This post is part of a series where Digital Sense presents key scientific contributions from our team members, translating advanced research into insights for a broader technical audience. In this edition, we explore a new method for satellite image-based 3D modeling developed by Luca Savant Aira, Thibaud Ehret, and Gabriele Facciolo, Senior Scientific Consultant at Digital Sense and Professor at ENS Paris-Saclay.
The research, titled “Gaussian Splatting for Efficient Satellite Image Photogrammetry”, is to be presented at CVPR 2025, and proposes a highly efficient framework for generating 3D terrain models from satellite images that speeds it up to 300× faster than previous state-of-the-art methods.
What is Multi-Date 3D Terrain Modeling from Satellite Images?
Multi-date 3D terrain modeling is the process of reconstructing the shape and appearance of Earth’s surface—buildings, vegetation, and ground elevation—using 2D satellite images captured at different times and from different viewing angles. The output is typically a Digital Surface Model (DSM) or a Digital Elevation Model (DEM), enriched with high-resolution texture and structural detail.
In the case of satellite imaging, synchronized stereo image pairs—images taken at the same time from calibrated sensors— for 3D reconstruction, can be expensive. On the other hand, regular satellite images are cheaper, but harder to use for precise 3D reconstruction. Satellite imagery is often acquired opportunistically, meaning that images are taken as the satellite passes over a region, dictated by orbital dynamics, mission planning constraints, and weather conditions. As a result, image sets are:
- Captured days, weeks, or months apart,
- Taken from varied and oblique angles,
- Subject to different lighting, seasons, and atmospheric conditions.
All of these factors pose challenges to accurate 3D reconstruction using multiple opportunistic captures.
Enabling Opportunistic Reconstruction
Traditional satellite stereo-vision pipelines work best when images are tightly aligned in time and geometry. However, this significantly limits their applicability since acquiring stereo-enabled satellite pairs is costly or not feasible in urgent situations.
Enter EO-NeRF
One of the first successful methods to address this limitation was EO-NeRF, a satellite-adapted version of Neural Radiance Fields (NeRF). EO-NeRF introduced critical innovations for remote sensing, such as accurate shadow modeling and physically consistent lighting, allowing it to reconstruct 3D terrain from non-simultaneous, multi-date imagery. This was a significant step forward—EO-NeRF showed that accurate 3D reconstructions were possible even when using images captured at different times and from diverse viewing geometries.
However, EO-NeRF has a critical limitation: computational cost. Training the EO-NeRF model for a single 256×256 m area can take up to 15 hours on high-end hardware. This severely limits its practicality for large-scale or time-sensitive applications.
The method presented in this work, EOGS (Earth Observation Gaussian Splatting), breaks this dependency while solving the speed bottleneck. It builds on the conceptual advances of EO-NeRF but replaces the computationally expensive volumetric rendering pipeline with a more efficient Gaussian-based approach—cutting training times from hours to just a few minutes, with only minimal trade-offs in accuracy.
What is Gaussian Splatting?
Gaussian splatting is a state-of-the-art technique for 3D reconstruction using inverse rendering that has recently emerged as a highly efficient alternative to neural radiance fields (NeRF). While NeRF models typically use multilayer perceptrons (MLPs) to represent scenes as continuous volumetric functions, Gaussian splatting opts for a set of discrete, learnable 3D Gaussian primitives. These primitives act as volumetric “building blocks” of a scene, and each is defined by a center, a covariance (its shape and orientation), an opacity, and a color or feature vector.
Each 3D Gaussian is projected (or “splatted”) onto a 2D image plane corresponding to a specific camera view. These projections are then composited using an alpha-blending strategy to generate novel views of the scene.
What makes Gaussian splatting exceptional is its computational efficiency: it avoids expensive ray-marching and instead leverages analytic projection and rasterization. This results in dramatic speed-ups for both training and rendering, while maintaining high visual fidelity and geometric accuracy.
From NeRF to Gaussian Splatting: A Paradigm Shift
Neural Radiance Fields (NeRF) have revolutionized view synthesis by modeling scenes as continuous volumetric fields. In Earth observation, EO-NeRF extended this approach to handle satellite imagery, incorporating elements like sun position and terrain occlusions. However, it remains computationally expensive—training on a single scene can take up to 15 hours.
In contrast, EOGS completes training in just 3 minutes on the same scene, with only marginal trade-offs in accuracy.
Comparative Performance
The table below (from the original paper) illustrates performance metrics (Mean Absolute Error in meters) and training time:
Table 1: EOGS achieves competitive accuracy with vastly reduced training time.
Key Innovations in EOGS
1. Affine Camera Approximation
To perform 3D reconstruction, geometric information relating pixels in the image to the spatial position of imaged objects is necessary. This information can be captured by modelling the image formation process of the satellite, referred to as the physical camera model. This highly complex physical camera model is often approximated by Rational Polynomial Coefficients (RPCs) as a way to simplify projection calculations. EOGS in turn approximates RPCs using affine transformations. This is computationally efficient and introduces only a negligible error (~0.012 pixels on average).
2. Physically-Based Shadow Mapping
Shadows in multi-date satellite imagery introduce appearance changes that negatively affect 3D reconstruction. EO-NeRF circumvented these issues by using ray-marching to simulate shadows enabling higher precision reconstructions on such scenarios. However, ray-marching-based shadow casting is not applicable in Gaussian splatting. EOGS introduces a novel shadow mapping method inspired by computer graphics, where the sun is modeled as a directional light and shadows are calculated through elevation comparisons.
Illustration: Shadow Consistency Logic
This formulation leads to more accurate shading, better elevation estimates, and higher photorealism without breaking the efficiency of Gaussian splatting.
Moreover, as it has been shown in another scientific paper by Digital Sense members that the modeling of shadows also improves the 3D reconstruction since shadows length also provide a cue of the altitude of the objects in the scene.
3. Tailored Regularization
To enhance quality and stability, EOGS incorporates three key regularization strategies:
- Sparsity: Encourages the model to use fewer Gaussian primitives by penalizing low-opacity ones. This leads to 2× faster training.
- View Consistency: Ensures consistent rendering across multiple satellite views, improving reconstruction reliability.
- Opaqueness: Penalizes semi-transparent shadow artifacts, encouraging binary shadow decisions.
Ablation Study: Importance of Each Component
Table 2: Each regularizer contributes to performance gains.
Results & Real-World Impact
Datasets Used
EOGS was evaluated on images extracted from benchmark satellite datasets:
- IARPA 2016 MVS Challenge
- IEEE GRSS Data Fusion Contest 2019
Each extract consists of WorldView-3 satellite images covering 256×256 m² with ~30–50 cm resolution. EOGS uses 10–20 views per scene and recovers elevation models with sub-meter accuracy.
Where EOGS Excels
- High-coverage areas: Best accuracy where terrain is visible from many angles.
- Structural elements: Outperforms EO-NeRF when foliage is excluded.
- Speed-critical environments: Ideal for large-scale deployment due to its fast training time.
Conclusion: A Step Toward Scalable Satellite 3D Modeling
By integrating Gaussian splatting into remote sensing photogrammetry, EOGS bridges the gap between high-fidelity modeling and operational scalability. It retains the precision of state-of-the-art NeRF-based methods but delivers results in minutes, not hours.
This is a critical advancement for institutions and companies that rely on timely, accurate terrain data—such as defense contractors, environmental monitoring agencies, and infrastructure planning teams.
About Digital Sense
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Whether you're optimizing satellite data pipelines, developing geospatial AI systems, or building scalable 3D modeling platforms, we provide the scientific rigor and engineering talent to help you succeed.
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Reference
Aira, L.S., Facciolo, G. and Ehret, T., 2024. Gaussian Splatting for Efficient Satellite Image Photogrammetry. arXiv preprint arXiv:2412.13047.
