Facial Shape-from-Shading Using Principal Geodesic Analysis and Robust Statistics

In this paper we make two contributions to the problem of recovering surface shape from single images of faces. The first of these is to develop a representation of the distribution of surface normals based on the exponential map, and to show how to model shape-deformations using principal geodesic analysis on the exponential map. The second contribution is to show how ideas from robust statistics can be used to fit the model to facial images in which there is significant self-shadowing. The method is evaluated on both synthetic and real-world images. It is demonstrated to effectively fill-in the facial surface when more than 30% of the area is subject to self-shadowing.

[1]  P. Thomas Fletcher,et al.  Principal geodesic analysis for the study of nonlinear statistics of shape , 2004, IEEE Transactions on Medical Imaging.

[2]  Tomaso A. Poggio,et al.  Reanimating Faces in Images and Video , 2003, Comput. Graph. Forum.

[3]  R. Basri,et al.  Statistical Symmetric Shape from Shading for 3D Structure Recovery of Faces , 2004, eccv 2004.

[4]  David J. Kriegman,et al.  From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Rama Chellappa,et al.  Illumination-insensitive face recognition using symmetric shape-from-shading , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[6]  Thomas Vetter,et al.  Face Recognition Based on Fitting a 3D Morphable Model , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Thomas Vetter,et al.  A morphable model for the synthesis of 3D faces , 1999, SIGGRAPH.

[8]  Olivier D. Faugeras,et al.  Unifying Approaches and Removing Unrealistic Assumptions in Shape from Shading: Mathematics Can Help , 2004, ECCV.

[9]  Rama Chellappa,et al.  A Method for Enforcing Integrability in Shape from Shading Algorithms , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[11]  Paul A. Griffin,et al.  Statistical Approach to Shape from Shading: Reconstruction of Three-Dimensional Face Surfaces from Single Two-Dimensional Images , 1996, Neural Computation.

[12]  X. Pennec.  Probabilities and Statistics on Riemannian Manifolds : A Geometric approach , 2004 .

[13]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.