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Partial difference operators on weighted graphs for image processing on surfaces and point clouds

François Lozes 1 Abderrahim Elmoataz 1 Olivier Lézoray 1
1 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : PDEs and variational methods for image processing on Euclidean domains spaces are very well established because they permit to solve a large range of real computer vision problems. With the recent advent of many 3D sensors, there is a growing interest in transposing and solving PDEs on surfaces and point clouds. In this paper, we propose a simple method to solve such PDEs using the framework of Partial difference Equations (PdEs) on graphs. This latter approach enables us to transcribe, for surfaces and point clouds, many models and algorithms designed for image processing. To illustrate our proposal, three problems are considered: p-Laplacian restoration and inpainting, PDEs Mathematical Morphology, and active contours segmentation.
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François Lozes, Abderrahim Elmoataz, Olivier Lézoray. Partial difference operators on weighted graphs for image processing on surfaces and point clouds. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2014, 23 (9), pp.3896 - 3909. ⟨10.1109/TIP.2014.2336548⟩. ⟨hal-01096304⟩

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