Fast adaptive alternatives to nonlinear diffusion in image enhancement: Green's function approximators and nonlocal filters

Abstract

Nonlinear diffusion, as well as image-driven nonlinear filtering, provide improved contrast enhancement and noise reduction relative to linear techniques, but are too computationally expensive for use in real-time vision applications. In this paper we review several recently developed methods which achieve results comparable to those obtained from nonlinear diffusion at considerably less computational cost. In the first technique, we train a function approximator to learn a kernel function which produces nonlinear diffusion-type results via spatial integration of the kernels across the image. The second method involves the construction of a vector field of “offsets” at which to apply a (single-scale) filter. When combined with space-variant (e.g. log polar) architectures, which themselves provide between one and three orders of magnitude of speed-up relative to conventional image representations, we are able to achieve frame rate image enhancement similar to that of nonlinear diffusion.