Morphological PDEs on graphs for filtering and inpainting of point clouds

Lozes, François; Elmoataz, Abderrahim; Lézoray, Olivier

doi:10.1109/ispa.2013.6703800

Cited by 3 publications

(3 citation statements)

References 13 publications

(18 reference statements)

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“…Figure 9 illustrates results of graph inpainting for 3D point cloud color reconstruction. In this case, the graph is built as a nonlocal graph from the point cloud using the definition of patches on point cloud proposed by [36]. The function f to be interpolated associates a color vector to each vertex of the graph.…”

Section: Nonlocal Image Inpaintingmentioning

confidence: 99%

On the $p$-Laplacian and $\infty$-Laplacian on Graphs with Applications in Image and Data Processing

Elmoataz

Toutain

Tenbrinck³

2015

SIAM J. Imaging Sci.

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International audienceIn this paper we introduce a new family of partial difference operators on graphs and study equations involving these operators. This family covers local variational $p$-Laplacian, $\infty$-Laplacian, nonlocal $p$-Laplacian and $\infty$-Laplacian, $p$-Laplacian with gradient terms, and gradient operators used in morphology based on the partial differential equation. We analyze a corresponding parabolic equation involving these operators which enables us to interpolate adaptively between $p$-Laplacian diffusion-based filtering and morphological filtering, i.e., erosion and dilation. Then, we consider the elliptic partial difference equation with its corresponding Dirichlet problem and we prove the existence and uniqueness of respective solutions. For $p=\infty$, we investigate the connection with Tug-of-War games. Finally, we demonstrate the adaptability of this new formulation for different tasks in image and point cloud processing, such as filtering, segmentation, clustering, and inpainting

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“…Because the obtained orientation depends highly on the most predominant axis, one can find different patches orientations for similar points repartitions, and conversely. Recently we have proposed another strategy (see [2]). We have proposed to estimate the patch orientation from the normals.…”

Section: B Patch Orientationmentioning

confidence: 99%

“…With point clouds, the data to process is not organized on any Cartesian grid and the neighbors of a point have to be defined. Our previous works aim at representing point clouds as weighted graphs to perform nonlocal graph processing [2], [3]. With such a point of view, raw 3D colored point clouds are considered as a specific class of graph signals where a color vector is associated to a point (i.e., a vertex) located in a 3D Euclidean space.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal segmentation of point clouds with graphs

Lozes

Hidane

Elmoataz

et al. 2013

2013 IEEE Global Conference on Signal and Information Processing

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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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Morphological PDEs on graphs for filtering and inpainting of point clouds

Cited by 3 publications

References 13 publications

On the $p$-Laplacian and $\infty$-Laplacian on Graphs with Applications in Image and Data Processing

Nonlocal segmentation of point clouds with graphs

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