We stated before that we want to use the CIE LUV color difference formula. CIE LUV space was designed to approach a perceptually uniform color space, but it was designed in strictly set laboratory conditions, with adapted observers. In every day life, we are rarely fully adapted to any particular luminance level. Most of the time we are in complex environments, where our eyes do not have enough time to fully adapt to one specific luminance level. The perception in complex environments has still not been studied extensively. Hunt [Hunt92] and Nemcsics [Nemc93] studied perception in complex environments. Nemcsics developed a new color space called coloroid [Hunt92], [Nemc80], [Nemc87], which is designed for complex environments and solid colors (not for self-emitting media).
It is interesting that Nemcsics reports that just noticeable color
difference can be up to 4 times larger in a complex environment,
than for the fully adapted eye. After experiments with 2500
observers Nemcsics concluded that the brightness L is
proportional to 
, rather than to 
as proposed
in CIE LUV formula (for a complex viewing environment, of course).
We made a compromise and use a modified CIE LUV formula such that
L is proportional to and the chromacity component is
computed using CIE uv, but as functions of the new L':
This method is certainly not one hundred percent correct, but finding a better one will exceed the scope of this thesis.
Furthermore, we modified the color difference formula as well. Namely it is known that colors that have a CIE LUV difference of less than 1 appear to be the same. This limit value changes with view conditions, frequency of stimuli etc. Therefore, if two colors are intended to be different, it is recommendable to choose colors with a CIE LUV difference of 6 or more.
Since we are not able to see color differences less than 1, we modified the difference formula so that all original differences of less than 1 are set to 0. Note that this modification makes it possible that images A and B are the same, images B and C are the same, but images A and C are different. This is not a metric in the mathematical sense any more, but it has some other advantages.
Of course the modified difference formula should be applied to each particular rectangle pair and not on the final difference. In this way, if the total average difference is some small number (e.g. 0.5) it means that there is a visible difference somewhere in the image.