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This paper 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 implicit use of the Gauss map between the surface and a unit sphere. We assume that the material brightness is monotonic with respect to the angle between the illuminant direction and the surface normal. Under conditions in which the light source and the viewer directions are identical, we show how a tabular representation of the surface radiance function can be estimated using the cumulative distribution of image gradients. Using this tabular representation of the radiance function, 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 present two applications which make use of the estimated radiance function. The first of these illustrates how the radiance function estimates can be used to render objects when the light and viewer directions are no longer coincident. The second application involves applying corrected Lambertian radiance to rough and shiny surfaces.