CN104680566B - A kind of Grid-oriented animation sequence is for the method for vertex trajectories component dimensionality reduction - Google Patents

Abstract

The invention discloses the method for a kind of Grid-oriented animation sequence for vertex trajectories component dimensionality reduction.First the present invention utilizes PCA to analyze the Main way finding model sport, and is projected in the direction in which by all apex coordinates, obtains new coordinate figure, then builds track matrix respectively at three new change in coordinate axis direction, performs second time PCA dimensionality reduction respectively.The present invention improves efficiency of data compression effectively.

Description

A kind of Grid-oriented animation sequence is for the method for vertex trajectories component dimensionality reduction

Technical field

The invention belongs to multimedia technology field relevant to portable mobile equipment in wireless network, be specifically related to the method for a kind of Grid-oriented animation sequence for vertex trajectories component dimensionality reduction.

Background technology

In mesh animation data compression technique, the compression method of Based PC A is the most frequently used is also the method the most effectively reducing data volume, and the dimensionality reduction of data is carried out in the main spatial domain from model and time domain two aspects at present.

In the spatial domain of model, refer to utilize every frame corresponding grid static model internal vertex data between redundancy, the quantity dimension carrying out opposite vertexes carries out dimensionality reduction.Although the minimizing data volume that the program can be obvious, when the model that opposite vertexes number is more carries out SVD decomposition, easily there is the problem that internal memory overflows and the situation that distortion is serious because losing important based component.And if model vertices data are excessive, still easily there is low memory when carrying out feature decomposition and the phenomenon such as counting yield is low.

And dimensionality reduction is carried out for the time domain aspect of model, refer to that the track dimension of opposite vertexes carries out dimensionality reduction, reasonablely solve the problems referred to above.But existing algorithm is just simply by the vertex trajectories matrix building the overall situation, and reckon without the uncertainty of different animation model when moving on direction, thus at x, y, displacement difference on z direction has larger difference, during dimensionality reduction, the number of the required key character vector chosen is also different, therefore can be relatively easy to the situation occurring model distortion during reconstruct.

In sum, that how to change utilizes PCA to be study the important directions that grid cartoon compression person pays close attention at present to carry out dimensionality reduction thus to reduce data volume in the summit dimension of model.

Summary of the invention

The present invention is directed to the deficiency of existing mesh animation Method of Data with Adding Windows, provide the method for a kind of Grid-oriented animation sequence for vertex trajectories component dimensionality reduction.

The technical solution adopted for the present invention to solve the technical problems is as follows:

First the present invention utilizes PCA to analyze the Main way finding model sport, and all apex coordinates are projected in the direction in which, obtain new coordinate figure, then track matrix is built respectively at three new change in coordinate axis direction, perform second time PCA dimensionality reduction respectively, thus promote efficiency of data compression further.

Beneficial effect of the present invention: the present invention be a kind of Grid-oriented animation sequence for the method for vertex trajectories component dimensionality reduction, improve efficiency of data compression further.

Embodiment

After server end imports mesh animation sequence, consider the uncertainty of different animation model when moving on direction, thus at x, y, displacement difference on z direction has larger difference, therefore in order to promote compression effectiveness further, on existing track PCA analytical algorithm basis, a kind of method of carrying out dimensionality reduction for vertex trajectories component is proposed.

The present invention specifically imports mesh animation sequence A (M at server end ₁, M ₂..., M _f), wherein M _l, l ∈ [1, F] represents the static network lattice model that every frame is corresponding, and its number of vertices is N, and F represents the frame number of this mesh animation.

1) calculate the central point of all vertex trajectories, construct the center matrix of this mesh animation.

Be A (M in mesh animation sequence ₁, M ₂..., M _f) middle M _i, i ∈ [1, F] represents the static network lattice model that every frame is corresponding, and its apex coordinate matrix is

$M_i=\left[\begin{array}{ccc}v_1^i{}_x& ......& v_N^i{}_x\\ v_1^i{}_y& ......& v_N^i{}_y\\ v_1^i{}_z& ......& v_N^i{}_z\end{array}\right]$

Wherein represent the X on a jth summit in the i-th frame model respectively, Y, Z coordinate figure.Then the overall trajectory on a jth summit central point ( _xp _j, _yp _j, _zp _j) be defined as

$\left\{\begin{array}{c}p_j^x=\left(\underset{k=1}{\overset{F}{\mathrm{\Σ}}}v_j^k{}_x\right)/F\\ p_j^y=\left(\underset{k=1}{\overset{F}{\mathrm{\Σ}}}v_j^k{}_y\right)/F,j\∈(\mathrm{1,2},...,N)\\ p_j^z=\left(\underset{k=1}{\overset{F}{\mathrm{\Σ}}}v_j^k{}_z\right)/F\end{array}\right.$

Therefore the center point coordinate matrix finally obtained is:

$P_c=\left[\begin{array}{ccc}p_1^x& ......& p_N^x\\ p_1^y& ......& p_N^y\\ p_1^z& ......& p_N^z\end{array}\right]$

2) to above-mentioned central point matrix P _ccarry out SVD decomposition, i.e. P _c=U Σ V ^t.

3) using the U matrix that obtains above as transformation matrix of coordinates, frame by frame coordinate transform is carried out to all summits, obtains new apex coordinate matrix

4) movement locus of all summits in XYZ direction is separated, construct 3 vertex trajectories

Matrix _xt, _yt, _zt, as follows, and one by one second time PCA decomposition is carried out to it.

$T_x=(t_1^x,t_2^x,...,t_N^x)=\left(\begin{array}{c}M_1^x\\ M_2^x\\ ...\\ M_F^x\end{array}\right)=\left[\begin{array}{ccc}v_1^1{}_x& ...& v_N^1{}_x\\ ...& ...& ...\\ v_1^F{}_x& ...& v_N^F{}_x\end{array}\right]$

$T_y=(t_1^y,t_2^y,...,t_N^y)=\left(\begin{array}{c}M_1^y\\ M_2^y\\ ...\\ M_F^y\end{array}\right)=\left[\begin{array}{ccc}v_1^1{}_y& ...& v_N^1{}_y\\ ...& ...& ...\\ v_1^F{}_y& ...& v_N^F{}_y\end{array}\right]$

$T_z=(t_1^z,t_2^z,...,t_N^z)=\left(\begin{array}{c}M_1^z\\ M_2^z\\ ...\\ M_F^z\end{array}\right)=\left[\begin{array}{ccc}v_1^1{}_z& ...& v_N^1{}_z\\ ...& ...& ...\\ v_1^F{}_z& ...& v_N^F{}_z\end{array}\right]$

Wherein _xt _j, _yt _j, _zt _jrepresent jth respectively, the movement locus of j ∈ [1, N] individual summit in XYZ direction.

5) size of all proper vectors of all directions according to its individual features value is sorted separately.

Because eigenwert is larger, show that the importance of its characteristic of correspondence vector is larger, therefore we only need choose a in XYZ direction separately, b, namely most important proper vector corresponding to c eigenvalue of maximum is as one group of base of its trajectory range, so just, this space can be represented with the less coefficient be mapped on this group base, thus reach the object of dimensionality reduction.

Claims (1)

1. Grid-oriented animation sequence is for a method for vertex trajectories component dimensionality reduction, it is characterized in that the method comprises the steps:

Mesh animation sequence A (M is imported at server end ₁, M ₂..., M _f), wherein M _l, l ∈ [1, F] represents the static network lattice model that every frame is corresponding, and its number of vertices is N, and F represents the frame number of this mesh animation;

1) calculate the central point of all vertex trajectories, construct the center point coordinate matrix of this mesh animation;

Be A (M in mesh animation sequence ₁, M ₂..., M _f) middle M _i, i ∈ [1, F] represents the static network lattice model that every frame is corresponding, and its apex coordinate matrix is:

$M_i=\left[\begin{array}{ccc}v_1^i{}_x& ......& v_N^i{}_x\\ v_1^i{}_y& ......& v_N^i{}_y\\ v_1^i{}_z& ......& v_N^i{}_z\end{array}\right]$

Wherein represent the X on a jth summit in the i-th frame model respectively, Y, Z coordinate figure; Then the overall trajectory on a jth summit central point ( _xp _j, _yp _j, _zp _j) be defined as:

$\left\{\begin{array}{c}{p_x}_j=\left(\underset{k=1}{\overset{F}{\Σ}}v_j^k{}_x\right)/F\\ {p_y}_j=\left(\underset{k=1}{\overset{F}{\Σ}}v_j^k{}_y\right)/F\\ {p_z}_j=\left(\underset{k=1}{\overset{F}{\Σ}}v_j^k{}_z\right)/F\end{array}\right.,j\∈(1,2,\mathrm{...},N)$

The center point coordinate matrix obtained thus is:

$P_c=\left[\begin{array}{ccc}{p_x}_1& ......& {p_x}_N\\ {p_y}_1& ......& {p_y}_N\\ {p_z}_1& ......& {p_z}_N\end{array}\right]$

2) to above-mentioned center point coordinate matrix P _ccarry out SVD decomposition, i.e. P _c=U Σ V ^t;

3) using U matrix as transformation matrix of coordinates, frame by frame coordinate transform is carried out to all summits, obtains new apex coordinate matrix $M_i^{*}=U_i\·M_i,i\∈\[1,F\];$

4) movement locus of all summits in XYZ direction is separated, construct three vertex trajectories matrixes _xt, _yt, _zt, as follows, and one by one second time PCA decomposition is carried out to it;

$T_x=({t_x}_1,{t_x}_2,...,{t_x}_N)=\left(\begin{array}{c}{M_x}_1\\ {M_x}_2\\ \mathrm{...}\\ {M_x}_F\end{array}\right)=\left[\begin{array}{ccc}v_1^1{}_x& ...& v_N^1{}_x\\ ...& ...& ...\\ v_1^F{}_x& ...& v_N^F{}_x\end{array}\right]$

$T_y=({t_y}_1,{t_y}_2,...,{t_y}_N)=\left(\begin{array}{c}{M_y}_1\\ {M_y}_2\\ \mathrm{...}\\ {M_y}_F\end{array}\right)=\left[\begin{array}{ccc}v_1^1{}_y& ...& v_N^1{}_y\\ ...& ...& ...\\ v_1^F{}_y& ...& v_N^F{}_y\end{array}\right]$

$T_z=({t_z}_1,{t_z}_2,...,{t_z}_N)=\left(\begin{array}{c}{M_z}_1\\ {M_z}_2\\ \mathrm{...}\\ {M_z}_F\end{array}\right)=\left[\begin{array}{ccc}v_1^1{}_z& ...& v_N^1{}_z\\ ...& ...& ...\\ v_1^F{}_z& ...& v_N^F{}_z\end{array}\right]$

Wherein _xt _j, _yt _j, _zt _jrepresent jth respectively, the movement locus of j ∈ [1, N] individual summit in XYZ direction;

5) size of all proper vectors of all directions according to its individual features value is sorted separately; Choose a separately in XYZ direction, most important proper vector corresponding to b, c eigenvalue of maximum, as one group of base of its trajectory range, so just can represent this space with less coefficient be mapped on this group base, thus complete dimensionality reduction.