The Use of Size Functions for Comparison of Shapes Through Differential Invariants

  • Authors:

  • Françoise Dibos;Patrizio Frosini;Denis Pasquignon

  • Affiliations:

  • Centre de recherche CEREMADE, Université Paris IX Dauphine Place du Maréchal de Lattre de Tassigny 75775 Paris cedex 16. dibos@ceremade.dauphine.fr;Università di Bologna, Dipartimento di Matematica Piazza Porta San Donato, 5, I-40127 Bologna. frosini@dm.unibo.it;Centre de recherche CEREMADE, Université Paris IX Dauphine Place du Maréchal de Lattre de Tassigny 75775 Paris cedex 16. dpasquig@ceremade.dauphine.fr

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2004

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Abstract

For comparison of shapes under subgroups of the projective group, we can use a lot of invariants and especially differential invariants coming from multiscale analysis. But such invariants, as we have to compute curvature, are very sensitive to the noise induced by the dicretization grid. In order to resolve this problem we use size functions which can recognize the “qualitative similarity” between graphs of functions that should be theorically coinciding but, unfortunately, change their values due to the presence of noise. Moreover, we focus this study on a projective differential invariant which allows to decide if one shape can be considered as the deformation of another one by a rotation of the camera.