From now on, we will assume that the display device is calibrated, such
that it has linear response and input range [0,1]. This input range
corresponds to [0,255] for R, G and B color channels for today's
standard devices. Throughout this work "n" will be used for the
device input value, 
, and "L" for the computed luminance
value, 
. Our intention is to describe the various
functions n=f(L).
Most rendering software is still not able to render a raw image in absolute units. Rendering in absolute units can be quite a tricky job. When absolute units are required the exact data for light sources and materials are needed. This data is hard to get or measure, and sometimes the tolerance range of given data is too high. Data for artificial light sources can be obtained from the manufacturers and if natural light is used then the time of day, latitude and sky conditions should be taken into account. The data needed to define BRDFs for materials used in the scene is far more difficult to find than light source data is. The BRDF depends both on the chemical composition of the material and on the condition of the surface (smooth, rough, oxidized, etc.). Furthermore many common materials do not have spatially uniform BRDFs. Because of all these reasons most rendering tools still work with fictitious units. Some methods take absolute units into account and can not be used with raw images rendered in fictitious units.
Although human vision certainly does not use a linear scaling function, this group of mapping methods renders acceptable results for a wide range of applications. Its strengths are its simplicity and speed, and if the right method is chosen, the results can be acceptable for almost all applications if the raw image dynamic range is not too high.
The reason why linear mapping renders acceptable results, if the right scale factor is chosen, lies in the adaptation mechanism. If the right ``adaptation'' level is chosen the error introduced by using a linear mapping function is acceptable. The problem is only to find the right scale-factor.
As we want to get various images from computed luminances it is obvious that these computed values have to be stored. Usually these values are floating point numbers, one for each color channel (red, green and blue in most cases). Saving such a float image is very memory demanding (12 bytes per pixel). Greg Ward in [Ward92] suggests an elegant way of handling this problem and introduces a way how a float image can be stored using only 4 bytes per pixel and achieving almost the same result. There are also two other raw image formats (one supported by TIFF file type, and other introduced by Pixar). The raw image formats are described in the Appendix, as they are a necessity for this kind of image manipulation.
Another possibility of handling the float-image size problem is to use a low-resolution preview picture to find the parameters which will be used in the final high-resolution picture. The combination of these two methods should solve the memory problem even in computers with a very low amount of memory.
The first intuitive solution to the mapping problem is the use of a
linear scale-factor such that the maximum radiance 
is
mapped to 1,
This mapping is useless if the light source is visible or the image contrast is too high. In these cases the final image will be too dark. The results of this mapping method are shown and discussed in the Results chapter. An improvement of this method, especially popular in the radiosity community, is the mapping of the largest non self-emitting pixel to 1. Unfortunately, in the case of strong secondary light sources this method still renders very dark images. The second drawback is that pixel self-emittance is known only in the first rendering phase, therefore it is not possible to estimate which pixel is and which is not self emitting from the raw image.