Abstract
A significant cue for visual perception is the occlusion pattern in 2-D retinal images, which helps humans or robots navigate successfully in the 3-D environments. There have been many works in the literature on the modeling and analysis of the occlusion phenomenon, most of which are from the analytical or statistical points of view. The current paper presents a new theory of occlusion based on the simple topological definitions of preimages and a binary operation on them called “occlu.” We study numerous topological as well as algebraic structures of the resultant noncommutative preimage monoids (a monoid is a semigroup with identity). Some implications of the new theory in terms of real vision research are also addressed.
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Research is partially supported by NSF (USA) under the grant number DMS-0202565.
Jianhong (Jackie) Shen received the Ph.D degree in Applied Mathematics from the Massachusetts Institute of Technology in 1998, and the B.S. degree from the University of Science and Technology of China (USTC) in 1994. He was a CAM (Computational and Applied Mathematics) Assistant Professor at UCLA from 1998 to 2000. He is currently an Assistant Professor of Applied Mathematics in the University of Minnesota, MN, USA. His current research interests include image, signal, and information processing, vision modeling and computation, as well as multiscale and stochastic modeling in medical and biological sciences. His new book: Image Processing and Analysis - variational, PDE, wavelets, and stochastic methods, coauthored with Prof. Tony F. Chan (Dean of Physical Sciences, UCLA), will be published by the SIAM (Soc. Ind. Appl. Math.) Publisher in September 2005. Most of his research and teaching activities could be found at http://www.math.umn.edu/~jhshen.
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Shen, J. On the Foundations of Vision Modeling III. Noncommutative Monoids of Occlusive Preimages. J Math Imaging Vis 24, 5–17 (2006). https://doi.org/10.1007/s10851-005-3600-8
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DOI: https://doi.org/10.1007/s10851-005-3600-8