As stated above Schlick wanted to introduce a mapping function which
would act similar to a logarithmic function but which would be much
simpler to compute. He proposed the so-called rational mapping
function:
This function is intended to account for the non-linearities of both the display device and human perception. The biggest advantages of Schlick's mapping are its speed and automatic selection of the parameter p. The mapping is fast as it needs only one division, one multiplication, one subtraction, and one addition.
A free parameter in logarithmic and exponential mapping depends on many factors such as the adaptation level of the observer, the display device characteristics, human vision rules, etc. It would be ideal to involve all of these factors, but it would be computationally very expensive and some of the human vision mechanisms are not understood yet. There are methods that include more human vision characteristics, and they will be described in the next sections.
Schlick has made the assumption that the level of the darkest
non-black gray is what really changes under different viewing
conditions and device settings. The user should find the input level of the
darkest non-black gray level M and compute the parameter p according to
the following formula:
The idea is then to map the smallest non-zero pixel value of a raw image to the darkest non-black gray of a display device. 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.
Although this mapping is very fast we find its use limited to raw
images with a moderate overall contrast value. Using this mapping with
some high contrast raw images led us to unusable results. When we set
the parameter p manually the resulting images were great. The reason
why results are unsatisfactory for very high contrast images, lies in
the fact that the mapping is applied to the whole raw image
range. Suppose that there is only one pixel in the raw image that has
a very high luminance value 
. This pixel will cause p to
explode, and the whole mapping technique will become useless.
This method is ilustrated in color plates 1c, 6a, 10a, 10b and 10f.
A possible solution for high contrast raw images could be to combine Schlick's mapping with the minimum information loss method as described in chapter 6.
Schlick speculated about spatially non uniform mapping in his work as well, but ended up with just another spatially uniform solution, similar to the original one.