Color Image Enhancement by a Forward-and-Backward Adaptive Beltrami Flow

The Beltrami diffusion-type process, reformulated for the purpose of image processing, is generalized to an adaptive forward-andbackward process and applied in localized image features’ enhancement and denoising. Images are considered as manifolds, embedded in higher dimensional feature-spaces that incorporate image attributes and features such as edges, color, texture, orientation and convexity. To control and stabilize the process, a nonlinear structure tensor is incorporated. The structure tensor is locally adjusted according to a gradient-type measure. Whereas for smooth areas it assumes positive values, and thus the diffusion is forward, for edges (large gradients) it becomes negative and the diffusion switches to a backward (inverse) process. The resultant combined forward-and-backward process accomplishes both local denoising and feature enhancement.