Workshop on Bioimaging II / PDEs, Tue, 20 Nov, 2007
Speaker: Ron Kimmel
Abstract
We* have recently shown that a person's identity is associated with the intrinsic geometry the facial surface, while facial expressions are associated with the extrinsic geometry. Our first attempt in face recognition was to represent the intrinsic geometry of the surface by isometrically embedding it into a low-dimensional Euclidean space. The embedding is performed using Multidimensional Scaling (MDS). The result is an expression-invariant representation of the face we called canonical form. Using canonical forms, we could perform accurate face recognition. Next, we generalized the canonical forms concept by embedding into non-Euclidean spaces. Particularly, two- and three-dimensional spaces with spherical geometry were found to be appealing for the representation of faces, as the resulting metric distortion is usually smaller compared to a Euclidean space. More recently, we introduced the concept of Generalized Multidimensional Scaling (GMDS), which allows embedding into manifolds with an arbitrary geometric structure. Instead of embedding the facial surfaces into a common embedding space, we embed one surface into the other and use the metric distortion as a measure of their dissimilarity. We show that the Gromov-Housdorf distance is defined by three coupled GMDS problems. This formulation provides an efficient approximation for the distortion between almost isometric surfaces. The GMDS allows face recognition even when parts of the surfaces are missing. In this talk I will review the relation between these measures, the underlying theory, the resulting numerical machinery, and applications ranging from recognition of faces in shape analysis, to morphing, warping, and texture mapping.
*Based on joint work with Alex Bronstein and Michael Bronstein
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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