Multispectral Photometric Stereo for Spatially-Varying Spectral Reflectances: A well posed problem?

Multispectral photometric stereo (MPS) aims at recovering the surface normal of a scene from a single-shot multi-spectral image, which is known as an ill-posed problem. To make the problem well-posed, existing MPS methods rely on restrictive assumptions, such as shape prior, surfaces having a monochromatic with uniform albedo. This paper alleviates the restrictive assumptions in existing methods. We show that the problem becomes well-posed for a surface with a uniform chromaticity but spatially-varying albedos based on our new formulation. Specifically, if at least three (or two) scene points share the same chromaticity, the proposed method uniquely recovers their surface normals and spectral reflectance with the illumination of more than or equal to four (or five) spectral lights. Besides, our method can be made robust by having many (i.e., 4 or more) spectral bands using robust estimation techniques for conventional photometric stereo. Experiments on both synthetic and real-world scenes demonstrate the effectiveness of our method. Our data and result can be found at https://github.com/GH-HOME/MultispectralPS.git.