Adaptive Discrete Laplace Operator

  • Christophe Fiorio
  • Christian Mercat
  • Frédéric Rieux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6939)


Diffusion processes capture information about the geometry of an object such as its curvature, symmetries and particular points. The evolution of the diffusion is governed by the Laplace-Beltrami operator which presides to the diffusion on the manifold. In this paper, we define a new discrete adaptive Laplacian for digital objects, generalizing the operator defined on meshes. We study its eigenvalues and eigenvectors recovering interesting geometrical informations. We discuss its convergence towards the usual Laplacian operator especially on lattice of diamonds. We extend this definition to 3D shapes. Finally we use this Laplacian in classical but adaptive denoising of pictures preserving zones of interest like thin structures.


Heat Kernel Image Denoising Discrete Time Markov Chain Gray Intensity Heat Kernel Signature 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christophe Fiorio
    • 1
  • Christian Mercat
    • 2
  • Frédéric Rieux
    • 1
    • 3
  1. 1.LIRMMUniversité Montpellier 2MontpellierFrance
  2. 2.IREM, S2HEPUniversité Claude Bernard Lyon 1Villeurbanne cedexFrance
  3. 3.I3MUniversité Montpellier 2Montpellier Cedex 5France

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