Manifold reconstruction in arbitrary dimensions using witness complexes
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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One of the goals of biometrics research is to develop new techniques and/or algorithms for the automatic recognition of humans. In this paper, we propose the concept of a manifold of facial perception based on the observation that a perceived face in a set of similar face images-subjected to variations in pose, illumination and expression-defines a manifold in the high dimensional space. Such a manifold representation can be learned from images in a database of similar facial feature characteristics. This learned manifold can then be used as a basis for facial recognition. Development of a mathematical model for a nonlinear line attractor that represents a pattern manifold in the feature space is presented in this paper. The non-convex pattern manifolds in the feature space may be extremely complex and difficult to model. Therefore an adaptive divide and conquer modular approach which divides complex manifolds into smaller sub-manifolds in the feature space is also proposed for accurate modeling of the nonlinear line of attraction. A nonlinear dimensionality reduction technique using the learned matrices of the nonlinear line attractor network is then used to embed a set of related observations into a low-dimensional space that preserves the intrinsic dimensionality and metric structure of the data for fast and accurate face recognition. Results based on the proposed work from the first experiment of the FRGC version 2 database have shown promising performance in improving the accuracy in the face recognition.