In this paper, we propose an adaptation and transcription of the mean curvature level set equation on a general discrete domain (weighted graphs with arbitrary topology).We introduce the perimeters on graph using difference operators and define the curvature as the first variation of these perimeters. Our proposed approach of mean curvature unifies both local and non local notions of mean curvature on Euclidean domains. Furthermore, it allows the extension to the processing of manifolds and data which can be represented by graphs.
This paper presents an adaptation of the shock filter on weighted graphs using the formalism of Partial difference Equations. This adaptation leads to a new morphological operators that alternate the nonlocal dilation and nonlocal erosion type filter on graphs. Furthermore, this adaptation extends the shock filters applications to any data that can be represented by graphs. This paper also presents examples that illustrate our proposed approach.
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