Curvature-guided cartoon-texture decomposition of a color image

In this paper, we propose a novel curvature-guided variational model for color image decomposition. In particular, we integrate the curvature priors into the traditional variational model to steer the evolution towards preserving curvature information, meanwhile, we incorporate saturation-value total variation to regularize the cartoon component of a color image. Additionally, we utilize the $L^1$ norm to model the texture component in the saturation-value color space. The proposed variational model introduces an energy functional to achieve cartoon and texture decomposition in saturation-value color space, and preserves color information, fine structures/edges in the cartoon component. Theoretically, we explore the properties of the proposed model and provide a theoretical discussion about the existence of the solution. We then develop an effective and efficient algorithm to minimize the problem by utilizing the alternating direction method of multipliers. Numerical examples are presented to demonstrate that the performance of our framework competes favorably with other methods in terms of visual quality and metrics such as structure similarity (SSIM), peak signal-to-noise ratio (PSNR), quaternion structural similarity (QSSIM), S-CIELAB color metric, average local contrast (ALC), and discrete entropy (DE).