L0 image smoothing via iterating truncated L1 gradient regularization

Abstract

Edge-preserving image smoothing is a fundamental tool in computational photography and graphics. It aims to suppress insignificant details while maintaining salient structures. The classical L 0 filter provides an elegant framework for a variety of applications. However, it inclines to sharpen the salient edges, thus suffering from gradient reversals and color deviations. We propose a solution toward the objective of optimizing summed squared error regularized by the L 0 -norm of the gradients. The proposed solution explores an iterative strategy, where each iteration is an optimization problem based on the truncated L 1 regularization, which can be solved efficiently with the combination of alternating direction method of multipliers and Fourier domain optimization. Leveraging L 1 -norm limits the aggressive modifications of gradients during the iterative process, which alleviates various artifacts in classical L 0 filter. Experiment results indicate that the proposed method achieves superior performance in various applications, including texture removal, detail enhancement, HDR tone mapping, and compression artifact removal. The proposed filter can be conveniently implemented on GPU. It takes our filter 0.51 s to process a 720P color image on a NVIDIA GTX 1080 GPU.

Fast bilateral weighted least square for the detail enhancement of COVID-19 chest X-rays

“…Most of the methods are built upon range quantization, 37 , 38 range decomposition, 39 , 40 or spatial subsampling. 27 These strategies significantly accelerate the bilateral filter, but they may not be able to improve the quality of image decomposition over the naive bilateral filter.…”

“…Recent methods for detail enhancement mostly rely on image decomposition with edge-aware smoothing filters, such as the bilateral filter, 20 , 21 anisotropic diffusion filter, 22 guided filter, 23 , 24 soft clustering filter, 25 reconstruction filter, 26 filter, 27 generalized smoothing filter, 28 and weighted least square filter. 29 The decomposition-based methods consider the pixels in the neighborhood during the enhancement process, thus could alleviate the problems of the histogram equalization-based methods.…”