Gaussian Splatting for Efficient Satellite Image Photogrammetry

TL;DR

This work tackles efficient digital surface modeling from multi-date satellite imagery by reframing NeRF-era radiance field learning as Gaussian splatting with a compact 3D primitive representation. The Earth-observation Gaussian Splatting (EOGS) adapts 3DGS to remote sensing with affine camera projections, shadow mapping, and per-camera color corrections, together with three regularizers to promote sparsity, view consistency, and opaqueness. Empirical results on DFC2019 and IARPA2016 show EOGS achieves comparable elevation accuracy to EO-NeRF while being about $300\times$ faster, including a foliage-avoidance scenario. The work suggests that Gaussian splatting is a practical, scalable alternative for large-scale, multi-date satellite photogrammetry.

Abstract

Recently, Gaussian splatting has emerged as a strong alternative to NeRF, demonstrating impressive 3D modeling capabilities while requiring only a fraction of the training and rendering time. In this paper, we show how the standard Gaussian splatting framework can be adapted for remote sensing, retaining its high efficiency. This enables us to achieve state-of-the-art performance in just a few minutes, compared to the day-long optimization required by the best-performing NeRF-based Earth observation methods. The proposed framework incorporates remote-sensing improvements from EO-NeRF, such as radiometric correction and shadow modeling, while introducing novel components, including sparsity, view consistency, and opacity regularizations.

Figures (7)

• Figure 1: Using a limited number of satellite images of a given scene, the proposed EOGS method estimates the appearance and geometry of the scene. It achieves the same level of detail as EO-NeRF mari2023eonerf, such as the group of fans or the thin structures on top of the tall building on the left. However, EOGS requires only a few minutes of optimization, compared to the day-long training time required by EO-NeRF mari2023eonerf.
• Figure 2: Summary of the transformation from world-space to NDC-space and its affine approximation. The affine approximation is computationally efficient, compatible with the Gaussian splatting formulation, and well-suited for satellite images. The coordinate systems in the right red box represent 3D world coordinates (camera-independent), while the left blue box shows 2D coordinates (camera-dependent).
• Figure 3: Shadow mapping illustration. The point $\boldsymbol{\mathrm{u}}$ in the satellite image (affine camera $\mathcal{A}$) corresponds to a the the 3D point $\boldsymbol{\mathrm{x}}=\text{loc}^\mathcal{A}(\boldsymbol{\mathrm{u}})$ on the vertical wall. Projecting $\boldsymbol{\mathrm{x}}$ to the sun camera (affine camera $\mathcal{S}$), $\Tilde{\boldsymbol{\mathrm{u}}}=\mathcal{S}\boldsymbol{\mathrm{x}}$ is obtained. Then $\boldsymbol{\mathrm{y}}=\text{loc}^\mathcal{S}(\Tilde{\boldsymbol{\mathrm{u}}})$ is obtained localizing $\Tilde{\boldsymbol{\mathrm{u}}}$. The point $\boldsymbol{\mathrm{x}}$ and its pixel $\boldsymbol{\mathrm{u}}$ are in shadow because the elevation of $\boldsymbol{\mathrm{y}}$ is greater than the elevation of $\boldsymbol{\mathrm{x}}$. Indeed, all and only the points where the satellite elevation and the resampled sun elevation do not match should be shaded. On the bottom of the illustration are shown examples of the sun elevation, the resampled sun elevation, and the satellite elevation renderings, with shadows highlighted in red.
• Figure 4: From top-left to bottom-right, shadow maps of EO-NeRF, EOGS without the $\mathcal{L}_s$ penalizer, EOGS with the $\mathcal{L}_s$ penalizer, and the corresponding satellite image. Textures corresponding to the image content can be observed in the shadow map of EO-NeRF and EOGS without the $\mathcal{L}_s$ penalizer, but not in EOGS.
• Figure 5: From left to right: visual results on JAX_214 comparing SAT-NGP billouard2024satngp, EOGS, EO-NeRF mari2023eonerf and the ground truth.