AstroSplat: Physics-Based Gaussian Splatting for Rendering and Reconstruction of Small Celestial Bodies

1. Problem Statement

The exploration of small celestial bodies (asteroids, comets, moons) relies heavily on image-based surface reconstruction for navigation, landing site selection, and scientific analysis. However, these environments present unique challenges:

• Extreme Illumination Variability: Space environments lack atmospheric scattering, leading to high-contrast lighting and deep shadows.
• Limitations of Traditional Methods: The standard approach, Stereophotoclinometry (SPC), is accurate but requires high-quality a priori information and significant human intervention to correct alignment errors, limiting autonomy and scalability.
• Limitations of Current Neural Methods: Recent Gaussian Splatting (GS) techniques (specifically 2DGS) offer real-time rendering and reconstruction but rely on Spherical Harmonic (SH) parameterization. This approach is purely appearance-based; it encodes view-dependent intensity without modeling the underlying physics of light-surface interactions. Consequently, geometry (topography) and albedo (material reflectivity) become entangled, often causing the model to misattribute illumination changes to surface texture rather than shape.

2. Methodology: AstroSplat

The authors propose AstroSplat, a framework that integrates planetary reflectance models into the 2D Gaussian Splatting pipeline to decouple geometry from appearance.

Core Architecture

• Base Framework: Utilizes 2D Gaussian Splatting (2DGS), which represents a scene as a collection of planar Gaussian disks rather than 3D ellipsoids. This encourages alignment with surfaces for better geometric reconstruction.
• Physics-Based Intensity Computation: Instead of learning SH coefficients to predict pixel color, AstroSplat replaces the appearance encoder with a photometric function.
  • The intensity of each Gaussian is calculated based on:
    1. Surface Normal ($n$): Derived from the Gaussian's orientation.
    2. Illumination Direction ($s$): Known from spacecraft telemetry (Sun vector).
    3. Viewing Direction ($e$): Known from camera pose.
    4. Learned Albedo ($a$): A per-Gaussian parameter representing material properties.
• Reflectance Models Tested: The paper evaluates three specific physical models to determine pixel intensity:
  1. Lambert: Assumes perfect diffuse scattering ($d = \cos \iota$).
  2. Lommel-Seeliger (L-S): Models single scattering, common for airless bodies ($d = \frac{2\cos \iota}{\cos \iota + \cos \epsilon}$).
  3. Lunar-Lambert: A weighted sum of Lambert and L-S, modulated by a phase function to account for the opposition effect.
• Optimization: The system minimizes a loss function comprising:
  • Intensity Loss ($L_I$): A combination of L1 difference and SSIM between rendered and ground-truth images.
  • Normal Loss ($L_n$): Encourages the Gaussian normals to align with the gradient of the depth map.
  • Scale/Bias Correction: Learnable parameters per image to handle uncalibrated sensor data (DN values).

3. Key Contributions

1. Integration of Physics into GS: Successfully adapted 2DGS to use planetary photometric models, replacing the purely appearance-based SH parameterization.
2. Autonomous Reconstruction: Demonstrated a fully autonomous pipeline that does not require human-in-the-loop corrections or high-quality a priori shape models, unlike traditional SPC.
3. Albedo Estimation: Enabled the simultaneous estimation of surface albedo (material properties) alongside topography, a capability often lost in standard neural rendering.
4. Parameter Efficiency: The physics-based models require significantly fewer learnable parameters (only one albedo value per Gaussian) compared to the 16 parameters required for standard third-degree SH expansions.

4. Experimental Results

The framework was validated using real imagery from NASA's Dawn mission targeting Asteroid 4 Vesta (Cornelia crater) and Minor Planet 1 Ceres (Ikapati crater and Ahuna Mons).

• Rendering Quality:
  • Physics-based models consistently outperformed the standard SH approach across all metrics: PSNR, SSIM, and LPIPS.
  • The Lambert model generally yielded the best rendering results, followed closely by Lunar-Lambert.
• Geometric Reconstruction (Normals & Meshes):
  • Normal Accuracy: All physics-based models reduced the mean angular error in surface normals compared to SH. The Lommel-Seeliger model achieved the lowest error across all datasets.
  • Detail Preservation: Visual analysis showed that physics-based methods preserved fine topographical details (small craters, ridges) that were smoothed out or lost in the SH reconstructions.
  • Mesh Accuracy: The Hausdorff distance between the reconstructed meshes and ground truth (PhoMo) was consistently minimized by physics-based approaches.
• Albedo Accuracy:
  • The models successfully estimated albedo maps. For the Cornelia crater, the Lambert model provided the closest albedo match to ground truth, reducing error by ~20-30% compared to other models.

5. Significance

• Mission Autonomy: AstroSplat offers a path toward fully autonomous surface mapping for future deep-space missions, removing the bottleneck of human-dependent SPC processing.
• Scientific Fidelity: By explicitly modeling light-surface interactions, the method produces physically consistent reconstructions where geometry and material properties are correctly separated. This is crucial for scientific analysis of surface composition and topography.
• Generalizability: The framework demonstrates that incorporating domain-specific physics (planetary photometry) into general neural rendering architectures yields superior results for specialized applications like space exploration, suggesting a broader trend for "physics-aware" neural scene representations.

In summary, AstroSplat bridges the gap between the efficiency of neural rendering and the physical rigor of traditional photogrammetry, delivering higher fidelity reconstructions of small celestial bodies with greater autonomy.