Digitizations preserving shape

Antonio Giraldo

doi:10.1117/12.279665

20 October 1997 Digitizations preserving shape

Antonio Giraldo

Proceedings Volume 3168, Vision Geometry VI; (1997) https://doi.org/10.1117/12.279665
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

We show in this paper how it is possible to digitize a wide class of plane compacta in such a way that their digitization shave the same shape, in the sense of Borsuk, as the original set. This class is formed by all those compacta having the shape of finite polyhedra. As a corollary we get that for a still wide subclass, that whose elements are also absolute neighborhood retracts, the homotopy properties are also preserved under appropriate digitizations. Our results are based in approximation results by finite polyhedra and on the fact that the usual digitizations, when applied to finite polyhedra, preserve the homotopy type. Moreover, we show that if a set does not have the shape of a finite polyhedron, then there is not any possible way to digitize it while having its shape preserved.

Citation Download Citation

Antonio Giraldo "Digitizations preserving shape", Proc. SPIE 3168, Vision Geometry VI, (20 October 1997); https://doi.org/10.1117/12.279665

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