Approximating the Euclidean circle in the square grid using neighbourhood sequences

Details Approximating the Euclidean circle in the square grid using neighbourhood sequences Approximating the Euclidean circle in the square grid using neighbourhood sequences

2010-06-17

arxiv.org/abs/1006.3404v1

Pure Mathematics and Applications 17 (2006) 309-322

Mathematics

Metric Geometry

Lecture at the 6th Joint Conference on Mathematics and Computer Science (MACS '06) Pecs, Hungary, 12-15 July, 2006

Scientific paper

Distance measuring is a very important task in digital geometry and digital image processing. Due to our natural approach to geometry we think of the set of points that are equally far from a given point as a Euclidean circle. Using the classical neighbourhood relations on digital grids, we get circles that greatly differ from the Euclidean circle. In this paper we examine different methods of approximating the Euclidean circle in the square grid, considering the possible motivations as well. We compare the perimeter-, area-, curve- and noncompactness-based approximations and examine their realization using neighbourhood sequences. We also provide a table which summarizes our results, and can be used when developing applications that support neighbourhood sequences.

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