Algebraic topology for computer vision Book Section

Author(s): Freedman, Daniel; Chen, Chao
Article/Chapter Title: Algebraic topology for computer vision
Title Series: Computer Science, Technology and Applications
Affiliation IST Austria
Abstract: Algebraic topology is generally considered one of the purest subfield 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.
Book Title: Computer Vision
ISBN: 978-1-61209-399-4
Publisher: Nova Science Publishers  
Date Published: 2011-11-30
Start Page: 239
End Page: 268
Open access: no
IST Austria Authors
  1. Chao Chen
    14 Chen
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