Bilateral regularized optimization model for edge-preserving image smoothing

Edge-preserving image smoothing is vital in the field of image processing and computational photography. The state-of-the-art filters based on optimization models have achieved promising performance. However, most of them fail to consider the spatial support in the regularization term, thus limiting the edge-preserving capabilities. In this paper, inspired by the bilateral filter, which consists of a range kernel and a spatial kernel. we propose to leverage bilateral kernel as a penalty function, and embed it into an optimization model for edge-preserving image smoothing. Furthermore, we propose to incorporate an edge-aware weighted scheme in the data term design, which further improves the edge-preserving capability. The bilateral function is non-convex and can be non-trivial to solve. In this paper, we propose a novel iterative solution based on fixed point iteration, where the main burden in each iteration is a bilateral filtering process. We have conducted extensive experiments to evaluate the proposed filter. Experiment results indicate that our filter benefits a variety of image processing tasks. Moreover, we propose an efficient approximation of the proposed filter, which is able to significantly accelerate the filtering process with neglectable sacrifice of smoothing quality.