This mapping method was first introduced as a technical report in 1991 [TuRu91] and then in 1993 [TuRu93], and is still considered as state of the art in tone mapping. Unfortunately, it is developed for gray scale images only. It is very comprehensive but still not complete. It includes seven different parameters which should be set by the user, and some of them are not always available to common users. Just as in Ward's mapping, absolute units are required here. Note that it cannot be considered as a drawback, it is just a necessity if the lighting atmosphere is important. If a raw image is rendered in fictitious units, it is just not possible to say if the lighting in the scene is strong or weak.
Tumblin and Rushmeier find the inspiration for their work in the fact that most image synthesis algorithms do not know the difference between night and day - differences that are so obvious to the human eye. They wanted to display the original lighting atmosphere of the raw image in the final image. If the firefly illumination is simulated it should produce a very dark image, and on the other hand if the scene is lit with a very strong anti aircraft search light the final image should be almost completely white. The process of tone reproduction is well known in photography, where the original atmosphere of the scene should be displayed in the photo. Fortunately, computer graphics have unlimited possibilities in choosing the tone reproduction function. It can be very complex, and it is still quite easy to implement. Photographers, on the other hand, are limited with just a few chemicals and photo papers, and can not develop such sophisticated tone operators.
Tumblin and Rushmeier's (TR) mapping technique uses results obtained
by Stevens et al. [StSt63] regarding the brightness associated with a
luminance at a particular adaptation level. A power law that relates
luminance L measured in lamberts to brightness B in brils at
an adaptation level of 
is:
where 
and 
are:
In the first technical report [TuRu91] the authors used the
average value as the adaptation luminance, but in the final version
[TuRu93] they used another approach. They used the assumption
that the eye adapts in an attempt to keep most brightness near the
``brightness constancy'' contour of 
[StSt63] below
, therefore is:
where 
is the expected value of 
.
Although Tumblin and Rushmeier are aware that Stevens's data is not valid for complex viewing conditions and complex scenes (see section Human Vision), they still used this model, and not the improvement suggested by Bartelson et al. [BaBr67], because of lower computational cost, and problems with the root finding of the extended model.
The TR tone mapping operator attempts to match the brightness of the
real-world luminance with the brightness of the display luminance. By
setting 
where 
represents the brightness of a
real-world luminance and 
the brightness of a display
luminance, and using equations 5.4, 5.5, 5.6
as follows:
Note that 
and 
are functions of the
adapting luminance of the display 
. According to
eq. 5.7, 
should be known in order to compute
. To solve this problem, the authors suggest taking
as a constant, since it has little influence on
and . The suggested value is:
where 
is the maximum available display contrast, depending on
the display gamma, ambient illumination and maximum available display
luminance 
.
Finally the complete tone mapping operator can be written as:
This operator is designed to reproduce overall brightness appearance,
and not to reproduce visibility (in contrast to Ward's, Ferwerda's and
visibility matching mapping described later). We tested the TR
operator and the resulting images look a little bit too dark. We
suppose the reason lies in the fact that this mapping operates within
the whole range of human vision. The model functions up to luminances
of 
, and just for comparison, snow covered
ground in full sunlight emits 
or horizon sky
emits 
on a day with sunlit clouds. As the
bright images are reserved for such extreme lighting conditions
(search lights), normal light images tend too be a little bit too
dark in our opinion. We have applied the TR operator on each color
channel separately, just as Ward did in the RADIANCE [Ward94a]
package. We are aware that this is not the right way, but finding a
better way would certainly exceed the scope of this work.
Nevertheless, if the analysis of extreme lighting conditions is important this could be just the right model. It is complicated to implement this model exactly, but it is worth trying. Resulting images are shown in the results chapter, color plates 9e, 9f, 13c, 13d, 17c, and 17d.