The main goal of our method is to find the interval [A,B] such
that 
, where the C is the given clipping contrast, and
that a minimum amount of information is lost due to the applied
clipping. The clipping contrast depends on the display media, and should equal
the maximum displayable medium contrast. Clipping will be done in the
most simple way, thus setting values larger than B to B, and
those less than A to A. As we want the minimum amount of
information to be lost, let us first define what information is. Two
approaches will be introduced.
In the first approach each color component is considered as an equally important information unit. So minimizing the information loss means minimizing the total number of color components clipped. Note that the loss of e.g. 3% of color components could mean that 3% of the pixels are affected by clipping (if each of these 3% is affected in all 3 components) or up to 9% of the pixels are affected by clipping (if all of the clipped color components belong to different pixels). Usually there are not many pixels clipped only in one or two components. These are color highlights and saturated colors. As these pixels make up only a tiny part of an average image, the percentage of affected pixels tends to be close to 3%.
In the second approach the pixel is considered to be the essential information unit, so the number of affected pixels shall be minimized. Usually there are no big differences between the optimum intervals in these two approaches, but some difference almost always occurs. The first approach will be called minimum information loss, and the second minimum area loss.