Our intention is to find the [s,e] interval such that the final
image (produced by mapping [s,e] to the display device input values)
is satisfactory. This means that it shows the atmosphere supposed to
be in the scene, or that it shows lots of details in a selected area
of the image. The user varies contrast and aperture settings until the
image looks satisfactory. We assume that the display device is
calibrated, has linear response and the ratio between the maximum and
minimum displayable lightness is 
. We want to map [s,e]
to 
. We will call 
value 
. For most CRTs is about 50, which makes
equal to 0.02. Given the 
value, the aperture
value a and contrast c, the start point s of the interval is
and the end point e can be computed as
Once the interval is chosen, the mapping for float red, green, and blue
values can be done. The values outside the [s,e] interval should be
clipped to s and e prior to the mapping. This color clipping
produces visible color distortions in some cases. There are numerous
other clipping approaches but they are out of the scope of this
thesis. There are many ways of mapping [s,e] to 
. If
the chosen contrast c is the same as the available device contrast
, a linear mapping gives the best results. The linear mapping is
done by simply dividing the color components by e. The interval is
mapped linearly to [0,1] using the following formulas:
In the case when c differs from a linear mapping does
not give satisfactory results. According to human perception rules
[StSt63], [Hunt92] a mapping function of type 
can be
chosen for appropriate results. The value of n lies between 1/3
(e.g. in CIE LUV and CIE LAB lightness formulas) and 1/2 (e.g. in Hunter
LUV lightness formulae) [Hunt92]. We suggest taking n=0.4 as
default value. Two auxiliary values u and v for the mapping from
to 
are defined as :
The mapping functions for mapping the red, green and blue values (all
in the [s,e] range) to R,G,B (in the range) are:
Images mapped using this type of mapping function will be brighter than those mapped with the linear function, but they will show more details in the dark part of the image and they will be perceptionally more correct. Now R, G and B can be used as input to the display device look up table.