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provided by the user. One of the categories will be refined, whereas the other two
will undergo a Gouraud shading or directional shading as per the case. The process
stops when the distance between two successive images becomes less than the threshold
tolerated by the user.
Several works using perceptual models have also been undertaken in the field of
radiosity. A synopsis of these methods can be seen in (Prikryl &Purgathofer, 1999).
To conclude we can note that several interesting results were obtained in this field.
However, the assessment of vision models, especially the sophisticated ones, remains
expensive, and no satisfactory solution operating in real time is available till date.
15.3.2 Tone mapping
15.3.2.1 Introduction
While producing realistic images, it is desirable to calculate the value to be displayed in
each pixel in Watts
sr 1 , to make them as close to the physical aspects as possi-
ble. The luminance that we can observe in nature covers a range of 10 6 to 10 6 cd
m 2
·
·
·
m 2
·
10 5 cd
·
m 2 and the snow in
(a moonless night has a luminance of approximately 3
m 2 ) and the human
bright sunlight gives a luminance of approximately 16
·
10 3 cd
·
m 2 in a single glance.
Cathode ray tube monitors have a luminance range of 1 to 100 cd
visual system can accommodate a range of about 10 4 cd
·
m 2 , whereas
·
m 2 .
Then arises the problem of converting real data into display data. This problem
is called tone mapping . The solution to this problem is trying to make the observed
image closest possible to the visual sensation felt when the observer is in the real scene.
This problemwas formalised by Rushmeier et al. (1995). The (theoretical) solution
of the problem is provided by inserting a tone mapping operator, defined by V S V E E 1 ,
before the V E model of human vision operator adapted to the monitor.
Though the problem of tone mapping was introduced in computer graphics only
at the beginning of 1990s, it has been largely studied ever since. We will now describe
some of the models proposed in the literature.
These models are generally based on experimental data: the human visual system
is not sensitive to luminance, but to the changes in luminance. This leads to the concept
of differential threshold of luminance L f , defined as:
If a target has a luminance L f +
m 2 and a plasma screen 1 to 800 cd
an LCD screen has a range of 1 to 1300 cd
·
·
L f on a background of luminance L f , it will be
detectable; but it will not be detectable if it has a luminance L f
+
ε , with ε
L f .
This experimental data has lead to two laws used in tone mapping:
Weber's law (beginning of the twentieth century): L/L
0 . 02;
=
+
L 0 . 4
f
) 2 . 5 .
Blackwell's law (beginning of 1970s): L
0.054(1.2110
We will distinguish between two types of models: Models applied to static scenes and
those taking time into account.
Tone mapping for static images
Here too, we will see two types of methods - spatially uniform and non-uniform.
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