Technical Reports
HPL-2009-375
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Algebraic topology for computer vision
Freedman, Daniel; Chen, Chao
HP Laboratories
HPL-2009-375
Keyword(s): algebraic topology, persistent homology, computer vision, image processing
Abstract: Algebraic topology is generally considered one of the purest subfields of mathematics. However, over the last decade two interesting new lines of research have emerged, one focusing on algorithms for algebraic topology, and the other on applications of algebraic topology in engineering and science. Amongst the new areas in which the techniques have been applied are computer vision and image processing. In this paper, we survey the results of these endeavours. Because algebraic topology is an area of mathematics with which most computer vision practitioners have no experience, we review the machinery behind the theories of homology and persistent homology; our review emphasizes intuitive explanations. In terms of applications to computer vision, we focus on four illustrative problems: shape signatures, natural image statistics, image denoising, and segmentation. Our hope is that this review will stimulate interest on the part of computer vision researchers to both use and extend the tools of this new field.
25 Pages
External Posting Date: December 17, 2009 [Fulltext]. Approved for External Publication
Internal Posting Date: December 17, 2009 [Fulltext]