Image statistics and anisotropic diffusion

Many sensing techniques and image processing applica-tions are characterized by noisy, or corrupted, image data. Anisotropic diffusion is a popular, and theoretically well understood, technique for denoising such images. Diffu-sion approaches however require the selection of an “edge stopping ” function, the definition of which is typically ad hoc. We exploit and extend recent work on the statistics of natural images to define principled edge stopping func-tions for different types of imagery. We consider a variety of anisotropic diffusion schemes and note that they compute spatial derivatives at fixed scales from which we estimate the appropriate algorithm-specific image statistics. Going beyond traditional work on image statistics, we also model the statistics of the eigenvalues of the local structure tensor. Novel edge-stopping functions are derived from these image statistics giving a principled way of formulating anisotropic diffusion problems in which all edge-stopping parameters are learned from training data.