Path-based distance functions in n-dimensional generalizations of the face- and body-centered cubic grids

Authors:
Robin Strand;Benedek Nagy
Affiliations:
Centre for Image Analysis, Uppsala University, PO Box 337, SE-75105 Uppsala, Sweden;Department of Computer Science, Faculty of Informatics, University of Debrecen, PO Box 12, 4010, Debrecen, Hungary
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

Path-based distance functions are defined on n-dimensional generalizations of the face-centered cubic and body-centered cubic grids. The distance functions use both weights and neighborhood sequences. These distances share many properties with traditional path-based distance functions, such as the city-block distance, but are less rotational dependent. For the three-dimensional case, we introduce four different error functions which are used to find the optimal weights and neighborhood sequences that can be used to define the distance functions with low rotational dependency.