Anisotropic diffusion filtering through multi-objective optimization

Images are often corrupted by noise during their process of acquisition, storage and transmission. This alteration usually deteriorates the perception quality of the image. The central challenge in image denoising corresponds to eliminating the corrupted information while it is maintained the fine features of the original image. Anisotropic Diffusion (AD) is considered a well-established scheme for removing noise in digital images without deteriorating their edges. The selection of parameters that define the AD operation presents a very decisive implication in the filtering results. In spite of the importance of the AD operation, the problem of automatically calculating its parameter according to the image requirements has been scarcely considered in the literature. In this paper, a new multi-objective methodology to obtain the AD parameters for effective filter results is presented. In the proposed approach, the appropriate AD parameter values are obtained as the solution that involves the best possible trade-off between two conflicting scenarios: To minimize the noise content in the image while the contrast is maximized. Both objectives cannot be individually improved without worsening another. The proposed scheme uses to solve this formulation of the Non-dominated sorting genetic algorithm based on reference points (NSGA-III), which represent one of the most robust and powerful algorithms for multi-objective optimization. Then, the final solution is obtained from an analysis of the Optimal Pareto front. Experimental results demonstrate that the proposed method presents better results than existing filtering algorithms in terms of visual quality and standard performance metrics.