Riemannian Formulation of the CIEDE2000 Color Difference Formula

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).