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Distance Functions Based on Multiple Types of Weighted Steps Combined with Neighborhood Sequences
Eastern Mediterranean Univ, Dept Math, Mersin 10, Famagusta, North Cyprus, Turkey.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.ORCID iD: 0000-0001-7764-1787
Univ Nantes, LS2N, UMR, CNRS 6004, Nantes, France.
2018 (English)In: Journal of Mathematical Imaging and Vision, ISSN 0924-9907, E-ISSN 1573-7683, Vol. 60, no 8, p. 1209-1219Article in journal (Refereed) Published
Abstract [en]

In this paper, we present a general framework for digital distance functions, defined as minimal cost paths, on the square grid. Each path is a sequence of pixels, where any two consecutive pixels are adjacent and associated with a weight. The allowed weights between any two adjacent pixels along a path are given by a weight sequence, which can hold an arbitrary number of weights. We build on our previous results, where only two or three unique weights are considered, and present a framework that allows any number of weights. We show that the rotational dependency can be very low when as few as three or four unique weights are used. Moreover, by using n weights, the Euclidean distance can be perfectly obtained on the perimeter of a square with side length 2n. A sufficient condition for weight sequences to provide metrics is proven.

Place, publisher, year, edition, pages
2018. Vol. 60, no 8, p. 1209-1219
Keywords [en]
Distance functions, Weight sequences, Neighborhood sequences, Chamfer distances, Approximation of Euclidean distance
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:uu:diva-364167DOI: 10.1007/s10851-018-0805-1ISI: 000443369800003OAI: oai:DiVA.org:uu-364167DiVA, id: diva2:1260834
Available from: 2018-11-05 Created: 2018-11-05 Last updated: 2018-11-16Bibliographically approved

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Strand, Robin

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