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Volume: 18 | Article ID: art00019
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Riemannian Formulation of the CIEDE2000 Color Difference Formula
Dibakar Raj Pant
Ivar Farup
  DOI :  10.2352/CIC.2010.18.1.art00019  Published Online :  January 2010
Abstract

The CIELAB based CIEDE2000 colour difference formula to measure small to medium colour differences is the latest standard formula of today which incorporates different corrections for the non uniformity of CIELAB space. It also takes account of parametric factors. In this paper, we present a mathematical formulation of the CIEDE2000 by the line element to derive a Riemannian metric tensor in a color space. The coefficients of this metric give Just Noticeable Difference (JND) ellipsoids in three dimensions and ellipses in two dimensions. We also show how this metric can be transformed between various colour spaces by means of the Jacobian matrix. Finally, the CIEDE2000 JND ellipses are plotted into the xy chromaticity diagram and compared to the observed BFD-P colour matching ellipses by a comparing method described in Pant and Farup (CGIV2010).

Journal Title : Color and Imaging Conference
Publisher Name : Society of Imaging Science and Technology
Publisher Location : 7003 Kilworth Lane, Springfield, VA 22151, USA
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 DOI 10.2352/CIC.2010.18.1.art00019
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Dibakar Raj Pant, Ivar Farup, "Riemannian Formulation of the CIEDE2000 Color Difference Formula"  in Proc. IS&T 18th Color and Imaging Conf.,  2010,  pp 103 - 108,  https://doi.org/10.2352/CIC.2010.18.1.art00019

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Copyright © Society for Imaging Science and Technology 2010
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Color and Imaging Conference
color imaging conf
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Articles
Riemannian Formulation of the CIEDE2000 Color Difference Formula
PantDibakar Raj
FarupIvar
01012010
2010
1
103
108
2010
The CIELAB based CIEDE2000 colour difference formula to measure small to medium colour differences is the latest standard formula of today which incorporates different corrections for the non uniformity of CIELAB space. It also takes account of parametric factors. In this paper, we present a mathematical formulation of the CIEDE2000 by the line element to derive a Riemannian metric tensor in a color space. The coefficients of this metric give Just Noticeable Difference (JND) ellipsoids in three dimensions and ellipses in two dimensions. We also show how this metric can be transformed between various colour spaces by means of the Jacobian matrix. Finally, the CIEDE2000 JND ellipses are plotted into the xy chromaticity diagram and compared to the observed BFD-P colour matching ellipses by a comparing method described in Pant and Farup (CGIV2010).