Improving Lunar Topography with Deep Learning Schrödinger Bridges
Authors: Matthew Repasky, Erwan Mazarico, Michael K. Barker, Stefano Bertone, Terence J. Sabaka, Yao Xie
Abstract
Increasing the resolution of planetary topography models can enable a better understanding of surface processes and geomorphology; however, existing analytical super-resolution methods are expensive and difficult to apply at large scales. Generative models provide the tools to learn complex relationships within data and can be applied at scale due to hardware accelerators and parallelization. We present a diffusion-based Schrödinger Bridge (SB) generative modeling approach for lunar topography super-resolution, connecting the distribution of low-resolution topography to that of high-resolution topography, incorporating physically-constraining optical imagery. Our approach is inspired by existing Shape-from-Shading methods, which improve a priori low-resolution topography by using optical images at the target resolution. We train SBs on a novel dataset of rendered lunar topography, emulating optical imagery from the Lunar Reconnaissance Orbiter Narrow Angle Camera. The result is a flexible approach for topography super-resolution which can provide pixel-level uncertainties in the reconstruction.
This study presents a Shape from Shading (SfS) framework to enhance sub-metre resolution lunar digital elevation models (DEMs) using imagery from the Orbiter High Resolution Camera (OHRC) aboard Chandrayaan-2. The framework applies SfS to an independent OHRC image of the same region, enabling SfS not just as a refinement tool, but as a source of new topographic data, unconstrained by stereo baseline limitations. The method is applied across three lunar sites, including the Cyrillus crater, the Vikram landing region, and the lunar south pole (Mons Mouton), with a systematic three-stage parameter sweep on the SfS smoothness weight. Results show measurable topographic enhancement, particularly in surface slope statistics, revealing fine-scale crater morphology previously unresolved. A limiting case is also characterized, where large pitch angle separation between the shading image and stereo pair reduces SfS sensitivity, and partial footprint coverage of the shading image is identified as a factor influencing spatially variable enhancement quality.
High-resolution digital surface models (DSMs) play an important role in urban analysis, 3D building reconstruction, and infrastructure monitoring, yet their availability remains limited due to the high cost and complexity of data acquisition. In contrast, coarse DSMs from commercial satellite missions are widely accessible, and high-resolution optical imagery is increasingly available from aerial and satellite platforms. We address the resulting mismatch in spatial resolution and propose a DSM superresolution approach that enhances 5 m DSMs to 0.5 m resolution, using guidance from high-resolution spectral images. Our method employs denoising diffusion to transfer information that is visible only in the image, like crisp outlines and detailed roof structures, into the elevation maps. In this way, surface details are reconstructed more accurately than with conventional interpolation or filtering techniques. Experiments on several cities in Central Europe demonstrate that the proposed approach produces high-quality DSMs with improved structural detail and accurate surface geometry. Our results highlight the potential of guided super-resolution with foundational image priors as a means of reconstructing high-resolution surface models.
Armand Mihai Nicolicioiu, Dominik Narnhofer, Nando Metzger +3
Recent times have seen an increase in demand of high quality Digital Elevation Models (DEMs) for the lunar surface, because they are highly important for studying the moon and planning future missions. However, there is an evident lack of detailed elevation data on the Moon. To overcome this limitation, this study proposes a novel deep learning method that estimates and generates a surface elevation map directly from monocular images of the surface. The dataset used comprises of the Chandrayaan-2 Terrain Mapping Camera (TMC) images with their corresponding Digital Terrain Models (DTMs). The study proposes LunarDepthNet, which comprises of a UNet architecture to generate DEMS. It incorporates an EfficientNet encoder and custom layers to correctly learn how the light shadows on the surface relate to the actual elevation values. A combined loss function was also utilized to keep the terrain details accurate and smooth. During validation, the model showed a stable loss convergence of 12%. It achieved a mean nRMSE of 0.437 and an MAE of 4.5m in the testing stage. These results prove the model can generate dependable elevation maps from single orbital images, which are quite useful in regions of the moon where stereo-images are not available.