Isometric embedding of facial surfaces into S3

Authors:
Alexander M. Bronstein;Michael M. Bronstein;Ron Kimmel
Affiliations:
Department of Electrical Engineering;Department of Computer Science, Technion – Israel Institute of Technology, Haifa, Israel;Department of Computer Science, Technion – Israel Institute of Technology, Haifa, Israel
Venue:
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Year:
2005

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Abstract

The problem of isometry-invariant representation and comparison of surfaces is of cardinal importance in pattern recognition applications dealing with deformable objects. Particularly, in three-dimensional face recognition treating facial expressions as isometries of the facial surface allows to perform robust recognition insensitive to expressions. Isometry-invariant representation of surfaces can be constructed by isometrically embedding them into some convenient space, and carrying out the comparison in that space. Presented here is a discussion on isometric embedding into $\mathbb{S}^{\rm 3}$, which appears to be superior over the previously used Euclidean space in sense of the representation accuracy.