Multispectral Photometric Stereo for Spatially-Varying Spectral Reflectances

摘要

Multispectral photometric stereo (MPS) aims at recovering the surface normal of a scene measured under multiple light sources with different wavelengths. While it opens up a capability of a single-shot measurement of surface normal, the problem has been known ill-posed. 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 these restrictive assumptions in existing methods. We show that the problem becomes well-posed for surfaces with 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 with the illumination of no less than four (or five) spectral lights in a closed-form. In addition, we show that a more general setting of spatially-varying both chromaticities and albedos can become well-posed if the light spectra and camera spectral sensitivity are calibrated. For this general setting, we derive a unique and closed-form solution for MPS using the linear bases extracted from a spectral reflectance database. Experiments on both synthetic and real captured data with spatially-varying reflectance demonstrate the effectiveness of our method and show the potential applicability for multispectral heritage preservation.