BathyFacto: Refraction-Aware Two-Media Neural Radiance Fields for Bathymetry
Authors: Markus Brezovsky, Anatol Günthner, Frederik Schulte, Lukas Winiwarter, Boris Jutzi, Gottfried Mandlburger
Organizations: Department of Geodesy and Geoinformation, TU Wien, Vienna, Austria · Institute of Photogrammetry and Remote Sensing (IPF), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany · Unit of Geometry and Surveying, University of Innsbruck, Innsbruck, Austria
Abstract
Through-water photogrammetry from UAV imagery enables shallow-water bathymetry, but refraction at the air--water interface violates the straight-ray assumption of Structure-from-Motion and causes systematic depth bias. We present BathyFacto, a refraction-aware two-media extension of Nerfacto in Nerfstudio for metrically consistent underwater point clouds on simulated data. BathyFacto uses a shared hash-grid density field with a medium-conditioned color head and traces each camera ray as two segments: a straight air segment to a planar water surface and a refracted water segment computed using Snell's law and known refractive indices. A single proposal-network sampler operates on a virtual straight ray, while a kinked density wrapper corrects water-segment positions before density evaluation. Our pipeline converts photogrammetric reconstructions to Nerfstudio format, estimates the water plane from boundary markers, provides per-pixel medium masks, and supports refraction-corrected point-cloud export with reversible transforms to world and global frames. On a simulated scene with ground truth, BathyFacto achieves a Cloud-to-Mesh signed median deviation of −0.001,m and 85.7,% completeness at 0.2,m tolerance in the absolute global frame without rigid-body alignment. This compares with +1.370,m / 11.6,% for Nerfacto and +1.409,m / 9.9,% for BathyFacto without refraction. Even after a naive refractive-index depth correction, both baselines remain offset by approximately 0.4,m. Unlike a refraction-corrected Multi-View Stereo reference, which is reliable mainly for near-nadir views, BathyFacto recovers consistent geometry across the full range of camera incidence angles.
We propose Swimm3R, a unified framework that combines medium-aware structure-from-motion (SfM) with Underwater Beta Splatting to address scattering- and attenuation-induced failures in underwater 3D reconstruction. Swimm3R distills in-air geometric priors into a feed-forward backbone and uses a physics head to regress underwater image-formation parameters, camera poses, and restored point clouds. Additionally, we introduce Underwater Beta Splatting, which extends Gaussian splatting with Beta primitives and scattering-aware geometric gradients for stable underwater geometry representation. We further establish the Barbados underwater video dataset to demonstrate the effectiveness of our method in challenging underwater environments. On this dataset, Swimm3R robustly recovers underwater scene structure under challenging scattering conditions, yielding coherent seafloor geometry. Using these predicted point clouds, the proposed Underwater Beta Splatting improves average PSNR by 1.47 dB over WaterSplatting while increasing downstream localization performance by 2.0 and 2.4 percentage points in RRA@15 and RTA@15, respectively.
Underwater scene reconstruction is essential for immersive exploration of aquatic environments, yet remains challenging due to complex participating-media effects such as absorption and scattering, as well as the limited field of view (FoV) of conventional cameras. Although combining panoramic imaging with 3D Gaussian Splatting (3DGS) offers a promising direction for photorealistic underwater rendering, traditional 3DGS struggles with both spherical projection distortion and underwater medium degradation. In this paper, we propose \textbf{Underwater360}, a physics-informed omnidirectional 3DGS framework for underwater panoramic scene reconstruction. First, we introduce an Omnidirectional Gaussian Splatting module that performs ray casting directly in spherical camera space instead of relying on 2D projection approximations, thereby reducing geometric distortions under 360∘ FoV. Second, we design a physics-based appearance-medium modeling architecture with pose-conditioned appearance embeddings to explicitly decouple intrinsic scene radiance from depth-dependent backscatter and attenuation, enabling physically grounded scene appearance restoration. Finally, we establish a new panoramic underwater benchmark dataset containing both synthetic and real-world scenes. Extensive experiments demonstrate that Underwater360 achieves superior performance in underwater novel view synthesis and scene appearance restoration, delivering improved rendering quality and cross-view consistency in complex underwater environments. The code and datasets are released at https://github.com/SwcK423/Underwater360
Sonar is often the only modality suitable for high-resolution imaging underwater due to light attenuation and turbidity. Forward-looking imaging sonar provides measurements over range and horizontal angle but collapses vertical structure into a flat image, creating ambiguities that make 3D recovery challenging. A common use case for imaging sonar is underwater terrain mapping (bathymetry), yet current methods require many views, expensive multi-sensor setups, or significant training data, which limits use and adaptability to new environments. We present a training-free method that recovers bathymetry from a single sonar image in under 30 seconds via differentiable rendering, conditioned on a known seafloor tilt. To our knowledge, this is the first differentiable rendering approach for single-view height recovery in sonar. Our method implements differentiable sonar ray tracing and optimizes an explicit height field to reproduce the target image. On synthetic datasets, our approach outperforms a supervised CNN under distribution shift and remains close on rough terrain, while the CNN wins in-distribution. By modeling physically grounded priors of the sonar process, our method adapts across sensor configurations and environments without training data.