Regularized Gradient Kernel Anisotropic Diffusion for Better Image Filtering

Abstract

This paper proposes an extension to anisotropic diffusion filtering for a better preservation of semantically meaningful structures such as edges in an image in its smoothing/denoising process. The problem of separation of the gradients due to edges and the gradients due to noise is formulated as a nonlinearly separable classification problem. More specifically, the spatially-regularized image gradient is mapped to a higher dimensional Reproducing Kernel Hilbert Space (RKHS) in which the gradients of the edges from those of noise can be readily separated. This proper discrimination of edges prevents the filter from blurring the edges, while smoothing the image. Compared to the existing anisotropic filters, the proposed method improves the denoising and smoothing of an image on both synthetic and real images.