COIL-PS: continuous and online illumination planning for photometric stereo

Photometric stereo (PS) aims to recover high-fidelity surface normals by observing pixel-wise radiometric variations under different light directions. However, traditional PS methods require dense sampling of the incident light to mitigate non-Lambertian effects, such as cast shadows and specular highlights, creating a significant efficiency bottleneck for practical optical metrology. To address this efficiency bottleneck, illumination planning methods seek to identify an optimal set of light directions to maximize information gain with minimal measurements. A critical limitation of existing illumination planning paradigms is their reliance on selecting from a predefined, discrete set of candidate light directions. This discretization of the light space introduces an artificial bottleneck, severely limiting precision and adaptability. In this paper, we address this limitation by introducing a Continuous and Online ILlumination Planning framework for Photometric Stereo (COIL-PS). Instead of selecting from a fixed grid, our method formulates illumination planning as a continuous regression problem, adaptively steering light positioning in the continuous hemispherical domain. By coupling online illumination planning with feedback from intermediate normal estimates, COIL-PS adaptively navigates non-Lambertian effects such as shadows and specularities, which allow for the precise angular placement of illumination required to resolve geometric ambiguities that fall between fixed grid points. Extensive experiments on a synthetic dataset, semi-real benchmarks, and our custom-built real-world robotic validation system demonstrate that COIL-PS achieves superior normal reconstruction accuracy compared to state-of-the-art discrete planning methods, even with a budget of only ten lights, significantly outperforming discrete planning paradigms.