Semi-Calibrated Photometric Stereo

While conventional calibrated photometric stereo methods assume that light intensities and sensor exposures are known or unknown but identical across observed images, this assumption easily breaks down in practical settings due to individual light bulb's characteristics and limited control over sensors. This paper studies the effect of unknown and possibly non-uniform light intensities and sensor exposures among observed images on the shape recovery based on photometric stereo. This leads to the development of a "semi-calibrated" photometric stereo method, where the light directions are known but light intensities (and sensor exposures) are unknown. We show that the semi-calibrated photometric stereo becomes a bilinear problem, whose general form is difficult to solve, but in the photometric stereo context, there exists a unique solution for the surface normal and light intensities (or sensor exposures). We further show that there exists a linear solution method for the problem, and develop efficient and stable solution methods. The semi-calibrated photometric stereo is advantageous over conventional calibrated photometric stereo in accurate determination of surface normal, because it relaxes the assumption of known light intensity ratios/sensor exposures. The experimental results show superior accuracy of the semi-calibrated photometric stereo in comparison to conventional methods in practical settings.