Effects of illumination differences on photometric stereo shape-and-albedo-from-shading for precision lunar surface reconstruction

Photoclinometric surface reconstruction techniques such as Shape-from-Shading (SfS) and Shape-and-Albedo-from-Shading (SAfS) retrieve topographic information of a surface on the basis of the reflectance information embedded in the image intensity of each pixel. SfS or SAfS techniques have been utilized to generate pixel-resolution digital elevation models (DEMs) of the Moon and other planetary bodies. Photometric stereo SAfS analyzes images under multiple illumination conditions to improve the robustness of reconstruction. In this case, the directional difference in illumination between the images is likely to affect the quality of the reconstruction result. In this study, we quantitatively investigate the effects of illumination differences on photometric stereo SAfS. Firstly, an algorithm for photometric stereo SAfS is developed, and then, an error model is derived to analyze the relationships between the azimuthal and zenith angles of illumination of the images and the reconstruction qualities. The developed algorithm and error model were verified with high-resolution images collected by the Narrow Angle Camera (NAC) of the Lunar Reconnaissance Orbiter Camera (LROC). Experimental analyses reveal that (1) the resulting error in photometric stereo SAfS depends on both the azimuthal and the zenith angles of illumination as well as the general intensity of the images and (2) the predictions from the proposed error model are consistent with the actual slope errors obtained by photometric stereo SAfS using the LROC NAC images. The proposed error model enriches the theory of photometric stereo SAfS and is of significance for optimized lunar surface reconstruction based on SAfS techniques.