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Evaluating Color Difference Formulae by Riemannian Metric

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Title Evaluating Color Difference Formulae by Riemannian Metric
Title of Series The 5th European Conference on Colour in Graphics, Imaging, and Vision and the 12th International Symposium on Multispectral Colour Science (CGIV 2010/MCS'10)
Part Number 35
Number of Parts 43
Author Pant, Dibakar Raj
Farup, Ivar
License CC Attribution - NoDerivatives 2.0 UK: England & Wales:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
DOI 10.5446/18260
Publisher River Valley TV
Release Date 2011
Language English
Production Place Joensuu, Finland

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Subject Area Computer Science
Abstract For precision color matching, visual sensitivity to small color difference is an essential factor. Small color differences can be measured by the just noticeable difference (JND) ellipses. The points on the ellipse represent colours that are just noticably different from the colour of the centre point. Mathematically, such an ellipse can be described by a positive definite quadratic differential form, which is also known as the Riemannian metric. In this paper, we propose a method which makes use of the Riemannian metric and Jacobean transformations to transform JND ellipses between different colour spaces. As an example, we compute the JND ellipses of the CIELAB and CIELUV color difference formulae in the xy chromaticity diagram. We also propose a measure for comparing the similarity of a pair of ellipses and use that measure to compare the CIELAB and CIELUV ellipses to two previously established experimental sets of ellipses. The proposed measure takes into account the size, shape and orientation. The technique works by calculating the ratio of the area of the intersection and the area of the union of a pair of ellipses. The method developed can in principle be applied for comparing the performance of any color difference formula and experimentally obtained sets of colour discrimination ellipses.
Keywords The 5th European Conference on Colour in Graphics, Imaging
Vision and the 12th International Symposium on Multispectral Colour Science
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