Alexander V. Evako

Alexander V. Evako

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.

Alexander V. Evako

Transformations of digital spaces preserving local and global topology play an important role in thinning, skeletonization and simplification of digital images. In the present paper, we introduce and study contractions of simple pair of points based on the notions of a digital contractible space and contractible transformations of digital spaces. We show that the contraction of a simple pair of points preserves local and global topology of a digital space. Relying on the obtained results, we study properties if digital manifolds. In particular, we show that a digital n-manifold can be transformed to its compressed form with the minimal number of points by sequential contractions of simple pairs. Key Words: Graph, digital space, contraction, splitting, simple pair, homotopy, thinning