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Digital Geometry by Azriel Rosenfeld, Reinhard Klette

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CHAPTER 6

Topology

Digital geometry is often concerned with analyzing topologic properties of sets of pixels or voxels. The topology of Euclidean space was briefly discussed in Section 3.1.7. The definitions of open and closed regions in Section 5.1.4 indicated that these topologic concepts are applicable to discrete structures. This chapter summarizes basic topologic concepts and properties that are relevant to adjacency and incidence grids, defines digital topologies, and provides a brief introduction to combinatorial topology.

6.1 Topologic Spaces

In the last third of the 19th century, H. Poincaré and others established topology as a branch of modern mathematics. Point-set topology studies topologic spaces. In early publications about topology, ...

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