This section will describe an exponential mapping method introduced
by Ferschin et al. in [FeTP94]. The main idea of this mapping
method is to use an exponential function that will be not affected
by a few very dark pixels. This function has actually been developed
from the idea of using a stepwise linear mapping function. An
exponential function overcomes the problem of discontinuities in the
shadows when a stepwise linear function is used. The exponential
mapping function is:
Figure 5.1 shows the exponential mapping function for a
hypothetic raw image with luminances in range [0,5000], and an
average value of 1000.
Figure 5.1: Exponential mapping
The resulting images provide a smooth transition between all luminance gradients. The authors also introduced an alternative form of compression through the alignment of a reference white point of the radiosity scene with the white-point of the monitor actually used. This really interesting approach is realized by using the radiosity white point in the conversion of the radiosity results to the CIE XYZ, and then using the display device's white point by converting CIE XYZ values to the monitor values.
Authors have also experimented with clipping in CIE LUV and CIE LAB color spaces, and reported no visual differences between all three clippings. Therefore, they suggest using RGB clipping because of its reduced computational demands.
Note that this method is also an average based method. This means that the average value will always be mapped to the 0.632 input value, displaying dark scenes too bright and bright scenes too dark.
The resulting images rendered using this mapping are shown in the results chapter, color plates 1b and 5b.