CN109859322B - Spectral attitude migration method based on deformation graph - Google Patents
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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
Technical Field
The invention relates to the technical field of 3D model spectral attitude migration, in particular to a spectral attitude migration method based on a deformation map.
Background
The three-dimensional grid model has wide application in the aspects of 3D printing, virtual reality, entertainment games and the like. It is difficult to model complex geometries quickly and accurately using conventional manual modeling, scanning equipment, or modeling software. And the existing grid model is edited and reused, so that the re-modeling can be avoided. The method is used for obtaining the target grid with similar postures by using the existing postures of the reference grid as the example-based grid modeling technology deformation migration and posture migration, but how to accurately describe the posture of the source grid model and automatically guide the deformation of the target grid model is also a challenging subject.
Levy performs trivial pose migration between grids with the same connectivity by exchanging coefficients corresponding to low-frequency eigenfunctions (i.e., eigenfunctions corresponding to smaller eigenvalues) of the Laplacian matrix of the grids. But the expression result of the source grid and the reference grid is obviously different due to the difference of the Laplacian characteristic bases. The target grid model obtained after the posture migration has serious distortion and deformation phenomena, and the posture learning is insufficient. Kovnatsky and the like optimize Laplace matrix characteristic bases of two grid models with different connection relations to obtain coupling reference harmonics and bases with compatibility based on functional mapping, and then exchange low-frequency coefficients of the coupling reference harmonics and bases of the two grids to perform attitude migration between the grid models with different connection relations and different attitudes. Although this method solves the shape distortion phenomenon due to the feature basis difference, the posture learning is still insufficient. Yin et al propose a detail preserving spectral pose migration algorithm and a multi-layer migration framework. According to the method, on the basis of coupling calibration and base attitude migration, a subspace technology based on a generalized central coordinate is combined, the Cage is used as a geometric proxy to reduce the solving scale, the deformation freedom is reduced, and the solving stability is guaranteed. In order to solve the problem of insufficient posture learning, yin and the like propose a layered posture migration strategy, a region with insufficient migration posture is divided, the original posture which is not large-scale is converted into the large-scale posture of a local region, and then spectrum posture migration is carried out. Thereby obtaining better attitude migration effect. However, since the method uses the Cage and the mean coordinates to represent the source grid, and the mean coordinates do not satisfy the internal locality, the pose migration result is greatly influenced by the Cage.
The invention provides a spectral attitude migration method based on a deformation diagram, which utilizes an embedded deformation diagram editing method to replace a subspace technology of a generalized central coordinate, takes the deformation diagram as a geometric proxy and takes geodesic distance as weight to represent a source grid. The embedding deformation can better maintain the geometric details of the grid, and the influence of the geometric proxy on the migration result is reduced to a certain extent, so that the quality of the migration result is improved.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings of the prior art, and provides a spectral attitude migration method based on a deformation map. The embedding deformation can better maintain the geometric details of the grid, and the influence of the geometric proxy on the migration result is reduced to a certain extent, so that the quality of the migration result is improved.
In order to realize the purpose, the technical scheme provided by the invention is as follows: a spectral attitude migration method based on a deformation map comprises the following steps:
1) Simplifying the 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 (5) segmenting all regions with insufficient grid posture migration, and carrying out layered posture migration according to the steps from 2) to 4) until the posture migration is sufficient.
In step 1), simplifying a source grid by using an optimized quadratic error metric algorithm, namely a QEM (quantitative error metric) algorithm to generate a deformation graph, wherein the total folding cost of each edge of the grid in the optimized quadratic error metric algorithm is defined as:
cost(a,b)＝αQ QEM (a,b)+βQ F (a,b)+γQ Reg (a,b)+μQ Are (a,b)
in which a and b are the edges to be foldedTwo end points, alpha, beta, gamma, mu are scalar weights, Q QEM For QEM edge fold cost, Q F Is the offset, Q, of the adjacent minimum offset edge after the folded edge is folded Reg For the cost of regularity when folding edges (a, b) → v, Q Reg ＝|Reg(N F (v))-max{Reg(N F (a)),Reg(N F (b))}|，N F (a)、N F (b)、N F (v) Is an adjacent triangle set with vertexes a, b and v, reg (tri) =3-2R (tri), R (tri) = cos ([ alpha ]) + cos ([ beta ]) + cos ([ gamma ]), is the regularity of delta tri,
where S (tri) is the area of triangle tri.
In step 2), performing coupling alignment and basis-based spectral pose migration on the source grid by using the reference grid, comprising the following steps:
2.1 Calculating laplacian matrixes of the input reference grid M and the input source grid M' and corresponding spectrums and characteristic functions thereof, and calculating a laplacian matrix of the deformation graph G;
2.2 Selecting direct feature corresponding points of the reference grid and the source grid, and calculating an indication function of s neighborhood points of the corresponding points based on area approximation between the reference grid and the source grid as a corresponding function between grids;
2.3 ) optimizing the Laplace eigenbase of the reference grid M and the source grid M' to obtain a coupled reference tone and a coupled basis { phi i M }、{φ i M' Is calculated using a formula
Determining attitude transition results based on coupling criteria and bases
In the formula, alpha i M And alpha i M' Spectral coefficients of M and M', respectively, k being exchange alpha i M' And | V '| is the number of vertexes of M'.
In the step 3), after the attitude migration is carried out by utilizing the coupling alignment and the base,utilizing an optimized energy function to the attitude migration results
Solving the deformation graph after the attitude transition, wherein the peak constraint term
Terms of pailaplace coordinates
Scaling constraint items
Q is a geodesic distance weight matrix,
for the purpose of the solved deformation map or maps,
for the set of deformation map vertices to be solved,
is composed of
The number of the vertexes of (a),
as a result of the pose migration based on the coupling alignment and the basis,
for rotating the transformation matrix, delta i G To morph the laplace coordinates of the graph G,
for the laplace coordinates of the solved deformation map,
is composed of
Of a scaling matrix, λ 1 、λ 2 Is a scalar weight.
In step 4), the solved deformation map is deformed by using an embedded deformation map editing method to generate a target grid, and the method comprises the following steps:
4.1 Utilizing a minimum energy function
Optimizing the attitude transition result to obtain a rotation and translation matrix of the source grid deformation, wherein
Is composed of
Number of vertices, rotation term
Single vertex rotation term 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 Is a rotation matrix R at the vertex of the deformation graph j Column vector of (2), regularization term
N (j) is a vertex v j T is the translation transformation, α jn =1.0, vertex constraint term
For the generated target netGrid (C)
The top of the upper vertex is a vertex of the lower vertex,
is a deformation diagram
Vertex of (a), w rot 、w reg 、w con Is scalar weight;
4.2 Using a formula after obtaining a rotational-translation matrix
Computing a target grid
Set of vertices of
Wherein w j (v l ') is a geodesic distance weight,
in order to be a matrix of rotations,
to translate the matrix, v l ' being the vertices of the source mesh, g j (v i ') is associated with the source mesh vertex v i ' geodetically nearest m vertex sets on the deformation map G,
are the vertices on the final target mesh sought.
In step 5), dividing the reference grid, the generated target grid and the deformation map thereof into regions with insufficient posture migration, and carrying out layered posture migration according to the steps 2) to 4) until the posture migration is sufficient, wherein the method comprises the following steps:
5.1 Select the local grid with insufficient gesture learning to correspond toReference grid M, generated target grid M' and deformation graph
Dividing to obtain corresponding partial sub-grids S, S' and G s ；
5.2 Using steps 2) to 3) to obtain a local deformation map G s Deformation map after attitude migration
5.3 Calculate G) s Dividing the average offset of the boundary vertex position before and after the attitude transition, and adding it to the average offset
The respective vertex of (a);
5.4 Utilize
Updating the deformation map of the vertex information
5.5 Utilizing step 4) to obtain a final attitude migration result.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the method simplifies the source grid by using an optimized Quadratic Error Metric (QEM) algorithm to generate a vertex distribution uniform deformation graph, and can generate a better effect when the grid of the driving source deforms.
2. The invention utilizes an embedded deformation editing method to replace the subspace technology of the generalized central coordinate, takes the deformation diagram as a geometric proxy, and expresses the source grid by the geodesic distance weight, thereby effectively improving the quality of the target grid generated by the attitude migration.
3. When the layered attitude migration is performed, the local area grid (sub-grid) is directly translated to be spliced with the whole grid, and orientation adjustment is not needed.
Drawings
FIG. 1 is a flow chart of the gesture migration of the present invention.
FIG. 2 is a schematic diagram of a gesture migration process according to the present invention.
FIG. 3 is a diagram illustrating the results of performing a gesture migration based on coupling and basis according to the present invention.
FIG. 4 is a diagram illustrating the result of pose migration transformation according to the present invention.
Detailed Description
The present invention will be further described with reference to the following specific examples.
As shown in fig. 1 and fig. 2, the deformation map-based spectral pose migration method provided by this embodiment inputs a grid and a source grid, and includes the following steps:
1) Simplifying a source grid by utilizing a Quadratic Error Metric (QEM) algorithm to generate a deformation graph with uniformly distributed vertexes, wherein the total folding cost of each edge of the grid in the QEM algorithm is defined as:
cost(a,b)＝αQ QEM (a,b)+βQ F (a,b)+γQ Reg (a,b)+μQ Are (a,b)
in the formula, a and b are two end points of the edge to be folded respectively, alpha, beta, gamma and mu are scalar weight values respectively, and Q is QEM For QEM edge folding cost, Q F Is the offset, Q, of the adjacent minimum offset edge after the folded edge is folded Reg For the cost of regularity when folding edges (a, b) → v, Q Reg ＝|Reg(N F (v))-max{Reg(N F (a)),Reg(N F (b))}|， N F (a)、N F (b)、N F (v) Is an adjacent triangle set with vertexes a, b and v, reg (tri) =3-2R (tri), R (tri) = cos ([ alpha ]) + cos ([ beta ]) + cos ([ gamma ]), is the regularity of delta tri,
wherein S (tri) is the area of triangle tri.
2) Performing coupling-and-basis-based spectral pose migration on a source grid using a reference grid, comprising the steps of:
2.1 Calculating laplacian matrices of the input reference grid M and the source grid M' and corresponding spectra and characteristic functions thereof, and calculating the laplacian matrix of the deformation graph G;
2.2 Selecting direct characteristic corresponding points of the reference grid and the source grid, and calculating an indication function of s neighborhood points of the corresponding points between the reference grid and the source grid based on area approximation as a corresponding function between grids;
2.3 ) the Laplace eigen bases of the reference grid M and the source grid M' are optimized to obtain a coupling reference and a basis { φ i M }、{φ i M' Is calculated using a formula
Determining attitude transition results based on coupling criteria and bases
In the formula, alpha i M And alpha i M' Spectral coefficients of M and M', respectively, k being exchange alpha i M' And | V '| is the number of vertexes of M'. The resulting coupled-bin and base-based spectral pose migration results are shown in FIG. 3.
3) After the attitude migration is carried out by utilizing the coupling alignment and the base, the attitude migration result is utilized an optimized energy function
The deformation graph after the posture transition is obtained, and the peak constraint term in the formula is shown in FIG. 4
Terms of pailaplace coordinates
Scaling constraint terms
Q is a geodesic distance weight matrix,
for the purpose of the solved deformation map,
for the set of deformation map vertices to be solved,
is composed of
The number of the vertexes of (a),
as a result of the pose migration based on the coupling alignment and the basis,
for rotating the transformation matrix, delta i G To morph the laplace coordinates of the graph G,
for the laplace coordinates of the solved deformation map,
is composed of
A scaling matrix of 1 、λ 2 Is a scalar weight.
4) The method for generating the target grid by deforming the source grid by using the method for editing the embedded deformation diagram comprises the following steps:
4.1 Utilizing a minimum energy function
Optimizing the attitude transition result to obtain a rotation and translation matrix of the source grid deformation, wherein
Is composed of
Top ofNumber, rotation term
Single vertex rotation term 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 Is a rotation matrix R at the vertex of the deformation graph j Column vector of (2), regularization term
N (j) is a vertex v j T is the translation transformation, α jn =1.0, vertex constraint term
For the generated target mesh
The top of the upper vertex is a vertex of the lower vertex,
is a deformation diagram
Vertex of, w rot 、w reg 、w con Is scalar weight;
4.2 Using a formula after obtaining a rotational-translation matrix
Computing a target grid
Set of vertices of
Wherein w j (v l ') is a geodesic distance weight,
in order to be a matrix of rotations,
to translate the matrix, v l ' being the vertices of the source mesh, g j (v i ') is associated with the source mesh vertex v i ' geodetically nearest m vertex sets on the deformation map G,
are the vertices on the final target mesh sought.
The generated morphogram-based spectral pose migration low frequency pose migration results are shown in step 2-4 of FIG. 2.
5) Dividing the reference grid, the generated target grid and the deformation graph thereof in the insufficient posture migration area, and carrying out layered posture migration according to the steps 2) to 4) until the posture migration is sufficient, wherein the method comprises the following steps:
5.1 Selecting partial grids with insufficient posture learning, and generating a corresponding reference grid M, a generated target grid M' and a deformation map
Dividing to obtain corresponding partial sub-grids S, S' and G s ；
5.2 Using steps 2) to 3) to obtain a local deformation map G s Deformation map after posture migration
5.3 Calculate G) s The average offset of the division boundary vertex position before and after the attitude transition is added to
In a corresponding roofPoint;
5.4 Utilize
Updating the deformation map of the vertex information
5.5 Utilizing step 4) to obtain a final attitude migration result.
The layered pose migration process and the final result are shown as step 5 in fig. 2.
In conclusion, after the scheme is adopted, the invention provides a new method for three-dimensional model posture migration, and the embedded deformation graph editing method has better locality when representing the source grid, thereby reducing the influence of the quality of the geometric proxy on the result to a certain extent; the sub-meshes are spliced using simple offsets without having to make orientation adjustments. The quality of the target grid generated by the attitude migration is effectively improved, and the method has practical popularization value and is worth popularizing.
The above-mentioned embodiments are merely preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, so that the changes in the shape and principle of the present invention should be covered within the protection scope of the present invention.
Claims (2)
1. A spectral attitude migration method based on a deformation map is characterized by comprising the following steps:
1) Simplifying a source grid by utilizing a grid simplification algorithm to generate a source grid deformation graph;
simplifying a source grid by using an optimized secondary error metric algorithm, namely a QEM algorithm to generate a deformation graph, wherein the total folding cost of each edge of the grid in the optimized secondary error metric algorithm is defined as:
cost(a，b)＝αQ QEM (a，b)+βQ F (a，b)+γQ Reg (a，b)+μQ Are (a，b)
in the formula, a and b are two end points of the edge to be folded respectively, alpha, beta, gamma and mu are scalar weight values respectively, and Q is QEM For QEM edge folding cost, Q F Is to be foldedOffset, Q, adjacent to the minimum offset edge Reg For the cost of regularity when folding edges (a, b) → v, Q Reg ＝|Reg(N F (v))-max{Reg(N F (a))，Reg(N F (b))}|，N F (a)、N F (b)、N F (v) Is an adjacent triangle set with vertexes a, b and v, reg (tri) =3-2R (tri), R (tri) = cos (& lt alpha) + cos (& lt beta) + cos (& lt gamma), which is the regularity of the triangle tri,
wherein S (tri) is the area of triangle tri;
2) Performing coupling-alignment-and-basis-based spectral pose migration on a source grid using a reference grid, comprising the steps of:
2.1 Calculating laplacian matrixes of the input reference grid M and the input source grid M' and corresponding spectrums and characteristic functions thereof, and calculating a laplacian matrix of the deformation graph G;
2.2 Selecting direct characteristic corresponding points of the reference grid and the source grid, and calculating an indication function of s neighborhood points of the corresponding points between the reference grid and the source grid based on area approximation as a corresponding function between grids;
2.3 ) optimizing the Laplace eigenbase of the reference grid M and the source grid M' to obtain a coupled reference tone and a coupled basis { phi i M }、{φ i M′ Is calculated using a formula
Determining attitude transition results based on coupling criteria and bases
In the formula, alpha i M And alpha i M′ Spectral coefficients of M and M', respectively, k being exchange alpha i M′ The number of the vertexes, | V '| is the number of the vertexes of M';
3) Generating a post-attitude-migration deformation map by using an optimized energy function according to the attitude migration result and the source grid deformation map;
performing attitude using coupling alignment and basisAfter the state migration, utilizing an optimized energy function for the attitude migration result
Solving the deformation graph after the attitude transition, wherein the peak constraint term
Laplace coordinate item
Scaling constraint terms
Q is a geodesic distance weight matrix,
for the purpose of the solved deformation map,
for the set of deformation map vertices to be solved,
is composed of
The number of the vertexes of (a),
as a result of the pose migration based on the coupling alignment and the basis,
for rotating the transformation matrix, delta i G To morph the laplace coordinates of the graph G,
laplace sitting for the solved deformation mapThe mark is that,
is composed of
A scaling matrix of 1 、λ 2 Is a scalar weight;
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;
the method for generating the target grid by deforming the source grid by using the method for editing the embedded deformation diagram comprises the following steps:
4.1 Using a minimized energy function
Optimizing the attitude transition result to obtain a rotation and translation matrix of the source grid deformation, wherein
Is a deformation diagram
Number of vertices, rotation term
Single vertex rotation term 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 Is a rotation matrix R at the vertex of the deformation graph j Column vector of (2), regularization term
N (j) isVertex v j T is the translation transformation, α jn =1.0, vertex constraint term
For the generated target mesh
The top of the upper vertex is a vertex of the lower vertex,
is a deformation diagram
Vertex of, w rot 、w reg 、w con Is scalar weight;
4.2 Using a formula after obtaining a rotational-translation matrix
Computing a target grid
Set of vertices of
Wherein w j (v j ') is the geodesic distance weight,
in order to rotate the matrix of the matrix,
to translate the matrix, v l ' is the vertex of the source mesh, g j (v i ') is associated with the source mesh vertex v i ' geodetically nearest m vertex sets on the deformation map G,
the vertex on the final target mesh is calculated;
5) And (5) segmenting all regions with insufficient grid posture migration, and carrying out layered posture migration according to the steps from 2) to 4) until the posture migration is sufficient.
2. The method for migrating spectral poses based on deformation maps according to claim 1, characterized in that: in step 5), dividing the reference grid, the generated target grid and the deformation map thereof into regions with insufficient posture migration, and carrying out layered posture migration according to the steps 2) to 4) until the posture migration is sufficient, wherein the method comprises the following steps:
5.1 Selecting partial grids with insufficient posture learning, and generating a corresponding reference grid M, a generated target grid M' and a deformation map
Dividing to obtain corresponding local sub-grids S, S' and G s ；
5.2 Using steps 2) to 3) to obtain a local deformation map G s Deformation map after attitude migration
5.3 Calculate G) s The average offset of the division boundary vertex position before and after the attitude transition is added to
The respective vertex of (a);
5.4 Utilize
Updating the deformation map of the vertex information
5.5 Utilizing the step 4) to obtain a final posture migration result.
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