A Variational Approach for Image Decolorization by Variance Maximization

Zhengmeng Jin, Fang Li, Michael K. Ng*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

19 Citations (Scopus)
16 Downloads (Pure)


Color-to-grayscale conversion is the process used to convert a color image to a grayscale one, which is a basic tool in digital printing, photograph rendering, and single-channel image processing. The main aim of this paper is to propose a variational approach for image decolorization by variance maximization. Our idea is to use an energy functional to determine local transformations for combining red, green, and blue channel pixel values together by maximizing the local variance of the output grayscale image and preserving the brightness of the input color image. In order to minimize the differences among the local transformations at nearby pixel locations, the total variation regularization of the transformation is incorporated into the functional for the decolorization process. The existence and uniqueness of the minimizer of the variational model can be shown. We also present an effective algorithm for solving the variational model numerically, and show the convergence of the algorithm. Experimental results are reported to demonstrate the effectiveness of the proposed method, and its performance is better than those of the other testing methods for a set of benchmark color images.

Original languageEnglish
Pages (from-to)944-968
Number of pages25
JournalSIAM Journal on Imaging Sciences
Issue number2
Publication statusPublished - 13 May 2014

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Alternating minimization
  • Color-to-grayscale
  • Decolorization
  • Total variation
  • Variance maximization
  • Variational approach


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