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Acta Applicandae Mathematicae

, Volume 109, Issue 2, pp 527–554 | Cite as

Natural Pseudo-Distance and Optimal Matching between Reduced Size Functions

  • Michele d’Amico
  • Patrizio Frosini
  • Claudia Landi
Article

Abstract

This paper studies the properties of a new lower bound for the natural pseudo-distance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a real-valued continuous function. Measuring dissimilarity amounts to minimizing the change in the functions due to the application of homeomorphisms between topological spaces, with respect to the L -norm. In order to obtain the lower bound, a suitable metric between size functions, called matching distance, is introduced. It compares size functions by solving an optimal matching problem between countable point sets. The matching distance is shown to be resistant to perturbations, implying that it is always smaller than the natural pseudo-distance. We also prove that the lower bound so obtained is sharp and cannot be improved by any other distance between size functions.

Keywords

Shape comparison Shape representation Reduced size function Natural pseudo-distance 

Mathematics Subject Classification (2000)

68T10 58C05 49Q10 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Michele d’Amico
    • 1
  • Patrizio Frosini
    • 1
    • 2
  • Claudia Landi
    • 3
  1. 1.ARCESUniversità di BolognaBolognaItaly
  2. 2.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  3. 3.DISMIUniversità di Modena e Reggio EmiliaReggio EmiliaItaly

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