Characterizing obstacle-avoiding paths using cohomology theory

Authors:
Paweł Dłotko;Walter G. Kropatsch;Hubert Wagner
Affiliations:
Institute of Computer Science, Jagiellonian University, Poland;Pattern Recognition and Image Processing Group, Vienna University of Technology, Austria;Institute of Computer Science, Jagiellonian University, Poland
Venue:
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Year:
2011

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Abstract

In this paper, we investigate the problem of analyzing the shape of obstacle-avoiding paths in a space. Given a d-dimensional space with holes, representing obstacles, we ask if certain paths are equivalent, informally if one path can be continuously deformed into another, within this space. Algebraic topology is used to distinguish between topologically different paths. A compact yet complete signature of a path is constructed, based on cohomology theory. Possible applications include assisted living, residential, security and environmental monitoring. Numerical results will be presented in the final version of this paper.