Uncalibrated photometric stereo for unknown isotropic reflectances

We propose an uncalibrated photometric stereo method that works with general and unknown isotropic reflectances. Our method uses a pixel intensity profile, which is a sequence of radiance intensities recorded at a pixel across multi-illuminance images. We show that for general isotropic materials, the geodesic distance between intensity profiles is linearly related to the angular difference of their surface normals, and that the intensity distribution of an intensity profile conveys information about the reflectance properties, when the intensity profile is obtained under uniformly distributed directional lightings. Based on these observations, we show that surface normals can be estimated up to a convex/concave ambiguity. A solution method based on matrix decomposition with missing data is developed for a reliable estimation. Quantitative and qualitative evaluations of our method are performed using both synthetic and real-world scenes.