A relational generalization of the Khalimsky topology

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en

We discuss certain n-ary relations (n > 1 an integer) and show that each of them induces a connectedness on its underlying set. Of these n-ary relations, we study a particular one on the digital plane Z2 for every integer n > 1. As the main result, for each of the n-ary relations studied, we prove a digital analogue of the Jordan curve theorem for the induced connectedness. It follows that these n-ary relations may be used as convenient structures on the digital plane for the study of geometric properties of digital images. For n = 2, such a structure coincides with the (specialization order of the) Khalimsky topology and, for n > 2, it allows for a variety of Jordan curves richer than that provided by the Khalimsky topology.

n-ary relation, digital plane, Khalimsky topology, Jordan curve theorem

2017-06-01

Springer

Switzerland

978-3-319-59107-0

0302-9743

Combinatorial Image Analysis

Lecture Notes in Computer Science

10256

132–141

10