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Proceedings Paper

Description of 3D digital curves using the theory free groups
Author(s): Atsushi Imiya; Muneaki Oosawa
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Paper Abstract

In this paper, we propose a new descriptor for two- and three- dimensional digital curves using the theory of free groups. A spatial digital curve is expressed as a word which is an element of the free group which consists from three elements. These three symbols correspond to the directions of the orthogonal coordinates, respectively. Since a digital curve is treated as a word which is a sequence of alphabetical symbols, this expression permits us to describe any geometric operation as rewriting rules for words. Furthermore, the symbolic derivative of words yields geometric invariants of digital curves for digital Euclidean motion. These invariants enable us to design algorithms for the matching and searching procedures of partial structures of digital curves. Moreover, these symbolic descriptors define the global and local distances for digital curves as an editing distance.

Paper Details

Date Published: 23 September 1999
PDF: 10 pages
Proc. SPIE 3811, Vision Geometry VIII, (23 September 1999); doi: 10.1117/12.364116
Show Author Affiliations
Atsushi Imiya, Chiba Univ. (Japan)
Muneaki Oosawa, Chiba Univ. (Japan)


Published in SPIE Proceedings Vol. 3811:
Vision Geometry VIII
Longin Jan Latecki; Robert A. Melter; David M. Mount; Angela Y. Wu, Editor(s)

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