Simple pairs of points in digital spaces. Topology-preserving transformations of digital spaces by contracting simple pairs of points
This work addresses the need for efficient thinning and skeletonization in digital image processing, though it appears incremental as it builds on existing concepts of contractible spaces.
The paper tackles the problem of topology-preserving transformations in digital spaces by introducing contractions of simple pairs of points, showing that these preserve local and global topology and enabling the transformation of digital n-manifolds to a minimal compressed form.
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