<title>Non-Lambertian shading and photometric stereo</title>

Classical shape-from-shading and photometric stereo theones assume that diffuse reflection from real-world surfaces is Lambertian. However, there is considerable evidence that diffuse reflection from a large dass of surfaces is nonLambertian' . Using a Lambertian model to reconstruct such surfaces can cause serious errors in the reconstruction. In this paper, we propose a theory of non-Lambertian shading and photometric stereo. First, we explore the physics of scattering and obtain a realistic model for the reflectance map of non-Lambertian surfaces. The reflectance map is significantly non-linear. We then explore the number of light sources and the conditions on their placement for a globally unique inversion of the photometric stereo equation for this reflectance map. We theoretically establish the minimum number oflight sources needed to achieve this. These results are then extended in several directions. The main part of the extension is the joint estimation of surface normal along with the surface albedo. In the literature, this problem has been addressed only for Lambertian surfaces. We establish some basic results on the problem ofjoint estimation using the manifold structure of intensities obtained from photometric stereo. We will show that the joint estimation problem is ill-posed and propose a regularization scheme for it. Our experiments show that using the techniques proposed here, the fidelity of reconstruction can be increased by an order of magnitude over existing techniques.