Specularities Reduce Ambiguity of Uncalibrated Photometric Stereo

Lambertian photometric stereo with uncalibrated light directions and intensities determines the surface normals only up to an invertible linear transformation. We show that if object reflectance is a sum of Lambertian and specular terms, the ambiguity reduces into a 2dof group of transformations (compositions of isotropic scaling, rotation around the viewing vector, and change in coordinate frame handedness).Such ambiguity reduction is implied by the consistent viewpoint constraint which requires that all lights reflected around corresponding specular normals must give the same vector (the viewing direction). To employ the constraint, identification of specularities in images corresponding to four different point lights in general configuration suffices. When the consistent viewpoint constraint is combined with integrability constraint, binary convex/concave ambiguity composed with isotropic scaling results. The approach is verified experimentally.We observe that an analogical result applies to the case of uncalibrated geometric stereo with four affine cameras in a general configuration observing specularities from a single distant point light source.