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Digital Distances and Integer Sequences
LUNAM Université, Université de Nantes, IRCCyN UMR CNRS 6597, Polytech Nantes, Rue Christian Pauc, La Chantrerie, 44306 Nantes Cedex 3, France.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
2013 (English)In: Lecture Notes in Computer Science / [ed] Rocio Gonzalez-Diaz, Maria-Jose Jimenez, Belen Medran, 2013, 169-179 p.Conference paper, Published paper (Refereed)
Abstract [en]

In recent years, the theory behind distance functions defined by neighbourhood sequences has been developed in the digital geometry community. A neighbourhood sequence is a sequence of integers, where each element defines a neighbourhood. In this paper, we establish the equivalence between the representation of convex digital disks as an intersection of half-planes ( H -representation) and the expression of the distance as a maximum of non-decreasing functions.

Both forms can be deduced one from the other by taking advantage of the Lambek-Moser inverse of integer sequences.

Examples with finite sequences, cumulative sequences of periodic sequences and (almost) Beatty sequences are given. In each case, closed-form expressions are given for the distance function and H -representation of disks. The results can be used to compute the pair-wise distance between points in constant time and to find optimal parameters for neighbourhood sequences.

Place, publisher, year, edition, pages
2013. 169-179 p.
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-212566OAI: oai:DiVA.org:uu-212566DiVA: diva2:678333
Conference
17th IAPR International Conference, DGCI 2013, Seville, Spain
Available from: 2013-12-11 Created: 2013-12-11 Last updated: 2013-12-11

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