SoftCuts Super Resolution

Supported in part by NSF and NEC

Effective image prior is necessary for image super resolution, due to its severely under-determined nature. Although the edge smoothness prior can be effective, it is generally difficult to have analytical forms to evaluate the edge smoothness, especially for soft edges that exhibit gradual intensity transitions.

This paper finds the connection between the soft edge smoothness and a soft cut metric on an image grid by generalizing the Geocuts method, and proves that the soft edge smoothness measure approximates the average length of all level lines in an intensity image. This new finding not only leads to an analytical characterization of the soft edge smoothness prior, but also gives an intuitive geometric explanation. Regularizing the super resolution problem by this new form of prior can simultaneously minimize the length of all level lines, and thus resulting in visually appealing results. In addition, this paper presents a novel combination of this soft edge smoothness prior and the alpha matting technique for color image super resolution, by normalizing edge segments with their alpha channel description, to achieve a unified treatment of edges with different contrast and scale.


  1. Shengyang Dai, Mei Han, Wei Xu, Ying Wu, Yihong Gong, and Aggelos K. Katsaggelos, "SoftCuts: A Soft Edge Smoothness Prior for Color Image Super Resolution", IEEE Trans. on Image Processing. (Minor revision)
  2. Shengyang Dai, Mei Han, Wei Xu, Ying Wu, and Yihong Gong, "Soft Edge Smoothness Prior for Alpha Channel Super Resolution", IEEE Conference on Computer Vision and Pattern Recognition (CVPR'07), Minneapolis, Minnesota, USA, June 18-23, 2007. (Oral) [Slides]
  3. Shengyang Dai, Mei Han, Ying Wu, and Yihong, Gong, "Bilateral Back-Projection for Single Image Super Resolution", IEEE International Conference on Multimedia & Expo (ICME'07), Beijing, China, July 2-5, 2007.


  1. Soft Edge Smoothness Prior and its Application on Alpha Channel Super Resolution". Inventors: Shengyang Dai, Mei Han, Wei Xu, Ying Wu, and Yihong Gong. Patent pending.


Low resolution inputs   vs.   Our results with Softcuts


Results on tiny images


Level lines using different order of neighborhood

(larger neighborhood brings smoother results, please check paper for details)

    n=2                    n=4                    n =12


Visualization of the iteration process

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Updated 9/2008. Copyright © 2007-2008 Ying Wu