Cartoon and texture decomposition for color image in opponent color space

The Meyer model has been successfully applied to decompose cartoon component and texture component for the gray scale image, where the total variation (TV) norm and the G-norm are respectively modeled to capture the cartoon component and the texture component in an energy minimization method. In this paper, we extend this model to the color image in the opponent color space, which is closer to human perception than the RGB space. It is important to extend the TV norm and the G-norm correspondingly because the color image is viewed as a vector-valued vector. We introduce the definition of the L-1 norm and L-infinity norm for the vector-valued vector and accordingly define the TV norm and the G-norm for the color image. In order to handle the numerical difficulty caused by the non-differentiability of the TV norm and G-norm, the dual formulations are used to represent these norm. Then the decomposition problem is reformulated into a minimax problem. A first-order primal-dual algorithm is readily applied to compute the saddle point of the minimax problem. Numerical results are shown the performance of the proposed model. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

The Meyer model has been extended to color images in opponent color space, introducing L-1 and L-infinity norms for vector-valued vectors, and redefining TV and G-norms accordingly. Dual formulations are used to handle the non-differentiability of norms, and a first-order primal-dual algorithm is applied to compute the saddle point of the minimax problem for decomposition of color images. The proposed model shows promising performance in numerical results.