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Nonlocal Difference Operators on Graphs for Interpolation on Point Clouds

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Mathematical Morphology and Its Applications to Signal and Image Processing (ISMM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10225))

Abstract

In this paper we introduce a new general class of partial difference operators on graphs, which interpolate between the nonlocal \(\infty \)-Laplacian, the Laplacian, and a family of discrete gradient operators. In this context we investigate an associated Dirichlet problem for this general class of operators and prove the existence and uniqueness of respective solutions. We propose to use this class of operators as general framework to solve many interpolation problems in a unified manner as arising, e.g., in image and point cloud processing. (AE is supported by the European FEDER Grant (PLANUCA Project) and the project ANR GRAPHSIP.)

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Authors and Affiliations

  1. Université de Caen Basse-Normandie and the ENSICAEN in the GREYC UMR CNRS 6072 Laboratory, Image Team, 6 Boulevard Maréchal Juin, 14050, Caen Cedex, France

    François Lozes & Abderrahim Elmoataz

Authors
  1. François Lozes
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  2. Abderrahim Elmoataz
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Corresponding author

Correspondence to François Lozes .

Editor information

Editors and Affiliations

  1. MINES ParisTech, PSL-Research University, Fontainebleau, France

    Jesús Angulo

  2. MINES ParisTech, PSL-Research University , Fontainebleau, France

    Santiago Velasco-Forero

  3. MINES ParisTech, PSL-Research University, Fontainebleau, France

    Fernand Meyer

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Lozes, F., Elmoataz, A. (2017). Nonlocal Difference Operators on Graphs for Interpolation on Point Clouds. In: Angulo, J., Velasco-Forero, S., Meyer, F. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2017. Lecture Notes in Computer Science(), vol 10225. Springer, Cham. https://doi.org/10.1007/978-3-319-57240-6_25

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  • DOI: https://doi.org/10.1007/978-3-319-57240-6_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57239-0

  • Online ISBN: 978-3-319-57240-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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