A Variational Histogram Equalization Method for Image Contrast Enhancement

Wei Wang, Michael K. Ng*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

19 Citations (Scopus)
10 Downloads (Pure)


The main aim of this paper is to develop a histogram equalization algorithm for image contrast enhancement. Our idea is to propose a variational approach containing an energy functional to determine a local transformation such that the histogram can be redistributed locally, and the brightness of the transformed image can be preserved. In order to minimize the differences among the local transformation at the nearby pixel locations, the spatial regularization of the transformation is also incorporated into the functional for the equalization process. In the variational problem, we consider both H1-norm regularization and total variation regularization of the transformation in the model. The existence and uniqueness of the minimizers of the two proposed models are studied and analyzed. Experimental results are reported to show that the performance of the proposed models are competitive with the other compared methods for several testing images.

Original languageEnglish
Pages (from-to)1823-1849
Number of pages27
JournalSIAM Journal on Imaging Sciences
Issue number3
Publication statusPublished - 24 Sept 2013

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Alternating minimization
  • Contrast enhancement
  • Energy functional
  • Histogram equalization
  • Transformation function
  • Variational approach


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