A Geometric Approach to Color Image Regularization

TL;DR

This paper introduces a novel vectorial total variation method inspired by human visual cortex to improve color image filtering, reducing artifacts and enhancing restoration quality in inpainting, deblurring, and denoising.

Contribution

It proposes a new coupling mechanism based on a pullback-metric to better preserve color consistency, along with a non-convex higher-order regularization approach.

Findings

Achieves state-of-the-art results in image restoration tasks

Ensures well-posedness and existence of solutions for the convex variant

Effectively reduces color artifacts in filtering processes

Abstract

We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of vectorial total variation regularizers have insufficient (or no) coupling between the color channels and thus may introduce color artifacts. We address this problem by introducing a novel coupling between the color channels related to a pullback-metric from the opponent space to the data (RGB color) space. Our energy is a non-convex, non-smooth higher-order vectorial total variation approach and promotes color consistent image filtering via a coupling term. For a convex variant, we show well-posedness and existence of a solution in the space of vectorial bounded variation. For the higher-order scheme we employ a half-quadratic strategy, which model the non-convex energy terms as the infimum of a sequence of quadratic functions. In experiments, we elaborate on traditional image restoration applications of inpainting, deblurring and denoising. Regarding the latter, we demonstrate state of the art restoration quality with respect to structure coherence and color consistency.