On the Mean Curvature Flow on Graphs with Applications in Image and Manifold Processing

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.