Structural Properties of Shape-Spaces

  • Werner Dilger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4163)


General properties of distance functions and of affinity functions are discussed in this paper. Reasons are given why a distance function for (n based shape-spaces should be a metric. Several distance functions that are used in shape-spaces are examined and it is shown that not all of them are metrics. It is shown which impact the type of the distance function has on the shape-space, in particular on the form of recognition or affinity regions in the shape-space. Affinity functions should be defined in such a way that they determine an affinity region with positive values inside that region and zero or negative values outside. The form of an affinity function depends on the type of the underlying distance function. This is demonstrated with several examples.


Shape-space distance function metric affinity function affinity region 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Werner Dilger
    • 1
  1. 1.Chemnitz University of TechnologyChemnitzGermany

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