Portugaliae Mathematica

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Volume 67, Issue 1, 2010, pp. 75–89
DOI: 10.4171/PM/1858

Published online: 2010-02-01

The number of continuous curves in digital geometry

Shiva Samieinia[1]

(1) Uppsala University, Sweden

As a model for continuous curves in digital geometry, we study the Khalimsky-continuous functions defined on the integers and with values in the set of integers or the set of natural numbers. We determine the number of such functions on a given interval. It turns out that these numbers are related to the Delannoy and Schröder arrays, and a relation between these numbers is established.

Keywords: Digital geometry, Khalimsky topology, Khalimsky plane, Khalimsky-continuous function

Samieinia Shiva: The number of continuous curves in digital geometry. Port. Math. 67 (2010), 75-89. doi: 10.4171/PM/1858