computer animation virtual worlds LEARNING-BASED 3D FACE DETECTION 。。。。e。。。。●●●●●。。。。。●●●。。。。。。●。。。。。。。。e。e●。年年年年●。年●●。●。。。。。。。●。。。。。。。。。e●●●。 Using every voxel's IV value,we can easily calculate symmetric part,the geometric contexts over its voxelized the contour voxels'number included in any sub- surface form a large space of classifiers.We propose rectangle.For example,the voxels'number in rectangle to use AdaBoost learning to select the most effective (Figure 3(b))with upper-left point(xo,yo)and bottom- classifiers to construct a strong classifier,through which right point (xi,yi)is the symmetric part is judged whether it is or just contains the 3D face.We first describe our algorithm for IV(xo,yo,x1.y1)=IV(x1.y)+IV(xo.yo) identifying and extracting the reflective symmetric parts. -IV(xo.y1)-IV(x1,yo) (5) Reflective Symmetry Detection Similarly,for every voxel on 3D model surface,its value V and integral volume value IV can be defined 3D face region is reflective symmetric.That is,it is as follows, unchanged by reflecting about the symmetric plane P.In particular,for each vertex v:on the face part,its reflected 1V(x0,0,20)= ∑Vx,y动 vertex v;about Pexists on the face.Furthermore,for such (6) vertex pair (v;,vj),two symmetric conditions should be x≤0，y302≤0 satisfied, Now back to Subsection 'Definition of Geometric .some of their intrinsic geometric properties,for Context,'s (n),that is the surfacial voxels'number in nth example,mean and Gaussian curvatures should be sub-cube,can be easily obtained.Assuming that the nth equal; sub-cube has two diagonal vertices (xo,yo,zo)and (x1,y1, Other geometric properties,for example normal ),then, vectors,principle directions should be equivalent under reflection about P. s:(n)=IVx0,y%,20,x1,1,3） Our algorithm for detecting reflective symmetry is built =IV(x,y1,z1)+IV(x1,0,z0) upon searching possible symmetric vertex pairs,and accumulating the evidence of the symmetric plane P. -IW(x1,yh,20)-IV(x1,J0,z1) We densely sample the 3D model,and,for any vertex -IV(xo.y1.z)+IV(xo.y1.Zo) pair(vi,vj),judge if they are likely to be symmetric by -1V(x0,J0,20）+IV(x0,0,z1) (7) checking the above two symmetric conditions.If so,we record their potential symmetric plane P using a quad Obviously,with the above formula,the voxel v,'s ij=(a,b.c.d),where ax +by+cz+d=0 is the plane geometry context can be obtained easily. equation with d=(0,1).Pi;passes through the center In summary,the integral volume in fact defines a of vi and vj and meanwhile it is perpendicular to vvj. For efficiency,we select the feature vertices of 3D model searching table in the surrounding box.By means of it, as the sampled vertex pairs to detect symmetric plane. we can easily obtain the number of surfacial voxels in For instance,we can select those vertices whose mean each sub-cube.The computation of geometric contexts with different edge lengths R over model surface is thus curvatures exceed a given threshold.For the sake of very fast.In the following,we introduce the approach of noise,more complex descriptors,for example,integral 3D face detection with geometric context. spherels instead of the curvature can be used in the symmetry detection process. We then assemble all possible symmetric vertex Learning-Based 3D Face pairs.Their corresponding quads (Oi j}form a space. Obviously,those quads in this space that potentially Model Detection correspond to the real symmetric plane will be close enough.We can therefore cluster these close quads to Our basic observation is that 3D face part is reflective extract the symmetric plane(Figure 4). symmetric about a fixed plane.So the first step is to Note that,each symmetric plane detected needs to be extract the reflective symmetric and nearly reflective further verified by testing whether its supporting vertices symmetric parts in the input 3D model,through which are spatially adjacent on the model.Through such we reject those non-face regions and discover the verification,we simultaneously extract the approximate candidates for the face part as well.For each extracted symmetric area.Recall that a base plane is needed Copyright2007 John Wiley Sons,Ltd. 487 Comp.Anim.Virtual Worlds 2007;18:483-492 DOL:10.1002/caVLEARNING-BASED 3D FACE DETECTION ........................................................................................... Using every voxel’s IV value, we can easily calculate the contour voxels’ number included in any sub￾rectangle. For example, the voxels’ number in rectangle (Figure 3(b)) with upper-left point (x0, y0) and bottom￾right point (x1, y1) is IV(x0, y0, x1, y1) = IV(x1, y1) + IV(x0, y0) − IV(x0, y1) − IV(x1, y0) (5) Similarly, for every voxel on 3D model surface, its value V and integral volume value IV can be defined as follows, IV(x0, y0, z0) = x≤x0,y≤y0,z≤z0 V(x, y, z) (6) Now back to Subsection ‘Definition of Geometric Context,’ si(n), that is the surfacial voxels’ number in nth sub-cube, can be easily obtained. Assuming that the nth sub-cube has two diagonal vertices (x0, y0, z0) and (x1, y1, z1), then, si(n) = IV(x0, y0, z0, x1, y1, z1) = IV(x1, y1, z1) + IV(x1, y0, z0) − IV(x1, y1, z0) − IV(x1, y0, z1) − IV(x0, y1, z1) + IV(x0, y1, z0) − IV(x0, y0, z0) + IV(x0, y0, z1) (7) Obviously, with the above formula, the voxel vi’s geometry context can be obtained easily. In summary, the integral volume in fact defines a searching table in the surrounding box. By means of it, we can easily obtain the number of surfacial voxels in each sub-cube. The computation of geometric contexts with different edge lengths R over model surface is thus very fast. In the following, we introduce the approach of 3D face detection with geometric context. Learning-Based 3D Face Model Detection Our basic observation is that 3D face part is reflective symmetric about a fixed plane. So the first step is to extract the reflective symmetric and nearly reflective symmetric parts in the input 3D model, through which we reject those non-face regions and discover the candidates for the face part as well. For each extracted symmetric part, the geometric contexts over its voxelized surface form a large space of classifiers. We propose to use AdaBoost learning to select the most effective classifiers to construct a strong classifier, through which the symmetric part is judged whether it is or just contains the 3D face. We first describe our algorithm for identifying and extracting the reflective symmetric parts. Reflective Symmetry Detection 3D face region is reflective symmetric. That is, it is unchanged by reflecting about the symmetric plane P. In particular, for each vertex vi on the face part, its reflected vertex vj about P exists on the face. Furthermore, for such vertex pair (vi, vj ), two symmetric conditions should be satisfied,
some of their intrinsic geometric properties, for example, mean and Gaussian curvatures should be equal;
Other geometric properties, for example normal vectors, principle directions should be equivalent under reflection about P. Our algorithm for detecting reflective symmetry is built upon searching possible symmetric vertex pairs, and accumulating the evidence of the symmetric plane P. We densely sample the 3D model, and, for any vertex pair (vi, vj ), judge if they are likely to be symmetric by checking the above two symmetric conditions. If so, we record their potential symmetric plane Pij using a quad Qi,j = (a, b, c, d), where ax + by + cz + d = 0 is the plane equation with d = {0, 1}. Pij passes through the center of vi and vj and meanwhile it is perpendicular to vivj . For efficiency, we select the feature vertices of 3D model as the sampled vertex pairs to detect symmetric plane. For instance, we can select those vertices whose mean curvatures exceed a given threshold. For the sake of noise, more complex descriptors, for example, integral sphere18 instead of the curvature can be used in the symmetry detection process. We then assemble all possible symmetric vertex pairs. Their corresponding quads {Qi,j } form a space. Obviously, those quads in this space that potentially correspond to the real symmetric plane will be close enough. We can therefore cluster these close quads to extract the symmetric plane (Figure 4). Note that, each symmetric plane detected needs to be further verified by testing whetherits supporting vertices are spatially adjacent on the model. Through such verification, we simultaneously extract the approximate symmetric area. Recall that a base plane is needed ............................................................................................ Copyright © 2007 John Wiley & Sons, Ltd. 487 Comp. Anim. Virtual Worlds 2007; 18: 483–492 DOI: 10.1002/cav