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ISPRS Int. J. Geo-Inf. 2016, 5(11), 213; doi:10.3390/ijgi5110213

Morphological PDEs on Graphs for Image Processing on Surfaces and Point Clouds

1
A3SI Team, University of Paris-Est Marne-La-Vallée int the LIGIM Laboratory, Cité Descartes, Bâtiment Copernic-5, Boulevard Descartes, Champs sur Marne, 77454 Marne-la-Vallée Cedex 2, France
2
Image Team, University of Caen Normandy and the ENSICAEN in the GREYC Laboratory, 6 Boulevard Maréchal Juin, F-14050 Caen Cedex, France
*
Author to whom correspondence should be addressed.
Academic Editors: Beatriz Marcotegui and Wolfgang Kainz
Received: 30 June 2016 / Revised: 24 October 2016 / Accepted: 4 November 2016 / Published: 12 November 2016
(This article belongs to the Special Issue Mathematical Morphology in Geoinformatics)
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Abstract

Partial Differential Equations (PDEs)-based morphology offers a wide range of continuous operators to address various image processing problems. Most of these operators are formulated as Hamilton–Jacobi equations or curve evolution level set and morphological flows. In our previous works, we have proposed a simple method to solve PDEs on point clouds using the framework of PdEs (Partial difference Equations) on graphs. In this paper, we propose to apply a large class of morphological-based operators on graphs for processing raw 3D point clouds and extend their applications for the processing of colored point clouds of geo-informatics 3D data. Through illustrations, we show that this simple framework can be used in the resolution of many applications for geo-informatics purposes. View Full-Text
Keywords: generalized distance; Hamilton–Jacobi equation; weighted graphs; partial difference equations; mathematical morphology generalized distance; Hamilton–Jacobi equation; weighted graphs; partial difference equations; mathematical morphology
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Elmoataz, A.; Lozes, F.; Talbot, H. Morphological PDEs on Graphs for Image Processing on Surfaces and Point Clouds. ISPRS Int. J. Geo-Inf. 2016, 5, 213.

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