Lambertian Correction for Rough and Specular Surfaces

This paper describes a method for performing Lambertian reflectance for rough and specular surfaces. Rather than using an existing reflectance model, we present a method for estimating the reflectance function from image data. The method makes use of the Gauss map between a surface and a unit sphere. Under conditions in which the light source direction and the viewer direction are identical, we show how the reflectance function can be represented by a polar function on the unit sphere. We pose the problem of recovering the reflectance function as that of estimating a tabular representation of the polar function. A simple analysis shows how the tabular representation of the reflectance function can be obtained using the accumulative distribution of image gradients. By modifying the reflectance function and back-projecting, we can render the surface with alternative lighting models. Here, we choose to back-project a Lambertian reflectance model. This allows us to be remove specularities from shiny surfaces and compensate from boundary "flattening"for rough surfaces. We illustrate the utility of the method on a variety of real world imagery.