@article{Liu2015, 
author = {Qian Liu and Caiming Zhang and Qiang Guo and Yuanfeng Zhou},
title = {A nonlocal gradient concentration method for image smoothing},
year = {2015},
journal = {Computational Visual Media},
volume = {1},
number = {3},
pages = {197-209},
keywords = {image smoothing, nonlocal similarity, L0 norm, edge detection},
url = {https://www.sciopen.com/article/10.1007/s41095-015-0012-6},
doi = {10.1007/s41095-015-0012-6},
abstract = {It is challenging to consistently smooth natural images, yet smoothing results determine the quality of a broad range of applications in computer vision. To achieve consistent smoothing, we propose a novel optimization model making use of the redundancy of natural images, by defining a nonlocal concentration regularization term on the gradient. This nonlocal constraint is carefully combined with a gradient-sparsity constraint, allowing details throughout the whole image to be removed automatically in a data-driven manner. As variations in gradient between similar patches can be suppressed effectively, the new model has excellent edge preserving, detail removal, and visual consistency properties. Comparisons with state-of-the-art smoothing methods demonstrate the effectiveness of the new method. Several applications, including edge manipulation, image abstraction, detail magnification, and image resizing, show the applicability of the new method.}
}