Mathematical Morphology for Real-Valued Images on Riemannian Manifolds

  • Jesús Angulo
  • Santiago Velasco-Forero
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7883)


This paper introduces mathematical morphology for real-valued images whose support space is a Riemannian manifold. The starting point consists in replacing the Euclidean distance in the canonic quadratic structuring function by the Riemannian distance. Besides the definition of Riemannian dilation/erosion and Riemannian opening/closing, their properties are explored. We generalize also some theoretical results on Lasry–Lions regularization for Cartan–Hadamard manifolds. Theoretical connections with previous works on adaptive morphology and on manifold shape are considered. Various useful image manifolds are formalized, with an example using real-valued 3D surfaces.


Riemannian Manifold Geodesic Distance Parallel Transport Mathematical Morphology Hadamard Manifold 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jesús Angulo
    • 1
  • Santiago Velasco-Forero
    • 2
  1. 1.CMM-Centre de Morphologie Mathématique, Mathématiques et SystèmesMINES ParisTechFrance
  2. 2.ITWM - Fraunhofer InstituteKaiserlauternGermany

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