Mean curvature flow on graphs for image and manifold restoration and enhancement

• Adaptation of mean curvature on graphs.
• Morphological scheme for mean curvature flow.
• Connection with nonlocal mean curvature and Euclidean graphs.
• Images and data restoration and enhancement.

In this paper, we propose an adaptation and a transcription of the mean curvature level set equation on the general discrete domain, a weighted graph. For this, we introduce perimeters on graphs using difference operators and define the curvature as the first variation of these perimeters. Then we propose a morphological scheme that unifies both local and nonlocal notions of mean curvature on Euclidean domains. Furthermore, this scheme allows to extend the mean curvature applications to process images, manifolds and data which can be represented by graphs.