A robust and isotropic curved surface representation for 3D faces description

A novel curved surface representation which is relatively invariant under the transformations of the 3D motion group is introduced in this paper. It is computed from the superposition of the two geodesic potentials generated from a given couple of surface points. By considering a levels set of such geodesic potentials, finite invariant points are obtained. Two numerical methods are implemented and compared in order to find an efficient approximation of this representation in the sense of the Hausdorff shape distance. Its robustness under an imprecision of reference points positions is studied. Experimentations are performed on the 3D real faces of the database Bosphorus.

[1]  Faouzi Ghorbel.  Towards a unitary formulation for invariant image description: application to image coding , 1998, Ann. des Télécommunications.

[2]  Michael G. Strintzis,et al.  3D Model Search and Retrieval Using the Spherical Trace Transform , 2007, EURASIP J. Adv. Signal Process..

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

[4]  Masayuki Nakajima,et al.  Spherical Wavelet Descriptors for Content-based 3D Model Retrieval , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[5]  Liming Chen,et al.  A coarse-to-fine curvature analysis-based rotation invariant 3D face landmarking , 2009, 2009 IEEE 3rd International Conference on Biometrics: Theory, Applications, and Systems.

[6]  Yi Liu,et al.  The Generalized Shape Distributions for Shape Matching and Analysis , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[7]  Faouzi Ghorbel,et al.  Un ensemble d'invariants bipolaires pour les surfaces de R3. Application à la description du visage par une approche 3D , 2012, Traitement du Signal.

[8]  Paola Campadelli,et al.  Automatic Facial Feature Extraction for Face Recognition , 2007 .

[9]  Ming Ouhyoung,et al.  On Visual Similarity Based 3D Model Retrieval , 2003, Comput. Graph. Forum.

[10]  Katsushi Ikeuchi,et al.  The Complex EGI: A New Representation for 3-D Pose Determination , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[12]  F. Ghorbel,et al.  A new 3D surface registration approach depending on a suited resolution: Application to 3D faces , 2012, 2012 16th IEEE Mediterranean Electrotechnical Conference.

[13]  Dejan V. Vranic,et al.  3D model retrieval , 2004 .

[14]  Patrick J. Flynn,et al.  Overview of the face recognition grand challenge , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[15]  Petros Daras,et al.  Shape matching using the 3D Radon transform , 2004 .

[16]  Jean-Louis de Bougrenet de la Tocnaye,et al.  A three-dimensional primitive extraction of long bones obtained from bi-dimensional Fourier descriptors , 1992, Pattern Recognit. Lett..

[17]  Atilla Baskurt,et al.  Generalizations of angular radial transform for 2D and 3D shape retrieval , 2005, Pattern Recognit. Lett..

[18]  Szymon Rusinkiewicz,et al.  Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors , 2003, Symposium on Geometry Processing.

[19]  Sven J. Dickinson,et al.  Skeleton based shape matching and retrieval , 2003, 2003 Shape Modeling International..

[20]  Faouzi Ghorbel,et al.  A robust invariant bipolar representation for R3 surfaces: applied to the face description , 2013, Ann. des Télécommunications.

[21]  Laurent D. Cohen,et al.  Global Minimum for Active Contour Models: A Minimal Path Approach , 1997, International Journal of Computer Vision.

[22]  D. Struik.  Lectures on classical differential geometry , 1951 .

[23]  Faouzi Ghorbel,et al.  Three dimensional modeling of the left ventricle of the heart using spherical harmonic analysis , 2008, 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[24]  M. Hebert,et al.  The Representation, Recognition, and Locating of 3-D Objects , 1986 .

[25]  Arman Savran,et al.  Bosphorus Database for 3D Face Analysis , 2008, BIOID.

[26]  Anuj Srivastava,et al.  Elastic Shape Models for Face Analysis Using Curvilinear Coordinates , 2009, Journal of Mathematical Imaging and Vision.

[27]  Ernest L. Hall,et al.  Three-Dimensional Moment Invariants , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Tony Tung,et al.  The Augmented Multiresolution Reeb Graph Approach for Content-based Retrieval of 3d Shapes , 2005, Int. J. Shape Model..