Partial difference equations (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 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: (1) p -Laplacian restoration and inpainting; (2) PDEs mathematical morphology; and (3) active contours segmentation.

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Abstract-In this paper, we propose a nonlocal approach based on graphs to segment raw point clouds as a particular class of graph signals. Using the framework of Partial difference Equations (PdEs), we propose a transcription on graphs of recent continuous global active contours along with a minimization algorithm. To apply it on point clouds, we show how to represent a point cloud as a graph weighted with patches. Experiments show the benefits of the approach on raw colored point clouds obtained from real scans 1 .

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Abstract-In this paper, we propose an adaptation of morphological Partial Differential Equations (PDEs) on graphs using the framework of Partial difference Equations (PdEs). This enables to define adaptive morphological operators on graphs. We then show how these operators can be used for interpolation and filtering of raw point clouds. To enable a patch-based processing of point clouds, we show how a weighted graph based on patches can be associated with a point cloud. Finally, we present applications in cultural heritage1 .

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