Interreflection removal for photometric stereo by using spectrum-dependent albedo

Abstract

We present a novel method that can separate m-bounced light and remove the interreflections in a photometric stereo setup. Under the assumption of a uniformly colored lambertian surface, the intensity of a point in the scene is the sum of 1-bounced light through m-bounced light rays. Ruled by the law of diffuse reflection, whenever a light ray is bounced by the surface, its intensity will be attenuated by the factor of albedo ρ. This implies that the measured intensity value can be written as a polynomial function of ρ, and the intensity contribution of the m-bounced light rays are expressed by the term of ρ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> . Therefore, when we change the surface albedo, the intensity of the m-bounced light is changed to the order of m. This non-linearity gives us the possibility to separate the m-bounced light. In practice, we illuminate the scene with different light colors to effectively simulate different surface albedos since albedo is spectrum dependent. Once the m-bounced light rays are separated, we can perform the photometric stereo algorithm on the 1-bounced light (direct lighting) images to produce the 3D shape without the impact of interreflections. Experiments have shown that we get significantly improved scene reconstruction with a minimum of two color images.