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23 September 1999 Description of 3D digital curves using the theory free groups
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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.
© (1999) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Atsushi Imiya and Muneaki Oosawa "Description of 3D digital curves using the theory free groups", Proc. SPIE 3811, Vision Geometry VIII, (23 September 1999); https://doi.org/10.1117/12.364116
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