Simultaneous photometric invariance and shape recovery

In this paper, we identify the constraints under which the generally ill-posed problem of simultaneous recovery of surface shape and its photometric invariants can be rendered tractable. We examine the cases where a single or more images are acquired using different lighting directions with known illuminant power. Given these conditions, we state the constraints upon which the recovery of the surface geometry and its photometric parameters can be estimated. With these constraints, we then show how the recovery process may be formulated as an optimisation algorithm which aims to fit the reflectance models under study to the image reflectance. The approach presented here is general and can be applied to a family of reflectance models that are based on the Fresnel reflection theory. Thus, we provide a theoretical and computational background for recovering shape, material index of refraction and microscopic roughness from multi-spectral images.