Up to now we have proposed a fixed contrast, and we have found a
clipping interval such that the lost information is
minimized. Sometimes, for high contrast images, the information loss
will be too high. In this case, we propose to bound the information
loss, and to find the smallest clipping interval that causes no more
than the allowed information loss. As the clipping contrast will be
higher than the display device contrast in this case, a linear
mapping will not function properly any more. In order to match the
human vision characteristics, we propose to apply Schlick's mapping
on the clipping interval. One of the biggest disadvantages of
Schlick's mapping technique is the explosion of the parameter p if
the total image contrast is too high. If there are only few very,
very bright pixels in the image, they increase the overall contrast,
and the parameter p explodes. If our limited error loss scheme is
applied, for a proposed error (i.e. 10%
) the clipping contrast will be smaller than the
overall contrast, and Schlick's mapping will produce good
results. If there are few very bright or very dark pixels in the
image they will be clipped and will not contribute to the
computation of the parameter p. Note that almost the same results
would be obtained if a linear mapping on the log scale would be
applied. We recommend Schlick's mapping due to its lower
computational cost, and its ability to adjust the final image according
to the display media characteristic (the least non-black input
level). The following equation describes Schlick's mapping:
where n is the input level, 
, L is the luminance value
and p is:
where M is the smallest non-black input level, and N is the number
of input levels. In order to find M, Schlick proposes to display
squares of different grays randomly on a black background and to
select the darkest still recognizable square. Of course values
and 
in eq. 6.14 should be replaced with
A and B in our case.
Images mapped using these methods are shown in the results chapter, color plates 1d, 1e, 1f, 6b, 7a, 7b, 8a, and 8b.