Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

A variational approach for image decolorization by variance maximization

Language

English

Abstract

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. © 2014 Society for Industrial and Applied Mathematics.

Keywords

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

Publication Date

2014

Source Publication Title

SIAM Journal on Imaging Sciences

Volume

7

Issue

2

Start Page

944

End Page

968

Publisher

Society for Industrial and Applied Mathematics

DOI

10.1137/130935197

Link to Publisher's Edition

http://dx.doi.org/10.1137/130935197

ISSN (electronic)

19364954

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