Graphics Reference
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gonioreflectometers, or separately recorded during image acquisition. It also al-
lows more freedom of movement of the light source and makes the process more
stable, as the camera positioning equipment need not be separately calibrated.
At each illuminant position, a sequence of photographs of varying exposure
is captured by the primary camera, from which the HDR radiance map is re-
constructed (see Chapter 5). Each pixel then contains the reflected radiance at a
particular point on the sample. The corresponding direction with respect to the
normal on the sample surface is determined by the known shape of the sample
and the position of the pixel. Conceptually this amounts to tracing a hypothetical
ray from the camera viewpoint through the pixel on a virtual image plane to the
sphere on which the sample is affixed. The BRDF value is the ratio of the outgo-
ing radiance to the irradiance of the incident illumination. A conventional image
suffices for positioning; there is no need for an HDR image at the second cam-
era. Like Ward's method, each pixel in the primary image serves as a sample of
the BRDF, so the method provides a very dense sampling of the BRDF values in
the outgoing direction.
BRDF models created with novel ideas. The value of a BRDF for an arbi-
trary pair of directions can be approximated by interpolating the measured BRDF
data. As noted earlier, this is a difficult interpolation problem. Some mathemati-
cally sound interpolation methods result in unacceptable artifacts in the rendered
images. Another problem is that measurement noise is propagated by interpola-
tion. These issues have been one motivation for developing better BRDF mod-
els that can accurately represent observed BRDFs by smoothing out measured
data. A paper entitled “A Data-Driven Reflectance Model” by Wojciech Matusik,
Hanspeter Pfister, Matthew Brand, and Leonard McMillan [Matusik et al. 03] in-
troduced a method of constructing general BRDF models directly from measured
data. As in much of computer graphics, the “visual accuracy” is more important
than numeric accuracy: representing the visually significant elements of a BRDF
is more important than maintaining physically accurate values of the BRDF. The
paper describes a method for extracting physically significant data from a general
set of measured data in order to develop representative “basis” BRDFs. Arbitrary
BRDFs can then be represented by a weighted sum of these basis functions. Since
the basis functions are physically significant, the interpolation is more physically
meaningful and hopefully less prone to noise.
To acquire measurements, the authors used a device similar to the one de-
veloped by Steve Marschner and his colleagues described above. Conventional
BRDF measurements sample both the incoming angles in polar coordinates. A
problem with this approach is that it is difficult to concentrate samples
where they are important, such as at specular reflection. The method in the pa-
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