Physics-Informed Joint Super-Resolution Topography and Reflectance Inversion From Multi-Angular Planetary Imagery — The LUMOS Framework

Accurate characterisation of planetary surface topography and reflectance at metre and sub-metre scales is critical for geological interpretation, understanding regolith processes, and supporting surface exploration. We present LUMOS (LUminosity-constrained Multi-angular Observation Super-resolution), a physics-based framework for the joint reconstruction of super-resolution digital elevation models (DEMs), spatially varying surface reflectance, and uncertainty estimates from multi-angular orbital imagery. The method overcomes key limitations of classical shape-from-shading approaches, which typically assume Lambertian reflectance and provide no uncertainty quantification.

Figure 1 Area of the reconstructed terrain centred on the Apollo 15 landing site.
(a) LOLA elevation map at its native resolution. (b) LUMOS-derived DEM shown in nadir view.
(c,d) Oblique views of the LUMOS DEM.

LUMOS formulates surface reconstruction as a Bayesian inverse problem that explicitly couples topography and photometry. Observed radiance is modelled using a non-Lambertian, kernel-driven bidirectional reflectance distribution function (BRDF), adopting the Ross–Thick Li–Sparse (RTLS) formulation to represent isotropic, volumetric, and geometric scattering effects. This enables physically consistent treatment of anisotropic regolith scattering, shadowing, and viewing-geometry dependence. A low-resolution laser altimetry DEM is incorporated as a prior to constrain long-wavelength topography, while fine-scale surface structure is recovered from photometric variations across multiple illumination and viewing angles. The coupled system is solved efficiently using a Sylvester-equation-based formulation, avoiding empirical tuning parameters and allowing uncertainties in image radiance and prior information to propagate into the final products.

Figure 2 Slope uncertainty map. Uncertainty increases in shadowed regions and where viewing geometry is limited.

We demonstrate LUMOS using multi-angular LROC NAC observations of the Apollo 15 landing site. The reconstructed DEM achieves a spatial resolution of 0.53 m/pixel, corresponding to the native resolution of the NAC imagery and representing more than a two order of magnitude increase in sampling density relative to the Lunar Orbiter Laser Altimeter (LOLA) prior. Large-area comparisons show that the LUMOS DEM preserves consistency with LOLA-derived long wavelength trends while resolving fine scale morphological features, including small craters, subtle relief variations, and local undulations unresolved in altimetric data. Detailed views further illustrate surface continuity and the absence of illumination correlated artefacts.

Beyond elevation, LUMOS retrieves spatially resolved reflectance parameters and provides pixel-wise uncertainty estimates for both elevation and slope. Derived slope maps reveal metre-scale variations sensitive to reflectance modelling assumptions, with Lambertian-based reconstructions exhibiting systematic biases relative to the RTLS solution. These differences have implications not only for operational assessments, such as landing-site hazard evaluation, but also for scientific interpretation of small-scale morphology, regolith roughness, and slope-controlled geological processes.

The LUMOS framework is constrained primarily by observational resolution rather than algorithmic limitations. While the present results are bounded by the resolution of available NAC data, the methodology directly benefits from higher-resolution, multi-angular observations. As such, LUMOS constitutes a cornerstone of the ESA Máni mission (Phase A), which aims to acquire dense multi-angular imagery at spatial resolutions of approximately 0.17–0.2 m/pixel. Applied to Máni data, LUMOS is expected to further enhance topographic fidelity, reflectance characterisation, and uncertainty-aware surface mapping.