Properties of simple sets in digital spaces. Contractions of simple sets preserving the homotopy type of a digital space

Alexander V. Evako

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arXiv · 1503.03491

Properties of simple sets in digital spaces. Contractions of simple sets preserving the homotopy type of a digital space

Alexander V. Evako

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Abstract

A point of a digital space is called simple if it can be deleted from the space without altering topology. This paper introduces the notion simple set of points of a digital space. The definition is based on contractible spaces and contractible transformations. A set of points in a digital space is called simple if it can be contracted to a point without changing topology of the space. It is shown that contracting a simple set of points does not change the homotopy type of a digital space, and the number of points in a digital space without simple points can be reduces by contracting simple sets. Using the process of contracting, we can substantially compress a digital space while preserving the topology. The paper proposes a method for thinning a digital space which shows that this approach can contribute to computer science such as medical imaging, computer graphics and pattern analysis.

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Alexander V. Evako. 2015-03-11. Properties of simple sets in digital spaces. Contractions of simple sets preserving the homotopy type of a digital space. https://arxiv.org/abs/1503.03491

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