Three-Dimensional Face Recognition

An expression-invariant 3D face recognition approach is presented. Our basic assumption is that facial expressions can be modelled as isometries of the facial surface. This allows to construct expression-invariant representations of faces using the bending-invariant canonical forms approach. The result is an efficient and accurate face recognition algorithm, robust to facial expressions, that can distinguish between identical twins (the first two authors). We demonstrate a prototype system based on the proposed algorithm and compare its performance to classical face recognition methods.The numerical methods employed by our approach do not require the facial surface explicitly. The surface gradients field, or the surface metric, are sufficient for constructing the expression-invariant representation of any given face. It allows us to perform the 3D face recognition task while avoiding the surface reconstruction stage.

[1]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[2]  A. Householder,et al.  Discussion of a set of points in terms of their mutual distances , 1938 .

[3]  W. Arnoldi The principle of minimized iterations in the solution of the matrix eigenvalue problem , 1951 .

[4]  W. Torgerson Multidimensional scaling: I. Theory and method , 1952 .

[5]  J. Gower Some distance properties of latent root and vector methods used in multivariate analysis , 1966 .

[6]  L. Guttman A general nonmetric technique for finding the smallest coordinate space for a configuration of points , 1968 .

[7]  L. D. Harmon,et al.  Identification of human faces , 1971 .

[8]  P. Ekman Darwin and Facial Expression , 1973 .

[9]  Takeo Kanade,et al.  Picture Processing System by Computer Complex and Recognition of Human Faces , 1974 .

[10]  J. Barra,et al.  Recent Developments in Statistics , 1978 .

[11]  Carl Friedrich Gauss Disquisitiones generales circa superficies curvas , 1981 .

[12]  Jeffrey L. Posdamer,et al.  Surface measurement by space-encoded projected beam systems , 1982, Comput. Graph. Image Process..

[13]  Gene H. Golub,et al.  Matrix computations , 1983 .

[14]  J. Leeuw,et al.  Upper bounds for Kruskal's stress , 1984 .

[15]  Robert A. Hummel,et al.  Experiments with the intensity ratio depth sensor , 1985, Comput. Vis. Graph. Image Process..

[16]  L Sirovich,et al.  Low-dimensional procedure for the characterization of human faces. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[17]  Heinz Hugli,et al.  Generation And Use Of Color Pseudo Random Sequences For Coding Structured Light In Active Ranging , 1989, Other Conferences.

[18]  J. Cartoux,et al.  Face authentification or recognition by profile extraction from range images , 1989, [1989] Proceedings. Workshop on Interpretation of 3D Scenes.

[19]  V. Rich Personal communication , 1989, Nature.

[20]  Eric L. Schwartz,et al.  A Numerical Solution to the Generalized Mapmaker's Problem: Flattening Nonconvex Polyhedral Surfaces , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Evangelos E. Milios,et al.  Matching range images of human faces , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[22]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

[23]  André Oosterlinck,et al.  Range Image Acquisition with a Single Binary-Encoded Light Pattern , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Johji Tajima,et al.  3-D data acquisition by Rainbow Range Finder , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[25]  Alex Pentland,et al.  Face recognition using eigenfaces , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[26]  Erwin Kreyszig,et al.  Differential geometry , 1991 .

[27]  C. Gold Problems with handling spatial data ― the Voronoi approach , 1991 .

[28]  Zengo Furukawa,et al.  A General Framework for , 1991 .

[29]  I. Masuda,et al.  3D facial image analysis for human identification , 1992, [1992] Proceedings. 11th IAPR International Conference on Pattern Recognition.

[30]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[31]  Gaile G. Gordon,et al.  Face recognition based on depth and curvature features , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[32]  Roberto Brunelli,et al.  Face Recognition: Features Versus Templates , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Peter W. Hallinan A low-dimensional representation of human faces for arbitrary lighting conditions , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[34]  Alex Pentland,et al.  View-based and modular eigenspaces for face recognition , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[35]  J. Tsitsiklis,et al.  Efficient algorithms for globally optimal trajectories , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[36]  Anthony J. Kearsley,et al.  The Solution of the Metric STRESS and SSTRESS Problems in Multidimensional Scaling Using Newton's Method , 1995 .

[37]  Imre Leader,et al.  Infinite partition regular matrices , 1995, Comb..

[38]  Nathan Linial,et al.  The geometry of graphs and some of its algorithmic applications , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[39]  Marc Acheroy,et al.  Automatic face identification , 1995, Optics & Photonics.

[40]  Laurenz Wiskott,et al.  Labeled graphs and dynamic link matching for face recognition and scene analysis , 1995 .

[41]  Gaile G. Gordon,et al.  Face recognition from frontal and profile views , 1995 .

[42]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[43]  James A. Sethian,et al.  Theory, algorithms, and applications of level set methods for propagating interfaces , 1996, Acta Numerica.

[44]  Luc Van Gool,et al.  One-shot active 3D shape acquisition , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[45]  Ingemar J. Cox,et al.  Feature-based face recognition using mixture-distance , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[46]  Patrick J. F. Groenen,et al.  Modern Multidimensional Scaling: Theory and Applications , 2003 .

[47]  Tomaso A. Poggio,et al.  Linear Object Classes and Image Synthesis From a Single Example Image , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[48]  Horst Bunke,et al.  Face recognition using range images , 1997, Proceedings. International Conference on Virtual Systems and MultiMedia VSMM '97 (Cat. No.97TB100182).

[49]  Norbert Krüger,et al.  Face Recognition by Elastic Bunch Graph Matching , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[50]  Nahum Kiryati,et al.  Toward optimal structured light patterns , 1997, Proceedings. International Conference on Recent Advances in 3-D Digital Imaging and Modeling (Cat. No.97TB100134).

[51]  Norbert Krüger,et al.  Face Recognition by Elastic Bunch Graph Matching , 1997, CAIP.

[52]  Ron Kimmel,et al.  A general framework for low level vision , 1998, IEEE Trans. Image Process..

[53]  Marc Acheroy,et al.  Automatic Face Authentication from 3D surface , 1998, BMVC.

[54]  Hiromi T. Tanaka,et al.  Curvature-based face surface recognition using spherical correlation. Principal directions for curved object recognition , 1998, Proceedings Third IEEE International Conference on Automatic Face and Gesture Recognition.

[55]  David J. Kriegman,et al.  Illumination cones for recognition under variable lighting: faces , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[56]  Qian Chen,et al.  Building human face models from two images , 1998, 1998 IEEE Second Workshop on Multimedia Signal Processing (Cat. No.98EX175).

[57]  J A Sethian,et al.  Computing geodesic paths on manifolds. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[58]  Yi-Ping Hung,et al.  Reconstruction of complete 3D object model from multiview range images , 1999, Electronic Imaging.

[59]  J. A. Sethian,et al.  Fast Marching Methods , 1999, SIAM Rev..

[60]  P. Groenen,et al.  Modern Multidimensional Scaling: Theory and Applications , 1999 .

[61]  Julian Ashbourn,et al.  Biometrics: Advanced Identity Verification , 2000, Springer London.

[62]  Jack Dongarra,et al.  Templates for the Solution of Algebraic Eigenvalue Problems , 2000, Software, environments, tools.

[63]  Horst Bunke,et al.  Classifying range images of human faces with Hausdorff distance , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

[64]  J. Leeuw Applications of Convex Analysis to Multidimensional Scaling , 2000 .

[65]  S. Nash A multigrid approach to discretized optimization problems , 2000 .

[66]  N. Mavridis,et al.  The HISCORE face recognition application : A ordable desktop face recognition based on a novel 3 D camera , 2001 .

[67]  SapiroGuillermo,et al.  Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces , 2001 .

[68]  David Chandler,et al.  Biometric Product Testing Final Report , 2001 .

[69]  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..

[70]  J. Bigun,et al.  Authentication gets personal with biometrics - Signal Processing Magazine, IEEE , 2001 .

[71]  Ron Kimmel,et al.  Bending invariant representations for surfaces , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[72]  Michael Elad,et al.  Content Based Retrieval of VRML Objects - An Iterative and Interactive Approach , 2001, Eurographics Multimedia Workshop.

[73]  F. Mémoli,et al.  Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces: 730 , 2001 .

[74]  Chin-Seng Chua,et al.  Facial feature detection and face recognition from 2D and 3D images , 2002, Pattern Recognit. Lett..

[75]  Ross T. Whitaker,et al.  Geometric surface smoothing via anisotropic diffusion of normals , 2002, IEEE Visualization, 2002. VIS 2002..

[76]  Kuo-Young Cheng,et al.  An automatic construction of a person's face model from the person's two orthogonal views , 2002, Geometric Modeling and Processing. Theory and Applications. GMP 2002. Proceedings.

[77]  Volker Blanz,et al.  Face Recognition Using Component-Based SVM Classification and Morphable Models , 2002, SVM.

[78]  Helge J. Ritter,et al.  On interactive visualization of high-dimensional data using the hyperbolic plane , 2002, KDD.

[79]  Ron Kimmel,et al.  Computational Surface Flattening: A Voxel-Based Approach , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[80]  Michael Elad,et al.  Content based retrieval of VRML objects: an iterative and interactive approach , 2002 .

[81]  R. Malladi Geometric methods in bio-medical image processing , 2002 .

[82]  Ron Kimmel,et al.  Texture Mapping Using Surface Flattening via Multidimensional Scaling , 2002, IEEE Trans. Vis. Comput. Graph..

[83]  Alexander M. Bronstein,et al.  Expression-Invariant 3D Face Recognition , 2003, AVBPA.

[84]  Ron Kimmel,et al.  An Algebraic Multigrid Approach for Image Analysis , 2002, SIAM J. Sci. Comput..

[85]  Gordon Erlebacher,et al.  A novel technique for face recognition using range imaging , 2003, Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings..

[86]  Patrick J. Flynn,et al.  Face Recognition Using 2D and 3D Facial Data , 2003 .

[87]  Michael G. Strintzis,et al.  Use of depth and colour eigenfaces for face recognition , 2003, Pattern Recognit. Lett..

[88]  Alexander M. Bronstein,et al.  High-Resolution Structured Light Range Scanner with Automatic Calibration , 2003 .

[89]  Daniel Cohen-Or,et al.  Bilateral mesh denoising , 2003 .

[90]  Ron Kimmel,et al.  On Bending Invariant Signatures for Surfaces , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[91]  Ron Kimmel,et al.  Numerical geometry of images - theory, algorithms, and applications , 2003 .

[92]  Patrick J. Flynn,et al.  A Survey Of 3D and Multi-Modal 3D+2D Face Recognition , 2004 .

[93]  Alexander M. Bronstein,et al.  Face Recognition from Facial Surface Metric , 2004, ECCV.

[94]  Alexander M. Bronstein,et al.  Fusion of 2D and 3D data in three-dimensional face recognition , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[95]  R. Kimmel,et al.  An efficient solution to the eikonal equation on parametric manifolds , 2004 .

[96]  Ron Kimmel,et al.  Numerical Geometry of Images , 2003, Springer New York.

[97]  Guillermo Sapiro,et al.  Comparing point clouds , 2004, SGP '04.

[98]  A. Bronstein,et al.  A MULTIGRID APPROACH FOR MULTI-DIMENSIONAL SCALING∗ , 2004 .

[99]  A. Grün,et al.  LEAST SQUARES 3D SURFACE MATCHING , 2004 .

[100]  Isometric Embedding of Facial Surfaces into S 3 , 2004 .

[101]  Alexander M. Bronstein,et al.  Isometric Embedding of Facial Surfaces into , 2005, Scale-Space.

[102]  Kai Hormann,et al.  Surface Parameterization: a Tutorial and Survey , 2005, Advances in Multiresolution for Geometric Modelling.

[103]  A. Bronstein,et al.  Expression-invariant representations for human faces , 2005 .

[104]  Zhengyou Zhang,et al.  Iterative point matching for registration of free-form curves and surfaces , 1994, International Journal of Computer Vision.

[105]  Alexander M. Bronstein,et al.  Expression-invariant face recognition via spherical embedding , 2005, IEEE International Conference on Image Processing 2005.

[106]  Ron Kimmel,et al.  Geometric Filters, Diffusion Flows, and Kernels in Image Processing , 2005 .