Back to articles
Articles
Volume: 27 | Article ID: art00018
Image
On an Euler-Lagrange equation for color to grayscale conversion
  DOI :  10.2352/issn.2169-2629.2019.27.18  Published OnlineOctober 2019
Abstract

In this paper we give a new method to find a grayscale image from a color image. The idea is that the structure tensors of the grayscale image and the color image should be as equal as possible. This is measured by the energy of the tensor differences. We deduce an Euler-Lagrange equation and a second variational inequality. The second variational inequality is remarkably simple in its form. Our equation does not involve several steps, such as finding a gradient first and then integrating it. We show that if a color image is at least two times continuous differentiable, the resulting grayscale image is not necessarily two times continuous differentiable.

Subject Areas :
Views 14
Downloads 2
 articleview.views 14
 articleview.downloads 2
  Cite this article 

Hans Jakob Rivertz, "On an Euler-Lagrange equation for color to grayscale conversionin Proc. IS&T 27th Color and Imaging Conf.,  2019,  pp 95 - 98,  https://doi.org/10.2352/issn.2169-2629.2019.27.18

 Copy citation
  Copyright statement 
Copyright © Society for Imaging Science and Technology 2019
72010350
Color and Imaging Conference
color imaging conf
2166-9635
Society for Imaging Science and Technology