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Figure 15.3 Composite typology of BRDF models
The first attempt was by Goel (1988) who divided the BRDF models into five groups
depending on whether they are empirical or are based on a precise characterisation
of the materials. As this classification was too general, Roujean (1991) suggested an
extension to the same, which however in an attempt to be extremely precise, was not
logical in terms of division.
In fact, some models can belong to several groups simultaneously. Besides, it is
sometimes difficult to classify them as some groups do not really have a practical
physical sense (like the mathematical or theoretical models). An in-depth description
of this typology can be found in (Claustres, 2000).
From the recent RAMI experiment (Pinty et al., 2001), which proposes a compar-
ison of radiation transfer models for earth surfaces that helps simulating the BRDF of
such environments, it is certainly possible to create a more recent typology, as shown in
figure 15.3. This classification is very open, like the one suggested by Goel, and helps
better understand the division of models on the basis of their manner of carrying out
the modelling, without repeating Roujean's mistakes of creating excessively specific
Needless to say that no typology is perfect and certain hybrid models that use
different strategies of modelling will always be tricky to classify, but we can say that it
is wiser to base the classification on the modelling process set in its application context
than simply on its result (a formula of such and such form).
Explicit modelling
An explicit model deduces or calculates the BRDF from an explicit description of
the target surface. Such a model thus offers a comprehension of physical processes
underlying the phenomenon of light reflection by describing the interaction between
the light and the material. The theory of radiative transfer (Chandrasekhar, 1950)
is applied in remote sensing and rarely in image synthesis to assess the energy flow
reflected by the surface, but the reference for the choice of applicable theory is the
wavelength of the radiation. For rough surfaces, interaction between the light and
the material depends mainly on the diffraction by the micro or macro-structures of
the surface (DeumiƩ et al., 1996). In this case, the explicit models used are derived
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