In photography light measurement techniques work with the assumption
that the scene contrast is 32. The value two times greater than the
average measured lightness will be the white on the picture. The
logarithmic middle gray, which is very near to the perceptual middle
gray is 
times the lightness of white or 
times
the measured average value. All values larger than the white value (two
times average) will be clipped to white, and all values below
white/32=average/16=black will be clipped to black. In other
words, the clipping window on the logarithmic scale is logarithmic
middle gray 
. Let us consider an example from computer
graphics with classical mean value linear mapping. We assume a gamma
corrected display device with linear response and input range [0,1]. 0
corresponds to the minimum displayable luminance level (in our case
let it be 1/32) and 1 corresponds to the maximum displayable
luminance value (let it be 1). The values larger than two times the
average value will be clipped to 1, as in photography, but there is no
clipping for low values. 0 absolute luminance will be displayed as
1/32 in our example. Figure 6.1 illustrates the two approaches. The
differences in the final images are not significant because the main
difference occurs in dark image parts where our perception in bright
surroundings can not perceive them.
Figure 6.1: Photographic and CG mean value mapping