2012
DOI: 10.1109/jstsp.2012.2216504
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Abstract: In this paper, we introduce a new class of nonlocal p-Laplacian operators that interpolate between non-local Laplacian and infinity Laplacian. These operators are discrete analogous of the game p-laplacian operators on Euclidean spaces, and involve discrete morphological gradient on graphs. We study the Dirichlet problem associated with the new p-Laplacian equation and prove existence and uniqueness of it's solution. We also consider non-local diffusion on graphs involving these operators. Finally, we propose … Show more

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Cited by 41 publications
(39 citation statements)
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References 60 publications
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“…Secondly, several papers use the MBO algorithm on a graph to approximate motion by mean curvature [17,40]. It is important to note that the curvature is defined by means of the isotropic total variation [17] instead of the one-Laplacian as it is the case in [10,11,12,13].…”
Section: Morphological Operators Via Convolution On Graphmentioning
confidence: 99%
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“…Secondly, several papers use the MBO algorithm on a graph to approximate motion by mean curvature [17,40]. It is important to note that the curvature is defined by means of the isotropic total variation [17] instead of the one-Laplacian as it is the case in [10,11,12,13].…”
Section: Morphological Operators Via Convolution On Graphmentioning
confidence: 99%
“…On the other hand, some regularisation techniques and nonlinear operators have been introduced on function evaluated on graph via directional derivative [10] [11] [12] or discrete version of the p-Laplacian [13]. We adopt a different viewpoint, our approach is inspired from the signal processing approach on graphs [14,15,16,17].…”
Section: Introductionmentioning
confidence: 99%
“…Additionnaly, it was shown in [EDL12] that the non-local ∞−Laplacian (Eq. 8) depends on these NLD and NLE operators:…”
Section: Morphological Operators On Graphsmentioning
confidence: 99%
“…3) Interpolation and filtering algorithms: Whatever the problems (interpolation or filtering), works of [EDL12] have shown that both problems have a unique solution that can be obtained using the following iterative algorithm:…”
Section: Interpolation and Filtering On Weighted Graphsmentioning
confidence: 99%
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