@article{dai2009softcuts,
abstract = {Designing effective image priors is of great interest to image super-resolution (SR), which is a severely under-determined problem. An edge smoothness prior is favored since it is able to suppress the jagged edge artifact effectively. However, for soft image edges with gradual intensity transitions, it is generally difficult to obtain analytical forms for evaluating their smoothness. This paper characterizes soft edge smoothness based on a novel SoftCuts metric by generalizing the Geocuts method [1]. The proposed soft edge smoothness measure can approximate the average length of all level lines in an intensity image. Thus, the total length of all level lines can be minimized effectively by integrating this new form of prior. In addition, this paper presents a novel combination of this soft edge smoothness prior and the alpha matting technique for color image SR, by adaptively normalizing image edges according to their $\alpha$-channel description. This leads to the adaptive SoftCuts algorithm, which represents a unified treatment of edges with different contrasts and scales. Experimental results are presented which demonstrate the effectiveness of the proposed method. {\textcopyright} 2009 IEEE.},
author = {{Shengyang Dai} and {Mei Han} and {Wei Xu} and {Ying Wu} and {Yihong Gong} and Katsaggelos, Aggelos K A.K. and Dai, Shengyang and Han, Mei and Xu, Wei and Wu, Ying and Gong, Yihong and Katsaggelos, Aggelos K A.K.},
doi = {10.1109/TIP.2009.2012908},
issn = {1057-7149},
journal = {IEEE Transactions on Image Processing},
keywords = {Edge smoothness,SoftCuts,Super-resolution (SR),$\alpha$-channel description},
month = {may},
number = {5},
pages = {969--981},
publisher = {IEEE},
title = {{SoftCuts: A Soft Edge Smoothness Prior for Color Image Super-Resolution}},
url = {http://ieeexplore.ieee.org/document/4808429/},
volume = {18},
year = {2009}
}

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The proposed soft edge smoothness measure can approximate the average length of all level lines in an intensity image. Thus, the total length of all level lines can be minimized effectively by integrating this new form of prior. In addition, this paper presents a novel combination of this soft edge smoothness prior and the alpha matting technique for color image SR, by adaptively normalizing image edges according to their $α$-channel description. This leads to the adaptive SoftCuts algorithm, which represents a unified treatment of edges with different contrasts and scales. 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