ICT
VGL
Cosine Lobe Based Relighting from Gradient Illumination Photographs  
SIGGRAPH 2009 Poster 

Graham Fyffe  
USC Institute for Creative Technologies 
Introduction:
We present an imagebased method for relighting a scene by analytically fitting a cosine
lobe to the reflectance function at each pixel, based on gradient illumination
photographs. Relit images are computed simply by sampling the cosine lobe reflectance
functions for each light source in the novel illumination condition. Realistic results for
many materials are obtained using a single perpixel cosine lobe obtained from just two
color photographs: one under uniform white illumination and the other under colored
gradient illumination. See figure 1. For materials with wavelengthdependent scattering,
a better fit can be obtained using independent cosine lobes for the red, green, and blue
channels, obtained from three monochromatic gradient illumination conditions instead
of the colored gradient condition. See figure 2 on poster.
Method:
We photograph the subject under gradient illumination conditions
much like Ma et al. [2007], but instead of computing normals, we
analytically fit a cosine lobe reflectance model to the photographs. We
explore two cosine lobe reflectance functions. Hemispherical cosine
lobes of the form
work well for diffuse and specular
materials, but fail for broadly scattering materials such as fur. Spherical
cosine lobes of the form
work well for fur and still
produce visually plausible results for diffuse and specular materials. In
both models,
refers to the axis of the lobe, n and k are constants, and
Θ
refers to the angle of incident light. Figure 3 compares the two models.
Analysis of Fitted Exponents:
Ghosh et al. [2009] directly measure reflectance lobe
widths. We obtain the widths from fewer photographs
by imposing the cosine lobe model. Discounting
occlusion and interreflection, the hemispherical cosine
lobe exponent n will be 1 for Lambertian diffuse
materials, and higher for specular materials. Inspection
of the fitted exponents shows strong agreement with
the materials of the actual subject, suggesting that the
model is a good fit. Refer to figure 4. For example, the
golden body of the cat has exponents ranging from
1.2 up to 6.0 at grazing angles, indicating a specular
material with dependency on angle, in this case a gold
paint. The red collar, ears, and nose have exponents of
1.1 in the red channel, and higher in the green and
blue channels, indicating a dominant diffuse red
component with a small specular component in all
channels, in this case a semigloss red paint. The green
bib has exponents of 0.7 in the green channel, and
somewhat higher in the red and blue channels, in this
case a very soft diffuse green paint with a faint gloss.
Analysis of Relighting Results:
Figure 5 shows two novel illumination conditions with ground truth photographs, relighting results using the hemispherical cosine lobe model, and relighting results using the four input photographs as a linear basis for comparison. The linear basis results fail to reproduce the appearance of the different materials of the cat subject. The cosine lobe model, however, produces visually plausible results over a wide variety of materials and illumination conditions, using very few input observations.
Material:
CVMP 2009 Paper:
 CosineLobeBaseRelighting_cvmp2009.pdf, 49.7 MB. (Adobe Acrobat)
SIGGRAPH 2009 Poster:
 CosineLobeBaseRelighting _4ftx3ft_Poster.png, 5.89 MB.
 CosineLobeBaseRelighting_SIG2009.pdf, 5.27 MB. (Adobe Acrobat)
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