Shading and Geometric Constraint Neural Radiance Field for DSM Reconstruction from Multi-View Satellite Images

With the continued development of spatial information technologies, Digital Surface Models (DSMs) have become fundamental data products for urban planning, virtual reality, geographic information systems, and digital-earth applications. Neural Radiance Fields (NeRFs) have achieved remarkable success in multi-view 3D reconstruction in computer vision. Still, their application to DSM generation from satellite imagery remains challenging because of differences in imaging geometry, complex surface structure, and varying illumination conditions. To address these issues, this paper proposes a Shading and Geometric Constraint (SGC) method tailored to satellite photogrammetry and designed to integrate with existing NeRF-based frameworks such as Sat-NeRF and EO-NeRF. First, a physical imaging model based on Lambertian reflectance and spherical harmonics is introduced to represent the complex illumination variations in satellite images. Synthetic images generated by this model provide auxiliary supervision that improves robustness to illumination inconsistency. Second, inspired by classical shading-based refinement methods, we introduce a bilateral edge-preserving geometric constraint. Unlike standard smoothness terms, this constraint uses photometric discrepancies to weight geometric smoothing, thereby preserving sharp building boundaries while smoothing flat surfaces. We integrate the method into two state-of-the-art baselines, Sat-NeRF and EO-NeRF. EO-NeRF+SGC achieves up to a 57.93% reduction in elevation MAE relative to EO-NeRF, which is the largest relative MAE reduction reported in this study. The method also recovers finer structural details and sharper edges than recently published NeRF-based DSM reconstruction methods.