computer animation virtual worlds LEARNING-BASED 3D FACE DETECTION evaluation.Adaboost is a feature selection method to neighborhood vertices.These vectors can express the select discriminative features and to combine them(as configuration of local shape at the reference vertex weak classifiers)into a strong classifier with enhanced v:.Obviously,the sampled neighborhood vertices get discriminative power.4 Similarly in this paper,we adopt denser;the shape representation will be more exact, AdaBoost to construct the classifier for 3D face detection. hence this set of vectors is a rich shape description. Nevertheless,how to define efficient and discriminative But the full set of vectors as a shape descriptor geometric features are the key issues to be resolved. is much too detailed and it depends on the 3D model's representation form as well as sampling 3D Face Detection density of neighborhood vertices.So instead of the continuous and unitary representation,we identify Few methods were dedicated to the automatic detection the discrete distribution at relative positions as a of 3D face model.The method proposed by Funcket al.0 more robust and compact,yet highly discriminative is built upon the local geometry analysis around every descriptor. Given the 3D model,we first voxelize its surface. vertex of the model.It computes the average geometric curves distributed on the face model and compares them For every generated voxel vi,calculate its central with the studied curves to verify the face model.This surrounding box with edge length R.Since this shape algorithm's efficiency is rather low for the vertex-wise descriptor will only be applied to symmetric part of the computing.As mentioned in their paper,on ordinary input model,a fixed symmetric plane and a base plane PC hardware,the computing time ranges from several exist(see the details in Subsection Reflective Symmetry tens of minutes to an hour according to the complexity Detection').vi's surrounding box can thus be fixed by of input models.Colombo et al.5 detect the face model making its two vertical side faces respectively parallel using curvature analysis and PCA-based classifier.The to the symmetric plane and the base plane of model algorithm is mainly designed for onefold depth image surface. and is unsuitable to the arbitrary input 3D model. We then divide vi's surrounding box into N uniform sub-cubes,and define the number of sampling voxel v lying in vi's nth sub-cube as 3D model's shape in v,'s nth Geometric Context sub-cube, An effective 3D shape descriptor plays an important role si(n)=NUM(v,vE sub-cube;(n)) (1) in 3D face model detection,it can reduce the ambiguity in detecting process.For generating a compact,yet Here,n=1,....N denotes the index of nth sub- discriminative shape descriptor,we must make the cube and v represents the voxel of 3D model most of the predominant geometric facial features.One surface. plausible way is to take into account the curvature We further normalize si(n)with respect to sub- features of primary facial organs.But curvature analysis cube (n)'s full voxel volume, normally needs vertex-wise computation,which will cut down the detection efficiency and is prone to noise in si(n) (2) general.So for the robust and efficient detection,regional 3(n)=VOL(sub-cube:(n)) features rather than vertex features are preferred.As a key contribution,we define here 'geometric context'as The shape descriptor,geometric context,at a 3D shape descriptor,which encodes the local shape voxel v:can be defined as the following in-order of geometric model by recording the shape distribution array, of the reference vertex in its local surrounding box.The computation of geometric context can be accelerated us- S=(n)n=1,,N) (3) ing a new volume encoding form,named integral volume. Figure 1 demonstrates a 2D illustration of geometric Definition of Geometric Context context. In practice,the edge length of each sub-cube is valued For an arbitrary vertex v:on the input 3D model,consider with R/3,and empirically uniform subdivision of the the set of vectors originating from v:to its sampled surrounding box into N=27 sub-cubes is enough to Copyright2007 John Wiley Sons,Ltd. 485 Comp.Anim.Virtual Worlds 2007;18:483-492 DoL:10.1002/cawLEARNING-BASED 3D FACE DETECTION ........................................................................................... evaluation. Adaboost is a feature selection method to select discriminative features and to combine them (as weak classifiers) into a strong classifier with enhanced discriminative power.14 Similarly in this paper, we adopt AdaBoost to construct the classifier for 3D face detection. Nevertheless, how to define efficient and discriminative geometric features are the key issues to be resolved. 3D Face Detection Few methods were dedicated to the automatic detection of 3D face model. The method proposed by Funck et al. 10 is built upon the local geometry analysis around every vertex of the model. It computes the average geometric curves distributed on the face model and compares them with the studied curves to verify the face model. This algorithm’s efficiency is rather low for the vertex-wise computing. As mentioned in their paper, on ordinary PC hardware, the computing time ranges from several tens of minutes to an hour according to the complexity of input models. Colombo et al. 15 detect the face model using curvature analysis and PCA-based classifier. The algorithm is mainly designed for onefold depth image and is unsuitable to the arbitrary input 3D model. Geometric Context An effective 3D shape descriptor plays an important role in 3D face model detection, it can reduce the ambiguity in detecting process. For generating a compact, yet discriminative shape descriptor, we must make the most of the predominant geometric facial features. One plausible way is to take into account the curvature features of primary facial organs. But curvature analysis normally needs vertex-wise computation, which will cut down the detection efficiency and is prone to noise in general. So for the robust and efficient detection, regional features rather than vertex features are preferred. As a key contribution, we define here ‘geometric context’ as a 3D shape descriptor, which encodes the local shape of geometric model by recording the shape distribution of the reference vertex in its local surrounding box. The computation of geometric context can be accelerated us￾ing a new volume encoding form, named integral volume. Definition of Geometric Context For an arbitrary vertex vi on the input 3D model, consider the set of vectors originating from vi to its sampled neighborhood vertices. These vectors can express the configuration of local shape at the reference vertex vi. Obviously, the sampled neighborhood vertices get denser; the shape representation will be more exact, hence this set of vectors is a rich shape description. But the full set of vectors as a shape descriptor is much too detailed and it depends on the 3D model’s representation form as well as sampling density of neighborhood vertices. So instead of the continuous and unitary representation, we identify the discrete distribution at relative positions as a more robust and compact, yet highly discriminative descriptor. Given the 3D model, we first voxelize its surface. For every generated voxel vi, calculate its central surrounding box with edge length R. Since this shape descriptor will only be applied to symmetric part of the input model, a fixed symmetric plane and a base plane exist (see the details in Subsection ‘Reflective Symmetry Detection’). vi’s surrounding box can thus be fixed by making its two vertical side faces respectively parallel to the symmetric plane and the base plane of model surface. We then divide vi’s surrounding box into N uniform sub-cubes, and define the number of sampling voxel v lying in vi’s nth sub-cube as 3D model’s shape in vi’s nth sub-cube, si(n) = NUM{v, v ∈ sub-cubei(n)} (1) Here, n = 1,...,N denotes the index of nth sub￾cube and v represents the voxel of 3D model surface. We further normalize si(n) with respect to sub￾cubei(n)’s full voxel volume,
si(n) = si(n) VOL(sub-cubei(n)) (2) The shape descriptor, geometric context, at voxel vi can be defined as the following in-order array, Si = {
si(n)|n = 1,...,N} (3) Figure 1 demonstrates a 2D illustration of geometric context. In practice, the edge length of each sub-cube is valued with R/3, and empirically uniform subdivision of the surrounding box into N = 27 sub-cubes is enough to ............................................................................................ Copyright © 2007 John Wiley & Sons, Ltd. 485 Comp. Anim. Virtual Worlds 2007; 18: 483–492 DOI: 10.1002/cav