Estimating the surface radiance function from single images

This work describes a simple method for estimating the surface radiance function from single images of smooth surfaces made of materials whose reflectance function is isotropic and monotonic. The method makes use of an implicit mapping of the Gauss map between the surface and a unit sphere. By assuming the material brightness is monotonic with respect to the angle between the illuminant direction and the surface normal, we show how the radiance function can be represented by a polar function on the unit sphere. Under conditions in which the light source direction and the viewer direction are identical, we show how the recovery of the radiance function may be posed as that of estimating a tabular representation of this polar function. A simple differential geometry analysis shows how the tabular representation of the radiance function can be obtained using the cumulative distribution of image gradients. With the tabular representation of the radiance function at hand, surfaces may be rendered under varying light source direction by rotating the corresponding reflectance map on the Gauss sphere about the specular spike direction. We present a sensitivity study on synthetic and real-world imagery. We also illustrate the utility of the method for purposes of material classification.