CN109859322B - Spectral attitude migration method based on deformation graph - Google Patents

Spectral attitude migration method based on deformation graph Download PDF

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CN109859322B
CN109859322B CN201910056771.5A CN201910056771A CN109859322B CN 109859322 B CN109859322 B CN 109859322B CN 201910056771 A CN201910056771 A CN 201910056771A CN 109859322 B CN109859322 B CN 109859322B
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尹梦晓
苏鹏
林振峰
杨锋
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Guangxi University
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Abstract

The invention discloses a spectral attitude migration method based on a deformation map, which comprises the following steps: 1) Simplifying a source grid by utilizing a grid simplification algorithm to generate a source grid deformation graph; 2) Performing coupling-alignment-and-basis-based spectral pose migration on a source grid by using a reference grid; 3) Generating a deformation graph after the attitude migration by using an optimized energy function according to the attitude migration result and the source grid deformation graph; 4) Deforming the source grid to generate a target grid by using an embedded deformation graph editing method according to the deformation graph generated after the posture migration; 5) And segmenting all regions with insufficient grid posture migration, and carrying out layered posture migration until the posture migration is sufficient. The method has better locality when the source grid is represented by using the embedded deformation graph editing method, and reduces the influence of the quality of the geometric proxy on the result to a certain extent; the sub grids are spliced by simple offset, orientation adjustment is not needed, and the quality of the target grid generated by posture migration is effectively improved.

Description

一种基于变形图的谱姿态迁移方法A Spectral Pose Migration Method Based on Deformation Graph

技术领域technical field

本发明涉及3D模型谱姿态迁移的技术领域，尤其是指一种基于变形图的谱姿态迁移方法。The present invention relates to the technical field of 3D model spectrum pose migration, in particular to a deformation graph based spectrum pose migration method.

背景技术Background technique

三维网格模型在3D打印、虚拟现实、娱乐游戏等方面有广泛应用。利用传统手工建模、扫描设备或建模软件很难快速准确地对复杂的几何形状进行建模。而对已有的网格模型进行编辑和重用,可以避免重新建模。作为基于样例的网格建模技术变形迁移和姿态迁移利用参考网格的已有姿态得到具有相似姿态的目标网格.但是如何准确的描述源网格模型姿态,自动引导目标网格模型变形也是一个具有挑战性的课题。3D mesh models are widely used in 3D printing, virtual reality, entertainment games, etc. It is difficult to quickly and accurately model complex geometries using traditional manual modeling, scanning equipment, or modeling software. Editing and reusing existing mesh models can avoid remodeling. As example-based mesh modeling techniques, deformation migration and pose migration use the existing pose of the reference mesh to obtain a target mesh with a similar pose. But how to accurately describe the pose of the source mesh model and automatically guide the deformation of the target mesh model It is also a challenging subject.

Lévy通过交换网格的拉普拉斯(Laplacian)矩阵的低频特征函数(即较小特征值对应的特征函数)对应的系数在具有相同连接关系的网格之间进行平凡的姿态迁移。但是由于源网格和参考网格的拉普拉斯特征基的差异，导致其表达结果出现明显差异。姿态迁移后得到的目标网格模型会出现严重扭曲和变形现象，并且姿态学习不够充分。Kovnatsky等优化两个连接关系不同的网格模型的拉普拉斯矩阵特征基，得到基于泛函映射的具有兼容性的耦合准调和基，然后交换两个网格的耦合准调和基的低频系数进行连接关系不同的、姿态相异的网格模型之间的姿态迁移。虽然该方法解决了由于特征基差异导致的形状扭曲现象，但是姿态学习依然不够充分。Yin等提出了细节保持的谱姿态迁移算法和多层迁移框架。该方法在基于耦合准调和基姿态迁移的基础上，结合基于广义中心坐标的子空间技术，用Cage做为几何代理降低求解规模，减少变形的自由度，保证求解的稳定性。为了解决姿态学习不充分的问题，Yin等提出分层姿态迁移策略，对迁移姿态不充分的区域进行分割，将原本不是大尺度的姿态转化为局部区域的大尺度姿态，再进行谱姿态迁移。从而获得较好的姿态迁移效果。但由于该方法使用Cage和均值坐标来表示源网格,而均值坐标不满足内部局部性,因此姿态迁移结果受Cage的影响较大。Lévy performs trivial pose migration between grids with the same connection relationship by exchanging the coefficients corresponding to the low-frequency eigenfunctions (ie, the eigenfunctions corresponding to the smaller eigenvalues) of the Laplacian matrix of the grid. However, due to the difference in the Laplacian eigenbase of the source grid and the reference grid, the expression results are obviously different. The target mesh model obtained after pose transfer will be severely distorted and deformed, and the pose learning is not sufficient. Kovnatsky et al. optimized the Laplacian matrix eigenbasis of two grid models with different connection relationships, obtained a compatible coupled quasi-harmonic basis based on functional mapping, and then exchanged the low-frequency coefficients of the coupled quasi-harmonic basis of the two grids Perform pose migration between mesh models with different connection relationships and different poses. Although this method solves the shape distortion phenomenon caused by the difference of feature bases, the pose learning is still insufficient. Yin et al. proposed a detail-preserving spectral pose transfer algorithm and a multi-layer transfer framework. Based on the transfer of coupled quasi-harmonic and base attitude, this method combines the subspace technology based on generalized central coordinates, and uses Cage as a geometric proxy to reduce the solution scale, reduce the degree of freedom of deformation, and ensure the stability of the solution. In order to solve the problem of insufficient pose learning, Yin et al. proposed a hierarchical pose transfer strategy, which segmented the regions with insufficient transfer poses, converted the original non-large-scale poses into large-scale poses in local areas, and then performed spectrum pose transfer. So as to obtain a better attitude transfer effect. However, since this method uses Cage and mean coordinates to represent the source grid, and the mean coordinates do not satisfy internal locality, the pose transfer results are greatly affected by Cage.

本发明提供一种基于变形图的谱姿态迁移方法，利用嵌入变形图编辑方法代替广义中心坐标的子空间技术，以变形图作为几何代理、测地距离为权重表示源网格。嵌入变形能较好地保持网格的几何细节，这在一定程度上降低几何代理对迁移结果的影响，从而提高迁移结果的质量。The present invention provides a spectral attitude migration method based on a deformed graph, which uses an embedded deformed graph editing method to replace the subspace technology of the generalized center coordinates, and uses the deformed graph as a geometric agent and geodesic distance as a weight to represent a source grid. Embedding deformation can better maintain the geometric details of the mesh, which reduces the influence of geometric agents on the migration results to a certain extent, thereby improving the quality of the migration results.

发明内容Contents of the invention

本发明的目的在于克服现有技术的缺点与不足，提出了一种基于变形图的谱姿态迁移方法，利用优化二次误差度量方法简化源网格得到变形图，再利用嵌入变形图编辑方法代替广义中心坐标的子空间技术，以变形图作为几何代理、测地距离为权重表示源网格。嵌入变形能较好地保持网格的几何细节，这在一定程度上降低几何代理对迁移结果的影响，从而提高迁移结果的质量。The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art, and proposes a spectral attitude migration method based on deformation graphs, which uses the optimized quadratic error measurement method to simplify the source grid to obtain deformation graphs, and then uses the embedded deformation graph editing method to replace A subspace technique for generalized central coordinates, using deformed graphs as geometric proxies and geodesic distances as weights to represent source grids. Embedding deformation can better maintain the geometric details of the mesh, which reduces the influence of geometric agents on the migration results to a certain extent, thereby improving the quality of the migration results.

为实现上述目的，本发明所提供的技术方案为：一种基于变形图的谱姿态迁移方法，包括以下步骤：In order to achieve the above object, the technical solution provided by the present invention is: a method for spectral posture migration based on deformation graph, comprising the following steps:

1)利用网格简化算法简化源网格生成源网格变形图；1) Use the grid simplification algorithm to simplify the source grid to generate the source grid deformation map;

2)利用参考网格对源网格进行基于耦合准调和基的谱姿态迁移；2) Using the reference grid to perform spectral pose migration based on the coupled quasi-harmonic basis for the source grid;

3)根据姿态迁移结果和源网格变形图利用最优化能量函数生成姿态迁移后变形图；3) According to the posture migration result and the source grid deformation diagram, the optimized energy function is used to generate the deformation diagram after posture migration;

4)根据姿态迁移后生成的变形图利用嵌入变形图编辑方法变形源网格生成目标网格；4) According to the deformation map generated after pose migration, use the embedded deformation map editing method to deform the source mesh to generate the target mesh;

5)分割所有网格姿态迁移不充分区域，根据步骤2)至步骤4)进行分层姿态迁移，直到姿态迁移充分为止。5) Segment all regions where the pose transfer is insufficient, and perform hierarchical pose transfer according to steps 2) to 4) until the pose transfer is sufficient.

在步骤1)中，利用优化二次误差度量算法，即QEM(quadric error metric) 算法简化源网格生成变形图，优化二次误差度量算法中网格每条边的总折叠代价定义为:In step 1), the optimized quadric error metric algorithm, that is, the QEM (quadric error metric) algorithm is used to simplify the source grid to generate a deformation graph. The total folding cost of each edge of the grid in the optimized quadric error metric algorithm is defined as:

cost(a,b)＝αQQEM(a,b)+βQF(a,b)+γQReg(a,b)+μQAre(a,b)cost(a,b)＝αQ QEM (a,b)+βQ F (a,b)+γQ Reg (a,b)+μQ Are (a,b)

式中，a、b分别是待折叠边的两个端点，α、β、γ、μ分别为标量权值， QQEM为QEM边折叠代价，QF是待折叠边折叠后相邻最小偏移程度边的偏移量，QReg为折叠边(a,b)→v时的正则性代价，QReg＝|Reg(NF(v))-max{Reg(NF(a)),Reg(NF(b))}|，NF(a)、NF(b)、NF(v)为顶点a、b、v的邻接三角形集合，Reg(tri)＝3-2R(tri)，R(tri)＝cos(∠α)+cos(∠β)+cos(∠γ )，为Δtri 的正则性，

Figure GDA0003831548120000031
其中S(tri)为三角形tri的面积。In the formula, a and b are the two endpoints of the edge to be folded respectively, α, β, γ, and μ are scalar weights respectively, Q QEM is the QEM edge folding cost, and Q F is the minimum adjacent offset after the edge to be folded is folded The offset of the degree edge, Q Reg is the regularity cost when folding the edge (a,b)→v, Q Reg ＝|Reg(NF (v))-max { Reg(NF ( a)),Reg ( NF (b))}|, NF (a), NF (b), and NF (v) are the set of adjacent triangles of vertices a, b, v, Reg(tri)= 3-2R (tri) , R(tri)＝cos(∠α)+cos(∠β)+cos(∠γ ), which is the regularity of Δtri,
Figure GDA0003831548120000031
where S(tri) is the area of triangle tri.

在步骤2)中，利用参考网格对源网格进行基于耦合准调和基的谱姿态迁移，包括以下步骤：In step 2), the spectral attitude migration based on the coupled quasi-harmonic basis is performed on the source grid using the reference grid, including the following steps:

2.1)计算输入参考网格M、源网格M′的拉普拉斯矩阵及其对应的谱与特征函数，计算变形图G的拉普拉斯矩阵；2.1) Calculate the Laplace matrix of the input reference grid M, the source grid M' and their corresponding spectrum and characteristic functions, and calculate the Laplace matrix of the deformed graph G;

2.2)选取参考网格与源网格直接的特征对应点，计算参考网格与源网格之间的基于面积近似的对应点s个邻域点的指示函数作为网格之间的对应函数；2.2) Select the direct feature corresponding points between the reference grid and the source grid, and calculate the indicator function of the corresponding points based on area approximation between the reference grid and the source grid as the corresponding function between the grids;

2.3)优化参考网格M和源网格M′的拉普拉斯特征基，得到耦合准调和基 {φi M}、{φi M'}，利用公式

Figure GDA0003831548120000032
求出基于耦合准调和基的姿态迁移结果
Figure GDA0003831548120000033
式中，αi M和αi M'分别为M和M′的谱系数，k为交换αi M'的个数，|V'| 为M′的顶点个数。2.3) Optimize the Laplacian eigenbasis of the reference grid M and the source grid M′ to obtain the coupled quasi-harmonic basis {φ i M }, {φ i M' }, using the formula
Figure GDA0003831548120000032
Obtaining the Attitude Migration Results Based on Coupled Quasi-Harmonic Basis
Figure GDA0003831548120000033
In the formula, α i M and α i M' are the spectral coefficients of M and M' respectively, k is the number of exchanges α i M' , and |V'| is the number of vertices of M'.

在步骤3)中，利用耦合准调和基进行姿态迁移后，将姿态迁移结果利用最优化能量函数

Figure GDA0003831548120000034
求出姿态迁移后的变形图，式中顶点约束项
Figure GDA0003831548120000041
保拉普拉斯坐标项
Figure GDA0003831548120000042
缩放约束项
Figure GDA0003831548120000043
Q为测地距离权重矩阵，
Figure GDA0003831548120000044
为所求解的变形图，
Figure GDA0003831548120000045
为待求解的变形图顶点集合，
Figure GDA0003831548120000046
为
Figure GDA0003831548120000047
的顶点个数，
Figure GDA0003831548120000048
为基于耦合准调和基进行姿态迁移的结果，
Figure GDA0003831548120000049
为旋转变换矩阵，δi G为变形图G的拉普拉斯坐标，
Figure GDA00038315481200000410
为所求解变形图的拉普拉斯坐标，
Figure GDA00038315481200000411
为
Figure GDA00038315481200000412
的缩放矩阵，λ1、λ2为标量权值。In step 3), after using the coupled quasi-harmonic basis for attitude migration, the attitude migration result is used to optimize the energy function
Figure GDA0003831548120000034
Find the deformation graph after attitude migration, where the vertex constraint term
Figure GDA0003831548120000041
Paulaplacian coordinate term
Figure GDA0003831548120000042
scale constraints
Figure GDA0003831548120000043
Q is the geodesic distance weight matrix,
Figure GDA0003831548120000044
is the deformation graph to be solved,
Figure GDA0003831548120000045
is the vertex set of the deformed graph to be solved,
Figure GDA0003831548120000046
for
Figure GDA0003831548120000047
the number of vertices of
Figure GDA0003831548120000048
is the result of attitude transfer based on the coupled quasi-harmonic basis,
Figure GDA0003831548120000049
is the rotation transformation matrix, δ i G is the Laplace coordinates of the deformed graph G,
Figure GDA00038315481200000410
is the Laplace coordinates of the solved deformation graph,
Figure GDA00038315481200000411
for
Figure GDA00038315481200000412
The scaling matrix of , λ 1 , λ 2 are scalar weights.

在步骤4)中，将求解得到的变形图利用嵌入变形图编辑方法变形源网格生成目标网格，包括以下步骤：In step 4), the obtained deformation map is transformed into a target mesh by using the embedded deformation map editing method to generate a target mesh, including the following steps:

4.1)利用最小化能量函数

Figure GDA00038315481200000413
优化姿态迁移结果得到源网格变形的旋转平移矩阵，其中
Figure GDA00038315481200000414
为
Figure GDA00038315481200000415
的顶点个数，旋转项
Figure GDA00038315481200000416
单个顶点旋转项 Rot(Rj)＝(c1·c2)2+(c1·c3)2+(c2·c3)2+(c1·c2)2+(c1·c1-1)2+(c2·c2-1)2+(c3·c3-1)2,c1、c2和c3是变形图顶点处旋转矩阵Rj的列向量，规则化项
Figure GDA00038315481200000417
N(j)为顶点vj的邻域，t 为平移变换，αjn＝1.0，顶点约束项
Figure GDA00038315481200000418
Figure GDA00038315481200000419
为生成的目标网格
Figure GDA00038315481200000420
上的顶点，
Figure GDA00038315481200000421
为变形图
Figure GDA00038315481200000422
的顶点，wrot、wreg、wcon为标量权值；4.1) Using the minimized energy function
Figure GDA00038315481200000413
The rotation and translation matrix of the source mesh deformation is obtained by optimizing the attitude transfer result, where
Figure GDA00038315481200000414
for
Figure GDA00038315481200000415
The number of vertices, the rotation term
Figure GDA00038315481200000416
Single vertex rotation item Rot(R j )＝(c 1 ·c 2 ) 2 +(c 1 ·c 3 ) 2 +(c 2 ·c 3 ) 2 +(c 1 ·c 2 ) 2 +(c 1 · c 1 -1) 2 +(c 2 ·c 2 -1) 2 +(c 3 ·c 3 -1) 2 , c 1 , c 2 and c 3 are the column vectors of the rotation matrix R j at the vertices of the deformed graph, regularization term
Figure GDA00038315481200000417
N(j) is the neighborhood of vertex v j , t is translation transformation, α jn =1.0, vertex constraint item
Figure GDA00038315481200000418
Figure GDA00038315481200000419
The target mesh generated for
Figure GDA00038315481200000420
apex on
Figure GDA00038315481200000421
is a deformation map
Figure GDA00038315481200000422
vertex, w rot , w reg , w con are scalar weights;

4.2)得到旋转平移矩阵后利用公式

Figure GDA00038315481200000423
计算目标网格
Figure GDA00038315481200000424
的顶点集
Figure GDA00038315481200000425
其中wj(vl')为测地距离权重，
Figure GDA00038315481200000426
为旋转矩阵，
Figure GDA00038315481200000427
为平移矩阵，vl'为源网格的顶点，gj(vi')是与源网格顶点vi'测地距离最近的 m个变形图G上的顶点集合，
Figure GDA00038315481200000428
为所求最终目标网格上的顶点。4.2) After obtaining the rotation and translation matrix, use the formula
Figure GDA00038315481200000423
Compute Target Grid
Figure GDA00038315481200000424
Vertex set of
Figure GDA00038315481200000425
where w j (v l ') is the geodesic distance weight,
Figure GDA00038315481200000426
is the rotation matrix,
Figure GDA00038315481200000427
is the translation matrix, v l ' is the vertex of the source grid, g j (v i ') is the set of vertices on the m deformed graph G with the closest geodesic distance to the source grid vertex v i ',
Figure GDA00038315481200000428
is the vertex on the desired final target mesh.

在步骤5)中，分割参考网格、生成的目标网格及其变形图姿态迁移不充分区域，根据步骤2)至步骤4)进行分层姿态迁移，直到姿态迁移充分为止，包括如下步骤：In step 5), segment the reference grid, the generated target grid and its deformed graph with insufficient pose transfer regions, perform layered pose transfer according to step 2) to step 4), until the pose transfer is sufficient, including the following steps:

5.1)选取姿态学习不充分的局部网格,将对应的参考网格M、生成的目标网格M′、变形图

Figure GDA0003831548120000051
进行分割,得到对应的局部子网格S、S′和Gs；5.1) Select a local grid with insufficient attitude learning, and combine the corresponding reference grid M, the generated target grid M′, and the deformation map
Figure GDA0003831548120000051
Carry out segmentation to obtain the corresponding local sub-grids S, S′ and G s ;

5.2)利用步骤2)至步骤3)求出局部变形图Gs姿态迁移后的变形图

Figure GDA0003831548120000052
5.2) Use steps 2) to 3) to obtain the deformation map after the local deformation map G s posture migration
Figure GDA0003831548120000052

5.3)计算Gs分割边界顶点位置在姿态迁移前后的平均偏移量，将其添加到

Figure GDA0003831548120000053
的相应顶点；5.3) Calculate the average offset of the G s segmentation boundary vertex position before and after attitude migration, and add it to
Figure GDA0003831548120000053
the corresponding vertices of

5.4)利用

Figure GDA0003831548120000054
的顶点信息更新变形图
Figure GDA0003831548120000055
5.4) Use
Figure GDA0003831548120000054
The vertex information updates the deformed graph
Figure GDA0003831548120000055

5.5)利用步骤4)得到最终姿态迁移结果。5.5) Use step 4) to obtain the final pose transfer result.

本发明与现有技术相比，具有如下优点与有益效果：Compared with the prior art, the present invention has the following advantages and beneficial effects:

1、本发明使用优化二次误差度量(quadric error metric,QEM)算法简化源网格生成顶点分布均匀变形图，在驱动源网格变形时能产生更好的效果。1. The present invention uses an optimized quadric error metric (QEM) algorithm to simplify the source grid to generate a vertex distribution uniform deformation map, which can produce better results when driving the deformation of the source grid.

2、本发明利用嵌入变形编辑方法代替广义中心坐标的子空间技术,以变形图作为几何代理、测地距离权重表示源网格，有效提高姿态迁移生成目标网格质量。2. The present invention uses the embedded deformation editing method to replace the subspace technology of the generalized center coordinates, uses the deformation graph as a geometric proxy, and uses geodesic distance weights to represent the source grid, effectively improving the quality of the target grid generated by attitude migration.

3、本发明在分层姿态迁移时，直接平移局部区域网格(子网格)进行与整体网格的拼接，不必进行朝向调整。3. The present invention directly translates the grid (sub-grid) of the local area to splice with the overall grid when the layered attitude is migrated, without orientation adjustment.

附图说明Description of drawings

图1为本发明姿态迁移流程图。Fig. 1 is a flow chart of attitude transfer in the present invention.

图2为本发明姿态迁移流程示意图。Fig. 2 is a schematic diagram of the attitude transfer process of the present invention.

图3为本发明进行基于耦合准调和基进行姿态迁移结果示意图。Fig. 3 is a schematic diagram of the posture transfer results based on the coupled quasi-harmonic basis in the present invention.

图4为本发明姿态迁移变形结果图示意图。Fig. 4 is a schematic diagram of the posture transfer deformation result diagram of the present invention.

具体实施方式detailed description

下面结合具体实施例对本发明作进一步说明。The present invention will be further described below in conjunction with specific examples.

如图1和图2所示，本实施例所提供的基于变形图的谱姿态迁移方法，输入网格和源网格，其包括以下步骤：As shown in Fig. 1 and Fig. 2, the spectrum pose migration method based on deformation map provided by this embodiment, input grid and source grid, it includes the following steps:

1)利用优化二次误差度量(quadric error metric,QEM)算法简化源网格生成顶点分布均匀的变形图，优化二次误差度量算法中网格每条边的总折叠代价定义为:1) Use the optimized quadric error metric (QEM) algorithm to simplify the source grid to generate a deformed graph with uniform distribution of vertices. The total folding cost of each edge of the grid in the optimized quadric error metric algorithm is defined as:

cost(a,b)＝αQQEM(a,b)+βQF(a,b)+γQReg(a,b)+μQAre(a,b)cost(a,b)＝αQ QEM (a,b)+βQ F (a,b)+γQ Reg (a,b)+μQ Are (a,b)

式中，a、b分别是待折叠边的两个端点，α、β、γ、μ分别为标量权值，QQEM为QEM边折叠代价，QF是待折叠边折叠后相邻最小偏移程度边的偏移量，QReg为折叠边(a,b)→v时的正则性代价，QReg＝|Reg(NF(v))-max{Reg(NF(a)),Reg(NF(b))}|， NF(a)、NF(b)、NF(v)为顶点a、b、v的邻接三角形集合，Reg(tri)＝3-2R(tri)， R(tri)＝cos(∠α)+cos(∠β)+cos(∠γ)，为Δtri的正则性，

Figure GDA0003831548120000061
其中S(tri)为三角形tri的面积。In the formula, a and b are the two endpoints of the edge to be folded respectively, α, β, γ, and μ are scalar weights respectively, Q QEM is the QEM edge folding cost, and Q F is the minimum adjacent offset after the edge to be folded is folded The offset of the degree edge, Q Reg is the regularity cost when folding the edge (a,b)→v, Q Reg ＝|Reg(NF (v))-max { Reg(NF ( a)),Reg ( NF (b))}|, NF (a), NF (b), and NF (v) are the set of adjacent triangles of vertices a, b, v, Reg(tri)= 3-2R (tri) , R(tri)＝cos(∠α)+cos(∠β)+cos(∠γ), which is the regularity of Δtri,
Figure GDA0003831548120000061
where S(tri) is the area of triangle tri.

2)利用参考网格对源网格进行基于耦合准调和基的谱姿态迁移，包括以下步骤：2) Using the reference grid to perform spectral attitude migration based on the coupled quasi-harmonic basis for the source grid, including the following steps:

2.1)计算输入参考网格M、源网格M′的拉普拉斯矩阵及其对应的谱与特征函数，计算变形图G的拉普拉斯矩阵；2.1) Calculate the Laplace matrix of the input reference grid M, the source grid M' and their corresponding spectrum and characteristic functions, and calculate the Laplace matrix of the deformed graph G;

2.2)选取参考网格与源网格直接的特征对应点，计算参考网格与源网格之间的基于面积近似的对应点s个邻域点的指示函数作为网格之间的对应函数；2.2) Select the direct feature corresponding points between the reference grid and the source grid, and calculate the indicator function of the corresponding points based on area approximation between the reference grid and the source grid as the corresponding function between the grids;

2.3)优化参考网格M和源网格M′的拉普拉斯特征基，得到耦合准调和基 {φi M}、{φi M'}，利用公式

Figure GDA0003831548120000062
求出基于耦合准调和基的姿态迁移结果
Figure GDA0003831548120000063
式中，αi M和αi M'分别为M和M'的谱系数，k为交换αi M'的个数，|V'| 为M′的顶点个数。生成的基于耦合准调和基的谱姿态迁移结果如图3所示。2.3) Optimize the Laplacian eigenbasis of the reference grid M and the source grid M′ to obtain the coupled quasi-harmonic basis {φ i M }, {φ i M' }, using the formula
Figure GDA0003831548120000062
Obtaining the Attitude Migration Results Based on Coupled Quasi-Harmonic Basis
Figure GDA0003831548120000063
In the formula, α i M and α i M' are the spectral coefficients of M and M' respectively, k is the number of exchanges α i M' , and |V'| is the number of vertices of M'. The resulting spectral pose transfer results based on coupled quasi-harmonic basis are shown in Fig. 3.

3)利用耦合准调和基进行姿态迁移后，将姿态迁移结果利用最优化能量函数

Figure GDA0003831548120000071
求出姿态迁移后的变形图，如图4所示，式中顶点约束项
Figure GDA0003831548120000072
保拉普拉斯坐标项
Figure GDA0003831548120000073
缩放约束项
Figure GDA0003831548120000074
Q为测地距离权重矩阵，
Figure GDA0003831548120000075
为所求解的变形图，
Figure GDA0003831548120000076
为待求解的变形图顶点集合，
Figure GDA0003831548120000077
为
Figure GDA0003831548120000078
的顶点个数，
Figure GDA0003831548120000079
为基于耦合准调和基进行姿态迁移的结果，
Figure GDA00038315481200000710
为旋转变换矩阵，δi G为变形图G的拉普拉斯坐标，
Figure GDA00038315481200000711
为所求解变形图的拉普拉斯坐标，
Figure GDA00038315481200000712
为
Figure GDA00038315481200000713
的缩放矩阵，λ1、λ2为标量权值。3) After using the coupled quasi-harmonic basis for attitude migration, the attitude migration result is used to optimize the energy function
Figure GDA0003831548120000071
Calculate the deformation graph after posture migration, as shown in Figure 4, where the vertex constraint term
Figure GDA0003831548120000072
Paulaplacian coordinate term
Figure GDA0003831548120000073
scale constraints
Figure GDA0003831548120000074
Q is the geodesic distance weight matrix,
Figure GDA0003831548120000075
is the deformation graph to be solved,
Figure GDA0003831548120000076
is the vertex set of the deformed graph to be solved,
Figure GDA0003831548120000077
for
Figure GDA0003831548120000078
the number of vertices of
Figure GDA0003831548120000079
is the result of attitude transfer based on the coupled quasi-harmonic basis,
Figure GDA00038315481200000710
is the rotation transformation matrix, δ i G is the Laplace coordinates of the deformed graph G,
Figure GDA00038315481200000711
is the Laplace coordinates of the solved deformation graph,
Figure GDA00038315481200000712
for
Figure GDA00038315481200000713
The scaling matrix of , λ 1 , λ 2 are scalar weights.

4)将求解得到的变形图利用嵌入变形图编辑方法变形源网格生成目标网格，包括以下步骤：4) Deform the obtained deformation graph by using the embedded deformation graph editing method to deform the source grid to generate the target grid, including the following steps:

4.1)利用最小化能量函数

Figure GDA00038315481200000714
优化姿态迁移结果得到源网格变形的旋转平移矩阵，其中
Figure GDA00038315481200000715
为
Figure GDA00038315481200000716
的顶点个数，旋转项
Figure GDA00038315481200000717
单个顶点旋转项 Rot(Rj)＝(c1·c2)2+(c1·c3)2+(c2·c3)2+(c1·c2)2+(c1·c1-1)2+(c2·c2-1)2+(c3·c3-1)2,c1、c2和c3是变形图顶点处旋转矩阵Rj的列向量，规则化项
Figure GDA00038315481200000718
N(j)为顶点vj的邻域，t 为平移变换，αjn＝1.0，顶点约束项
Figure GDA00038315481200000719
Figure GDA00038315481200000720
为生成的目标网格
Figure GDA00038315481200000721
上的顶点，
Figure GDA00038315481200000722
为变形图
Figure GDA00038315481200000723
的顶点，wrot、wreg、wcon为标量权值；4.1) Using the minimized energy function
Figure GDA00038315481200000714
The rotation and translation matrix of the source mesh deformation is obtained by optimizing the attitude transfer result, where
Figure GDA00038315481200000715
for
Figure GDA00038315481200000716
The number of vertices, the rotation term
Figure GDA00038315481200000717
Single vertex rotation item Rot(R j )＝(c 1 ·c 2 ) 2 +(c 1 ·c 3 ) 2 +(c 2 ·c 3 ) 2 +(c 1 ·c 2 ) 2 +(c 1 · c 1 -1) 2 +(c 2 ·c 2 -1) 2 +(c 3 ·c 3 -1) 2 , c 1 , c 2 and c 3 are the column vectors of the rotation matrix R j at the vertices of the deformed graph, regularization term
Figure GDA00038315481200000718
N(j) is the neighborhood of vertex v j , t is translation transformation, α jn =1.0, vertex constraint item
Figure GDA00038315481200000719
Figure GDA00038315481200000720
The target mesh generated for
Figure GDA00038315481200000721
apex on
Figure GDA00038315481200000722
is a deformation map
Figure GDA00038315481200000723
vertex, w rot , w reg , w con are scalar weights;

4.2)得到旋转平移矩阵后利用公式

Figure GDA00038315481200000724
计算目标网格
Figure GDA00038315481200000725
的顶点集
Figure GDA00038315481200000726
其中wj(vl')为测地距离权重，
Figure GDA00038315481200000727
为旋转矩阵，
Figure GDA00038315481200000728
为平移矩阵，vl'为源网格的顶点，gj(vi')是与源网格顶点vi'测地距离最近的 m个变形图G上的顶点集合，
Figure GDA00038315481200000729
为所求最终目标网格上的顶点。4.2) After obtaining the rotation and translation matrix, use the formula
Figure GDA00038315481200000724
Compute Target Grid
Figure GDA00038315481200000725
Vertex set of
Figure GDA00038315481200000726
where w j (v l ') is the geodesic distance weight,
Figure GDA00038315481200000727
is the rotation matrix,
Figure GDA00038315481200000728
is the translation matrix, v l ' is the vertex of the source grid, g j (v i ') is the set of vertices on the m deformed graph G with the closest geodesic distance to the source grid vertex v i ',
Figure GDA00038315481200000729
is the vertex on the desired final target mesh.

生成的基于变形图的谱姿态迁移低频姿态迁移结果如图2中的步骤2-4所示。The resulting low-frequency pose transfer results for spectral pose transfer based on deformation maps are shown in steps 2-4 in Figure 2.

5)分割参考网格、生成的目标网格及其变形图姿态迁移不充分区域，根据步骤2)至步骤4)进行分层姿态迁移，直到姿态迁移充分为止，包括如下步骤：5) Segment the reference grid, the generated target grid and its deformed graph for insufficient pose transfer areas, perform layered pose transfer according to step 2) to step 4), until the pose transfer is sufficient, including the following steps:

5.1)选取姿态学习不充分的局部网格,将对应的参考网格M、生成的目标网格M′、变形图

Figure GDA0003831548120000081
进行分割,得到对应的局部子网格S、S′和Gs；5.1) Select a local grid with insufficient attitude learning, and combine the corresponding reference grid M, the generated target grid M′, and the deformation map
Figure GDA0003831548120000081
Carry out segmentation to obtain the corresponding local sub-grids S, S′ and G s ;

5.2)利用步骤2)至步骤3)求出局部变形图Gs姿态迁移后的变形图

Figure GDA0003831548120000082
5.2) Use steps 2) to 3) to obtain the deformation map after the local deformation map G s posture migration
Figure GDA0003831548120000082

5.3)计算Gs分割边界顶点位置在姿态迁移前后的平均偏移量，将其添加到

Figure GDA0003831548120000083
的相应顶点；5.3) Calculate the average offset of the G s segmentation boundary vertex position before and after attitude migration, and add it to
Figure GDA0003831548120000083
the corresponding vertices of

5.4)利用

Figure GDA0003831548120000084
的顶点信息更新变形图
Figure GDA0003831548120000085
5.4) Use
Figure GDA0003831548120000084
The vertex information updates the deformed graph
Figure GDA0003831548120000085

5.5)利用步骤4)得到最终姿态迁移结果。5.5) Use step 4) to obtain the final pose transfer result.

分层姿态迁移过程及最终结果如图2中的步骤5所示。The hierarchical pose transfer process and the final result are shown in step 5 in Fig. 2.

综上所述，在采用以上方案后，本发明为三维模型姿态迁移提供了新的方法，利用嵌入变形图编辑方法表示源网格时具有较好的局部性，在一定程度上降低了几何代理质量对结果的影响；对子网格使用简单偏移拼接，不必进行朝向调整。有效提高姿态迁移生成目标网格的质量，具有实际推广价值，值得推广。To sum up, after adopting the above scheme, the present invention provides a new method for 3D model posture migration, and the editing method of embedding deformed graph has better locality when representing the source grid, which reduces the geometric proxy to a certain extent. The effect of quality on the result; using simple offset stitching for sub-grids, no orientation adjustments are necessary. Effectively improving the quality of the target grid generated by pose transfer has practical promotion value and is worth promoting.

以上所述实施例只为本发明之较佳实施例，并非以此限制本发明的实施范围，故凡依本发明之形状、原理所作的变化，均应涵盖在本发明的保护范围内。The above-described embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Therefore, all changes made according to the shape and principles of the present invention should be covered within the protection scope of the present invention.

Claims (2)

1.一种基于变形图的谱姿态迁移方法，其特征在于，包括以下步骤：1. A method for migrating spectrum posture based on deformation graph, it is characterized in that, comprising the following steps: 1)利用网格简化算法简化源网格生成源网格变形图；1) Use the grid simplification algorithm to simplify the source grid to generate the source grid deformation map; 利用优化二次误差度量算法，即QEM算法简化源网格生成变形图，优化二次误差度量算法中网格每条边的总折叠代价定义为：Using the optimized quadratic error measurement algorithm, that is, the QEM algorithm simplifies the source grid to generate a deformation graph, and the total folding cost of each edge of the grid in the optimized quadratic error measurement algorithm is defined as: cost(a，b)＝αQQEM(a，b)+βQF(a，b)+γQReg(a，b)+μQAre(a，b)cost(a,b)=αQ QEM (a,b)+βQ F (a,b)+γQ Reg (a,b)+μQ Are (a,b) 式中，a、b分别是待折叠边的两个端点，α、β、γ、μ分别为标量权值，QQEM为QEM边折叠代价，QF是待折叠边折叠后相邻最小偏移程度边的偏移量，QReg为折叠边(a，b)→v时的正则性代价，QReg＝|Reg(NF(v))-max{Reg(NF(a))，Reg(NF(b))}|，NF(a)、NF(b)、NF(v)为顶点a、b、v的邻接三角形集合，Reg(tri)＝3-2R(tri)，R(tri)＝cos(∠α)+cos(∠β)+cos(∠γ)，为三角形tri的正则性，
Figure FDA0003875400400000011
其中S(tri)为三角形tri的面积；In the formula, a and b are the two endpoints of the edge to be folded respectively, α, β, γ, and μ are scalar weights respectively, Q QEM is the QEM edge folding cost, and Q F is the minimum adjacent offset after the edge to be folded is folded The offset of the degree edge, Q Reg is the regularity cost when folding the edge (a, b)→v, Q Reg ＝|Reg(NF (v))-max { Reg(NF ( a)), Reg ( NF (b))}|, NF (a), NF (b), and NF (v) are the set of adjacent triangles of vertices a, b, v, Reg(tri)= 3-2R (tri) , R(tri)＝cos(∠α)+cos(∠β)+cos(∠γ), which is the regularity of triangle tri,
Figure FDA0003875400400000011
Where S(tri) is the area of triangle tri; 2)利用参考网格对源网格进行基于耦合准调和基的谱姿态迁移，包括以下步骤：2) Using the reference grid to perform spectral attitude migration based on the coupled quasi-harmonic basis for the source grid, including the following steps: 2.1)计算输入参考网格M、源网格M′的拉普拉斯矩阵及其对应的谱与特征函数，计算变形图G的拉普拉斯矩阵；2.1) Calculate the Laplace matrix of the input reference grid M, the source grid M' and their corresponding spectrum and characteristic functions, and calculate the Laplace matrix of the deformed graph G; 2.2)选取参考网格与源网格直接的特征对应点，计算参考网格与源网格之间的基于面积近似的对应点s个邻域点的指示函数作为网格之间的对应函数；2.2) Select the direct feature corresponding points between the reference grid and the source grid, and calculate the indicator function of the corresponding points based on area approximation between the reference grid and the source grid as the corresponding function between the grids; 2.3)优化参考网格M和源网格M′的拉普拉斯特征基，得到耦合准调和基{φi M}、{φi M′}，利用公式
Figure FDA0003875400400000012
求出基于耦合准调和基的姿态迁移结果
Figure FDA0003875400400000013
式中，αi M和αi M′分别为M和M′的谱系数，k为交换αi M′的个数，|V′|为M′的顶点个数；2.3) Optimize the Laplacian eigenbasis of the reference grid M and the source grid M′ to obtain the coupled quasi-harmonic basis {φ i M }, {φ i M′ }, using the formula
Figure FDA0003875400400000012
Obtaining the Attitude Migration Results Based on Coupled Quasi-Harmonic Basis
Figure FDA0003875400400000013
In the formula, α i M and α i M' are the spectral coefficients of M and M' respectively, k is the number of exchanges α i M' , |V'| is the number of vertices of M'; 3)根据姿态迁移结果和源网格变形图利用最优化能量函数生成姿态迁移后变形图；3) According to the posture migration result and the source grid deformation diagram, the optimized energy function is used to generate the deformation diagram after posture migration; 利用耦合准调和基进行姿态迁移后，将姿态迁移结果利用最优化能量函数
Figure FDA0003875400400000021
求出姿态迁移后的变形图，式中顶点约束项
Figure FDA0003875400400000022
拉普拉斯坐标项
Figure FDA0003875400400000023
缩放约束项
Figure FDA0003875400400000024
Q为测地距离权重矩阵，
Figure FDA0003875400400000025
为所求解的变形图，
Figure FDA0003875400400000026
为待求解的变形图顶点集合，
Figure FDA0003875400400000027
为
Figure FDA0003875400400000028
的顶点个数，
Figure FDA0003875400400000029
为基于耦合准调和基进行姿态迁移的结果，
Figure FDA00038754004000000210
为旋转变换矩阵，δi G为变形图G的拉普拉斯坐标，
Figure FDA00038754004000000211
为所求解变形图的拉普拉斯坐标，
Figure FDA00038754004000000212
为
Figure FDA00038754004000000213
的缩放矩阵，λ1、λ2为标量权值；After using the coupled quasi-harmonic basis for attitude migration, the attitude migration results are used to optimize the energy function
Figure FDA0003875400400000021
Find the deformation graph after attitude migration, where the vertex constraint term
Figure FDA0003875400400000022
Laplace coordinate term
Figure FDA0003875400400000023
scale constraints
Figure FDA0003875400400000024
Q is the geodesic distance weight matrix,
Figure FDA0003875400400000025
is the deformation graph to be solved,
Figure FDA0003875400400000026
is the vertex set of the deformed graph to be solved,
Figure FDA0003875400400000027
for
Figure FDA0003875400400000028
the number of vertices of
Figure FDA0003875400400000029
is the result of attitude transfer based on the coupled quasi-harmonic basis,
Figure FDA00038754004000000210
is the rotation transformation matrix, δ i G is the Laplace coordinates of the deformed graph G,
Figure FDA00038754004000000211
is the Laplace coordinates of the solved deformation graph,
Figure FDA00038754004000000212
for
Figure FDA00038754004000000213
The scaling matrix of , λ 1 , λ 2 are scalar weights; 4)根据姿态迁移后生成的变形图利用嵌入变形图编辑方法变形源网格生成目标网格；4) According to the deformation map generated after pose migration, use the embedded deformation map editing method to deform the source mesh to generate the target mesh; 将求解得到的变形图利用嵌入变形图编辑方法变形源网格生成目标网格，包括以下步骤：The deformation map obtained by solving is used to deform the source mesh to generate the target mesh by using the embedded deformation map editing method, including the following steps: 4.1)利用最小化能量函数
Figure FDA00038754004000000214
优化姿态迁移结果得到源网格变形的旋转平移矩阵，其中
Figure FDA00038754004000000215
为变形图
Figure FDA00038754004000000216
的顶点个数，旋转项
Figure FDA00038754004000000217
单个顶点旋转项Rot(Rj)＝(c1·c2)2+(c1·c3)2+(c2·c3)2+(c1·c2)2+(c1·c1-1)2+(c2·c2-1)2+(c3·c3-1)2，c1、c2和c3是变形图顶点处旋转矩阵Rj的列向量，规则化项
Figure FDA00038754004000000218
N(j)为顶点vj的邻域，t为平移变换，αjn＝1.0，顶点约束项
Figure FDA00038754004000000219
Figure FDA00038754004000000220
为生成的目标网格
Figure FDA00038754004000000221
上的顶点，
Figure FDA00038754004000000222
为变形图
Figure FDA00038754004000000223
的顶点，wrot、wreg、wcon为标量权值；4.1) Using the minimized energy function
Figure FDA00038754004000000214
The rotation and translation matrix of the source mesh deformation is obtained by optimizing the attitude transfer result, where
Figure FDA00038754004000000215
is a deformation map
Figure FDA00038754004000000216
The number of vertices, the rotation term
Figure FDA00038754004000000217
Single vertex rotation item Rot(R j )＝(c 1 ·c 2 ) 2 +(c 1 ·c 3 ) 2 +(c 2 ·c 3 ) 2 +(c 1 ·c 2 ) 2 +(c 1 · c 1 -1) 2 +(c 2 ·c 2 -1) 2 +(c 3 ·c 3 -1) 2 , c 1 , c 2 and c 3 are the column vectors of the rotation matrix R j at the vertices of the deformed graph, regularization term
Figure FDA00038754004000000218
N(j) is the neighborhood of vertex v j , t is translation transformation, α jn =1.0, vertex constraint item
Figure FDA00038754004000000219
Figure FDA00038754004000000220
The target mesh generated for
Figure FDA00038754004000000221
apex on
Figure FDA00038754004000000222
is a deformation map
Figure FDA00038754004000000223
vertex, w rot , w reg , w con are scalar weights; 4.2)得到旋转平移矩阵后利用公式
Figure FDA0003875400400000031
计算目标网格
Figure FDA0003875400400000032
的顶点集
Figure FDA0003875400400000033
其中wj(vj′)为测地距离权重，
Figure FDA0003875400400000034
为旋转矩阵，
Figure FDA0003875400400000035
为平移矩阵，vl′为源网格的顶点，gj(vi′)是与源网格顶点vi′测地距离最近的m个变形图G上的顶点集合，
Figure FDA0003875400400000036
为所求最终目标网格上的顶点；4.2) After obtaining the rotation and translation matrix, use the formula
Figure FDA0003875400400000031
Compute Target Grid
Figure FDA0003875400400000032
Vertex set of
Figure FDA0003875400400000033
where w j (v j ′) is the geodesic distance weight,
Figure FDA0003875400400000034
is the rotation matrix,
Figure FDA0003875400400000035
is the translation matrix, v l ′ is the vertex of the source grid, g j (v i ′) is the set of vertices on the m deformed graph G with the closest geodesic distance to the source grid vertex v i ′,
Figure FDA0003875400400000036
is the vertex on the desired final target grid; 5)分割所有网格姿态迁移不充分区域，根据步骤2)至步骤4)进行分层姿态迁移，直到姿态迁移充分为止。5) Segment all regions where the pose transfer is insufficient, and perform hierarchical pose transfer according to steps 2) to 4) until the pose transfer is sufficient. 2.根据权利要求1所述的一种基于变形图的谱姿态迁移方法，其特征在于：在步骤5)中，分割参考网格、生成的目标网格及其变形图姿态迁移不充分区域，根据步骤2)至步骤4)进行分层姿态迁移，直到姿态迁移充分为止，包括如下步骤：2. A kind of spectral pose transfer method based on deformation map according to claim 1, is characterized in that: in step 5), segmentation reference mesh, the target mesh of generation and its deformation map pose migration insufficient region, According to step 2) to step 4), perform layered attitude migration until the attitude migration is sufficient, including the following steps: 5.1)选取姿态学习不充分的局部网格，将对应的参考网格M、生成的目标网格M′、变形图
Figure FDA0003875400400000037
进行分割，得到对应的局部子网格S、S′和Gs；5.1) Select a local grid with insufficient attitude learning, and combine the corresponding reference grid M, the generated target grid M′, and the deformation map
Figure FDA0003875400400000037
Carry out segmentation to obtain the corresponding local sub-grids S, S′ and G s ; 5.2)利用步骤2)至步骤3)求出局部变形图Gs姿态迁移后的变形图
Figure FDA0003875400400000038
5.2) Use steps 2) to 3) to obtain the deformation map after the local deformation map G s posture migration
Figure FDA0003875400400000038
 5.3)计算Gs分割边界顶点位置在姿态迁移前后的平均偏移量，将其添加到
Figure FDA0003875400400000039
的相应顶点；5.3) Calculate the average offset of the G s segmentation boundary vertex position before and after attitude migration, and add it to
Figure FDA0003875400400000039
the corresponding vertices of 5.4)利用
Figure FDA00038754004000000310
的顶点信息更新变形图
Figure FDA00038754004000000311
5.4) Use
Figure FDA00038754004000000310
The vertex information updates the deformed graph
Figure FDA00038754004000000311
 5.5)利用步骤4)得到最终姿态迁移结果。5.5) Use step 4) to obtain the final pose transfer result.
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