Photometric stereo under a light source with arbitrary motion

Abstract

A new photometric-stereo method for estimating the surface normal and the surface reflectance of objects without a priori knowledge of the light-source direction or the light-source intensity is proposed. First, I construct a p × f image data matrix I from p pixel image intensity data through f frames by moving a light source arbitrarily. Under the Lambertian assumption the image data matrix I can be written as the product of two matrices S and L, with S representing the surface normal and the surface reflectance and L representing the light-source direction and the light-source intensity. Using this formulation, I show that the image data matrix I is of rank 3. On the basis of this observation, I use a singular-value decomposition technique and useful constraints to factorize the image data matrix. This method can also be used to treat cast shadows and self-shadows without assumptions. The effectiveness of this method is demonstrated through performance analysis, laboratory experiment, and out-of-laboratory experiment.