pigmented colorants: dependence on media and time - Cornell ...

scattering and absorption properties. The following research demonstrates the
usefulness of K-M theory to simulate the appearance of <strong>pigmented</strong> materials.
Haase and Mayer introduced the Kubelka-Munk model to computer graphics,
using the K-M equations for rendering and color mixing in both interactive and
offline applications [HM92]. The work included a simple airbrush tool, where users
could work with real-world <strong>pigmented</strong> paints, instead of arbitrary RGB colors.
The program stored and updated the current K and S values for every pixel in
the image, using a custom four-wavelengths representation based on Meyer’s previ-
ous work [Mey88]. The four-wavelength encoding was based on integrating against
the human visual response functions in ACC color space. The interpolation of the
wavelengths used to compute tristimulus values from spectral data was done using
Gaussian quadrature. Computing reflectance values for K and S values over the
entire visible spectrum is very computationally expensive, and therefore limiting
the wavelength information is necessary for the purposes of real-time interaction.
Since the reflectance spectral curves are reasonably smooth functions, the errors
caused by this minimal sampling are minimized.
The results of this theory are illustrated in Figure 4.6. A real photograph
painted with varying concentrations of two red paints and a white paint is simu-
lated using RGB values and Kubelka-Munk theory. The spectral reflectances of
the paints are shown in Figure 4.7 and the dependencies of the absorption and
scattering coefficients are shown in Figure 4.8.
Curtis et al. used the Kubelka-Munk equations for optically compositing thin
glazes of paint in their watercolor simulation [CAS + 97]. The model uses a three
wavelength RGB representation for the K and S coefficients. The K and S values
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were not determined experimentally, but specified interactively. This method of