SatGeo-NeRF: Geometrically Regularized NeRF for Satellite Imagery

Valentin Wagner; Sebastian Bullinger; Michael Arens; Rainer Stiefelhagen

cs.CVMar 23, 2026

SatGeo-NeRF: Geometrically Regularized NeRF for Satellite Imagery

Authors: Valentin Wagner, Sebastian Bullinger, Michael Arens, Rainer Stiefelhagen

Organizations: Fraunhofer IOSB, Ettlingen, Germany · Karlsruhe Institute of Technology, Karlsruhe, Germany

Abstract

We present SatGeo-NeRF, a geometrically regularized NeRF for satellite imagery that mitigates overfitting-induced geometric artifacts observed in current state-of-the-art models using three model-agnostic regularizers. Gravity-Aligned Planarity Regularization aligns depth-inferred, approximated surface normals with the gravity axis to promote local planarity, coupling adjacent rays via a corresponding surface approximation to facilitate cross-ray gradient flow. Granularity Regularization enforces a coarse-to-fine geometry-learning scheme, and Depth-Supervised Regularization stabilizes early training for improved geometric accuracy. On the DFC2019 satellite reconstruction benchmark, SatGeo-NeRF improves the Mean Altitude Error by 13.9% and 11.7% relative to state-of-the-art baselines such as EO-NeRF and EO-GS.

Figures & tables

Panel of Figure 1 — Figure 1: Rendered depth estimations (top), closeups (middle), RGB and Lidar DSM ground truth (bottom). Our geometry regularization technique reduces high-frequency artifacts caused by overfitting to individual training images.

Figure 2: Gravity-Aligned Planarity Regularization : A local plane is estimated from three surface points on adjacent rays; its normal is constrained to align with the axis of gravity (approximated as UTM -up).

Figure 3: We augment a satellite‑domain–adapted backbone ( EO‑NeRF , Marí et al., (2023) ) with three model‑agnostic regularizers: (1) Gravity-Aligned Planarity Regularization : estimate explicit normals by sampling two adjacent rays per training ray and evaluating depth only; align normals with the axis of gravity to mitigate overfitting and enable cross‑ray smoothing. (2) Geometrical Granularity Regularization : coarse‑to‑fine masking of the input frequency encoding. (3) Depth‑Supervised Regularization : depth constraints from a sparse 3D point cloud obtained from a Bundle Adjustment preprocessing step.

Panel of Figure 4 — Figure 4: Rendered RGB images with their respective PSNR values. To human observers, the $6.6$ % relative PSNR difference is not perceptually noticeable under normal viewing.

Panel of Table 1 — Table 1: Evaluation of our proposed SatGeo-NeRF with state-of-the-art baselines. Our proposed regularization are able to improve the MAE by a mean of 14.0% on the DFC2019 dataset Le Saux et al., (2019) with only minimal impact on image render quality.

Panel of Table 2 — Table 2: Ablation study demonstrating improvements in reconstruction quality from our proposed regularization terms.

		MAE [m] $\downarrow$
Length	Samples	004	068	214	260	Mean
100%	$2\times 128$	1.30	1.08	2.13	1.39	1.48
50%	$2\times 64$	1.37	1.05	2.11	1.47	1.50
25%	$2\times 32$	1.91	1.02	2.12	1.45	1.63

Table 3: Ablation study on adjacent ray length and sample density for explicit normal calculation. Centering adjacent rays around main surface point with a length of 50 % reduces computation with minimal impact on MAE for most scenes.

Panel of Figure 5 — Figure 5: Explicit surface normal vectors determined based on predicted depth values of three adjacent rays; colors show normalized orientation (e.g., blue = upright). Planarity Regularization increases quality through alignment with the axis of gravity.

Panel of Figure 6 — Figure 6: Extracted DSM of our proposed regularization in comparison to the Lidar Ground Truth, EO-NeRF* Marí et al., (2023) and EO-GS Aira et al., (2024) . For each scene the view with minimal MAE is shown. Colors map height from blue (low) to red (high).

3D Reconstruction

3D reconstruction recovers a scene’s shape, appearance, and camera motion from images, video, depth, or other sensor measurements.

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Neural Radiance Fields (NeRF) have emerged as a powerful approach for photorealistic 3D reconstruction from multi-view images. However, deploying NeRF for satellite imagery remains challenging. Each scene requires individual training, and optimizing architectures via Neural Architecture Search (NAS) demands hours to days of GPU time. While existing approaches focus on architectural improvements, our SHAP analysis reveals that multi-view consistency, rather than model architecture, determines reconstruction quality. Based on this insight, we develop PreSCAN, a predictive framework that estimates NeRF quality prior to training using lightweight geometric and photometric descriptors. PreSCAN selects suitable architectures in < 30 seconds with < 1 dB prediction error, achieving 1000

\times

speedup over NAS. We further demonstrate PreSCAN's deployment utility on edge platforms (Jetson Orin), where combining its predictions with offline cost profiling reduces inference power by 26% and latency by 43% with minimal quality loss. Experiments on DFC2019 datasets confirm that PreSCAN generalizes across diverse satellite scenes without retraining.

Abstract

3D Reconstruction

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