ABSTRACT
This chapter introduces the isotropic and anisotropic p-Laplace operators as well as the associated p-Laplacian matrix. It provides detail on defining the graph topology and the graph weights. The chapter focuses on two classes of graphs: a modified version of k-nearest neighbors graphs and t-neighborhood graphs. It considers the case of an anisotropic regularization functional. The chapter explains how to perform image colorization with the proposed framework. It illustrates the abilities of p-Laplace (isotropic and anisotropic) regularization on graphs for simplification and interpolation of any function defined on a finite set of discrete data living in Rm. The chapter also illustrates the abilities of the authors' approach for the simplification of functions representing images or images' manifold. It illustrates the ability of the author's approach for the interpolation of missing values. The chapter considers the case of image in painting, and shows the interest of partial difference equations on graphs for image processing and analysis.
