On the infinity Laplacian Equation on Graph with Applications to image and Manifolds Processing

International audienceIn this paper, an adaptation of the infinity laplacian equation to the case of weighted graph is proposed. Our approach is based on a family of discrete morphological local and nonlocal gradient on graphs expressed by partial difference equations. Our formulation generalize local and nonlocal configurations in the context of image processing and extend this equation to the processing any data that can be represented by a graph in any dimension. An example of applications will be given to illustrate the use of infinity-harmonic functions for local and nonlocal inpainting