Distances based on neighbourhood sequences in non-standard three-dimensional grids

Authors:
Robin Strand;Benedek Nagy
Affiliations:
Centre for Image Analysis, Uppsala University, Lägerhyddsvägen 3, SE-75237 Uppsala, Sweden;Department of Computer Science, Faculty of Informatics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary and Research Group on Mathematical Linguistics, Rovira i Virgili University, Ta ...
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

Properties for distances based on neighbourhood sequences on the face-centred cubic (fcc) and the body-centred cubic (bcc) grids are presented. Formulas to both compute the distances and assure that the distances satisfy the conditions for being metrics are presented and proved to be correct. The formulas are used to calculate the neighbourhood sequences that generates distances with lowest deviation from the Euclidean distance.