Keypoint Detection and Local Feature Matching for Textured 3D Face Recognition |
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Authors: | Ajmal S Mian Mohammed Bennamoun Robyn Owens |
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Affiliation: | (1) Department of Mathematics, Stanford University, Palo Alto, CA 94305, USA |
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Abstract: | In this study we concentrate on qualitative topological analysis of the local behavior of the space of natural images. To
this end, we use a space of 3 by 3 high-contrast patches ℳ. We develop a theoretical model for the high-density 2-dimensional
submanifold of ℳ showing that it has the topology of the Klein bottle. Using our topological software package PLEX we experimentally
verify our theoretical conclusions. We use polynomial representation to give coordinatization to various subspaces of ℳ. We
find the best-fitting embedding of the Klein bottle into the ambient space of ℳ. Our results are currently being used in developing
a compression algorithm based on a Klein bottle dictionary. |
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Keywords: | Topology Natural images Manifold Filtration Klein bottle Persistent homology |
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