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Mathematical Problems in Engineering
Volume 2016, Article ID 9897064, 17 pages
Research Article

Variational Histogram Equalization for Single Color Image Defogging

Communication and Navigation Lab, Aerospace Engineering College, Air Force Engineering University, Xi’an 710038, China

Received 31 March 2016; Revised 21 June 2016; Accepted 10 July 2016

Academic Editor: Alberto Borboni

Copyright © 2016 Li Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Foggy images taken in the bad weather inevitably suffer from contrast loss and color distortion. Existing defogging methods merely resort to digging out an accurate scene transmission in ignorance of their unpleasing distortion and high complexity. Different from previous works, we propose a simple but powerful method based on histogram equalization and the physical degradation model. By revising two constraints in a variational histogram equalization framework, the intensity component of a fog-free image can be estimated in HSI color space, since the airlight is inferred through a color attenuation prior in advance. To cut down the time consumption, a general variation filter is proposed to obtain a numerical solution from the revised framework. After getting the estimated intensity component, it is easy to infer the saturation component from the physical degradation model in saturation channel. Accordingly, the fog-free image can be restored with the estimated intensity and saturation components. In the end, the proposed method is tested on several foggy images and assessed by two no-reference indexes. Experimental results reveal that our method is relatively superior to three groups of relevant and state-of-the-art defogging methods.