Classical Photometric Stereo in Point Lighting Environments: Error Analysis and Mitigation

While classical photometric stereo assumes parallel lighting and thus allows for efficient solutions, this assumption is rarely met in practice. In acquisition setups using point-like light sources such as LEDs, direction and intensity of incident light depend on the unknown surface position, which leads to a non-linear problem. Although numerous approaches explicitly accounting for non-parallel lighting are proposed, photometric stereo with the parallel lighting model is widely used in point lighting scenarios. This is done for reasons of computational efficiency and ease of system calibration, and justified with the observation that lighting becomes approximately parallel when light sources are placed in a sufficient distance from the object. However, as no account of the relation between light source distance and reconstruction errors is found in literature, it is not clear which light source distance would be ’sufficient’ for a given application. In this work, we propose an upper bound for mean errors resulting from using parallel-lighting models in point light setups, depending on the distance of light sources and the size of the object imaged. This bound is based on analytical considerations and previous results of photometric stereo error analysis, and validated vie a Monte Carlo simulation. These results are then used to justify an error mitigation strategy via local solutions that is applicable in use cases where an approximate depth is known a priori. The theoretical propositions are demonstrated on real-world data.