Graph regularization for color image processing

Nowadays color image processing is an essential issue in computer vision. Variational formulations provide a framework for color image restoration, smoothing and segmentation problems. The solutions of variational models can be obtained by minimizing appropriate energy functions and this minimization is usually performed by continuous partial differential equations (PDEs). The problem is usually considered as a regularization matter which minimizes a smoothness plus a regularization term. In this paper, we propose a general discrete regularization framework defined on weighted graphs of arbitrary topologies which can be seen as a discrete analogue of classical regularization theory. The smoothness term of the regularization uses a discrete definition of the p-Laplace operator. With this formulation, we propose a family of fast and simple anisotropic linear and nonlinear filters which do not involve PDEs. The proposed approach can be useful to process color images for restoration, denoising and segmentation purposes.