A Variational Retouching Algorithm for Jacquard Fabric Image Based on Mumford-Shah Model

Image retouching is an iterative technology for repairing damaged areas from images. Most existing retouching algorithms are local in nature and extrapolate information from neighboring pixels into the damaged regions. In this paper, a novel retouching algorithm based on the Mumford-Shah (MS) model was proposed. First, the Mumford-Shah model was improved by imposing some explicit smooth constrains on the formation of discontinuities. Then, a sequence of functionals Gamma-convergent to the retouching model was proposed. Finally, the gradient flow equation associated to the sequence of functional was defined, and the finite difference approximation for numerical solving of the gradient flow equation was also presented. Experimental results on noisy jacquard images demonstrate the effectiveness of the proposed retouching algorithm.