Incorporating the Torrance and Sparrow Model of Reflectance in Uncalibrated Photometric Stereo

Under the Lambertian reflectance model, uncalibrated photometric stereo with unknown light sources is inherently ambiguous. In this paper, we consider the use of a more general reflectance model, namely the Torrance and Sparrow model, in uncalibrated photometric stereo. We demonstrate that this can not only resolve the ambiguity when the light sources are unknown, but can also result in more accurate surface reconstructions and can capture the reflectance properties of a large number of non-Lambertian surfaces. Our method uses single light source images with unknown lighting and no knowledge about the parameters of the reflectance model. It can recover the 3-D shape of surfaces (up to the binary convex/concave ambiguity) together with their reflectance properties. We have successfully tested our algorithm on a variety of non-Lambertian surfaces demonstrating the effectiveness of our approach. In the case of human faces, the estimated skin reflectance has been shown to closely resemble the measured skin reflectance reported in the literature. We also demonstrate improved recognition results on 4050 images of 10 faces with variable lighting and viewpoint when the synthetic image-based representations of the faces are generated using the surface reconstructions and reflectance properties recovered while assuming the extended reflectance model.