Digital Distances and Integer Sequences
2013 (English)In: Lecture Notes in Computer Science / [ed] Rocio Gonzalez-Diaz, Maria-Jose Jimenez, Belen Medran, 2013, 169-179 p.Conference paper (Refereed)
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.
IdentifiersURN: urn:nbn:se:uu:diva-212566OAI: oai:DiVA.org:uu-212566DiVA: diva2:678333
17th IAPR International Conference, DGCI 2013, Seville, Spain