BathyFacto: Refraction-aware two-media Neural Radiance Fields for bathymetry

Abstract

Through-water photogrammetry based on 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 integrated into Nerfstudio that targets metrically consistent underwater point clouds on simulated data. BathyFacto uses a shared hash-grid-based density field with a medium-conditioned color head that receives a one-bit medium flag (air or water) and traces each camera ray as two segments: a straight segment in air up to a planar water surface and a refracted segment in water computed via Snell’s law with known refractive indices. To allocate samples efficiently across the air–water boundary, we employ a single proposal-network sampler that operates on a virtual straight ray spanning both media, combined with a kinked density wrapper that transparently corrects water-segment positions along the refracted direction before density evaluation. A data adaptation pipeline converts photogrammetric reconstructions to a Nerfstudio-compatible format, estimates the water plane from boundary markers, and provides per-pixel medium masks to gate refraction. We also extend the point cloud export with refraction-corrected backprojection and reversible coordinate transforms to world and global frames. On a simulated two-media scene with known ground truth, the refraction-aware BathyFacto achieves a Cloud-to-Mesh signed median deviation of −0.001 m and 85.7% completeness at 0.2 m tolerance, measured in the absolute global coordinate frame without any rigid-body alignment, compared to ＋1.370 m/11.6% for the single-medium Nerfacto baseline and ＋1.409 m/9.9% for BathyFacto without consideration of refraction. Even after a naive refractive-index depth correction, these baselines remain offset by ≈0.4 m. In contrast to a refraction-corrected Multi-View Stereo reference, which is reliable only for near-nadir viewing geometry, BathyFacto recovers consistent geometry across the full range of camera incidence angles.