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

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.