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Affine Invariant Distance Using Multiscale Analysis

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Abstract

In this paper we introduce an affine invariant distance definition from a \(2D\) point to the boundary of a bounded shape using morphological multiscale analysis. We study the mathematical behavior of this distance by examining separately the cases of convex and non-convex shapes. We prove that the proposed distance is bounded in the convex hull of the shape and infinite otherwise. A numerical scheme is given as well as experiments illustrating the behavior of the affine invariant distance.

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Acknowledgments

Work partly founded by the European Research Council (advanced Grant Twelve Labours) and the Office of Naval research (ONR Grant N00014-14-1-0023).

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Authors and Affiliations

  1. Departamento de Informatica y Sistemas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira, 35017, Las Palmas, Spain

    Luis Alvarez, Carmelo Cuenca, Julio Esclarín & Luis Mazorra

  2. CMLA - ENS Cachan, bat, Laplace, 1er étage, 61 av. du président Wilson, 94235, Cachan cedex, France

    Jean-Michel Morel

Authors
  1. Luis Alvarez
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  2. Carmelo Cuenca
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  3. Julio Esclarín
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  4. Luis Mazorra
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  5. Jean-Michel Morel
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Correspondence to Luis Alvarez.

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Alvarez, L., Cuenca, C., Esclarín, J. et al. Affine Invariant Distance Using Multiscale Analysis. J Math Imaging Vis 55, 199–209 (2016). https://doi.org/10.1007/s10851-015-0585-9

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  • DOI: https://doi.org/10.1007/s10851-015-0585-9

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