Can two specular pixels calibrate photometric stereo?

Lambertian photometric stereo with unknown light source parameters is ambiguous. Provided that the object imaged constitutes a surface, the ambiguity is represented by the group of generalised bas-relief (GBR) transformations. We show that this ambiguity is resolved when specular reflection is present in two images taken under two different light source directions. We identify all configurations of the two directional lights which are singular and show that they can easily be tested for. While previous work used optimisation algorithms to apply the constraints implied by the specular reflectance component, we have developed a linear algorithm to achieve this goal. Our theory can be utilised to construct fast algorithms for automatic reconstruction of smooth glossy surfaces