Weighted distances based on neighborhood sequences for point-lattices

  • Authors:

  • Robin Strand

  • Affiliations:

  • Centre for Image Analysis, Uppsala University, Box 337, SE-75105 Uppsala, Sweden

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2009

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Abstract

A path-based distance is defined as the minimal cost-path between two points. One such distance function is the weighted distance based on a neighborhood sequence. It can be defined using any number of neighborhood relations and weights in conjunction with a neighborhood sequence. The neighborhood sequence restricts some steps in the path to a smaller neighborhood. We give formulas for computing the point-to-point distance and conditions for metricity for weighted distances based on neighborhood sequences with two neighborhood relations for the general case of point-lattices.