Continuous shape transformation and metrics on regions

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A natural approach to defining continuous change of shape is in terms of a metric that measures the difference between two regions. We consider four such metrics over regions: the Hausdorff distance, the dual-Hausdorff distance, the area of the symmetric difference, and the optimal-homeomorphism metric (a generalization of the Fréchet distance). Each of these gives a different criterion for continuous change. We establish qualitative properties of all of these; in particular, the continuity of basic functions such as union, intersection, set difference, area, distance, and smoothed circumference and the transition graph between RCC-8 relations. We also show that the history-based definition of continuity proposed by Muller is equivalent to continuity with respect to the Hausdorff distance.

Original languageEnglish (US)
Pages (from-to)31-54
Number of pages24
JournalFundamenta Informaticae
Issue number1-2
StatePublished - Apr 2001

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Information Systems
  • Computational Theory and Mathematics


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