Secondary scattering shape from shading for precise terrain reconstruction of the lunar permanently shadowed regions

High-resolution digital elevation models (DEMs) of permanently shadowed regions (PSRs) at the lunar South Pole are crucial for upcoming exploration missions. Recent advances, such as high-resolution images acquired from ShadowCam, utilize indirect lighting to image PSRs. This provides data for the Shape from Shading (SFS) technique, which can extract subtle topographic details from single-image to reconstruct high-resolution terrain. However, traditional SFS methods are not suitable for complex secondary scattering scenes in PSRs with multiple secondary light sources. To address this issue, a novel secondary scattering SFS (SS-SFS) method is developed for pixel-wise 3D reconstruction of PSR surfaces, which utilizes indirect illuminated imagery and the corresponding low-resolution DEM to generate DEM with high resolution matches the input image. The proposed method effectively extracts and simplifies multiple incident facets associated with each shadowed facet through clustering, while constructing and optimizing the SS-SFS loss function. Experiments were conducted using ShadowCam images of two areas including both PSRs and temporary shadowed areas, to demonstrate the performance of the proposed method. The SS-SFS DEMs effectively capture intricate topographic details, and comparisons with adjusted Lunar Orbiter Laser Altimeter laser points indicate that the SS-SFS DEMs exhibit high overall accuracy. The high-resolution slope map of PSRs was calculated based on the SS-SFS DEMs, and overcome the limitation that surface slope is relatively underestimated from LOLA DEMs. Additionally, the SS-SFS DEMs were comprehensively compared with the traditional SFS DEMs generated using Narrow Angle Camera imagery in a small temporarily shadowed area, revealing strong consistency and further validating the effectiveness of detailed reconstruction. Overall, the proposed SS-SFS method is essential for generating high-resolution DEMs of PSRs, supporting future lunar South Pole exploration missions.