calculate the joint position of the character head mesh; S2: Skin decomposition: S21: Implement identity transformation of joint rotation matrix based on quaternion; S22: Update joint transformation matrix; S221: The objective function E is updated by the transformation matrix as in formula (1a) A Solve the joint transformation matrix of facial 4D expressions; E A =E M +γE N +λE V +βE J (1a) The E M is a constraint designed to minimize the vertex position reconstruction error. V is the vertex normal transformation direction constraint, and the γ, λ, and β are the regularization coefficients of each constraint, all of which are greater than or equal to 0 and can be adjusted. N is the surface normal constraint term, the E J It is a soft constraint for joints; S222: As shown in formula (1b), in E M In the example, the focus area vertices are set to be the set of vertices with the initial maximum influence, and their initial influence is defined as I0 For other vertices in the face 4D expression character head mesh, their influence is based on the distance d i It decays exponentially, with a distance d i Indicates i The shortest path distance between a vertex and the nearest vertex in the key area vertex set; The attenuation formula is: in τ＞0 is the parameter that controls the decay rate, e is a natural constant; Make sure the minimum influence of a vertex does not fall below 1.0; The s represents the total number of all other arbitrary expressions input, the m represents that each expression has m vertices, and the {v k :k=1...s}The i-th vertex position is Indicates that j is the jth joint, is the weight of the character’s neutral model. The i-th vertex position of the neutral expression u is represented by u i Indicates that the transformation from the neutral expression u to the kth expression v k The transformation matrix of the j-th joint is S223: As shown in formula (1d), in E V middle, is the input k-th character expression grid {v k :k=1...s}, the unit normal vector of the i-th vertex, describes the normal vector of the i-th vertex in the character's neutral mesh u, which is deformed 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 Represents the weight coefficient of the corresponding joint. In order to ensure that the final normal vector is still a unit normal vector, the above results are normalized; Said is the modulus of the above result, and E in the above formula (1a) M 、E N 、E V and E J Limited by S23: updating the weights based on the weight update objective function of the joint weight distribution and optimizing cyclically with the updated joint transformation matrix; S3: Facial component transfer: Radial basis function (RBF) is used to transfer these components by selecting control points on the head mesh of the template and integrating Gaussian functions into the radial basis function to calculate the deformation of the components from the template to the specific character.

2. The automatic facial binding method based on skin decomposition according to claim 1, characterized in that: In step S23, the weight is updated by the weight update objective function in formula (2a), and E in formula (2a) W The specific content is 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 to the i-th vertex is expressed as The E W is the weight distribution constraint.

3. The facial automatic binding method based on skin decomposition according to claim 2, characterized in that: The E N The specific content is shown in formula (1c): in is the input k-th character expression grid {v k :k=1...s}, the unit normal vector of the fth face, is the role binding weight w u The function refers to the character neutral mesh u using the character binding weight w u And the joint transformation matrix {R, T} is deformed to reproduce the unit normal vector of the f-th face of the k-th expression.

4. The facial automatic binding method based on skin decomposition according to claim 1, characterized in that: The E J The specific content is shown in formula (1e): Among them, β is used to balance E M and E J As β increases, the actual joint position corresponding to the kth expression Deviation from expected joint position The degree will be smaller.

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