Transformation of the L*a*b* color space to obtain a more uniform chromaticity diagram

The color matching ellipsoid theory has been extensively used to improve the relationship between the human perception and numerical representation of color differences evaluation. This theory can be described thanks to logarithmic functions which approximate the orientation, the position and the size of ellipses. By carrying out these observations to the study of the a*b* chromaticity plane we have obtain a partition of this plane. This partition separates each area for which the distribution of ellipses can be locally approximated by the same logarithmic function. Then we can interpolate the orientation and the dimension of ellipses for each position of each area This logarithmic function points out that the perception of colors is non-uniform at once “locally” for each area considered separately and “globally” for the set of areas. Inversely, we can claim that if we take the “inverse function” of this logarithmic function we can transform the distribution of ellipses in a convenient form in order to obtain an uniform distribution of circles. This process can be applied to each area of the chromatic plane and can be scaled to compute a distribution composed of equal-sized circles. Then, this transformation allows to set a new color space which is more uniform than the L*a*b* color space: we will call it the L°a°b° color space.