Photometric stereo shape-and-albedo-from-shading for pixel-level resolution lunar surface reconstruction

Abstract

Shape and Albedo from Shading (SAfS) techniques recover pixel-wise surface details based on the relationship between terrain slopes, illumination and imaging geometry, and the energy response (i.e., image intensity) captured by the sensing system. Multiple images with different illumination geometries (i.e., photometric stereo) can provide better SAfS surface reconstruction due to the increase in observations. Photometric stereo SAfS is suitable for detailed surface reconstruction of the Moon and other extra-terrestrial bodies due to the availability of photometric stereo and the less complex surface reflecting properties (i.e., albedo) of the target bodies as compared to the Earth. Considering only one photometric stereo pair (i.e., two images), pixel-variant albedo is still a major obstacle to satisfactory reconstruction and it needs to be regulated by the SAfS algorithm. The illumination directional difference between the two images also becomes an important factor affecting the reconstruction quality. This paper presents a photometric stereo SAfS algorithm for pixel-level resolution lunar surface reconstruction. The algorithm includes a hierarchical optimization architecture for handling pixel-variant albedo and improving performance. With the use of Lunar Reconnaissance Orbiter Camera - Narrow Angle Camera (LROC NAC) photometric stereo images, the reconstructed topography (i.e., the DEM) is compared with the DEM produced independently by photogrammetric methods. This paper also addresses the effect of illumination directional difference in between one photometric stereo pair on the reconstruction quality of the proposed algorithm by both mathematical and experimental analysis. In this case, LROC NAC images under multiple illumination directions are utilized by the proposed algorithm for experimental comparison. The mathematical derivation suggests an illumination azimuthal difference of 90 degrees between two images is recommended to achieve minimal error in SAfS reconstruction while results using real data presents similar pattern. Although the algorithm is designed for lunar surface reconstruction, it is likely to be applicable on other extra-terrestrial bodies such as Mars. The results and findings from this research is of significance for the practical use of photometric stereo and SAfS in the domain of planetary remote sensing and mapping.