Lambertian-TRF: Lambertian Tensorial Radiance Fields for Underwater 3-D Reconstruction Using Imaging Sonar
Haowen Gao, Binyu Nie, Wenjie Lu, Yunxuan Feng, Manman Hu · IEEE Transactions on Instrumentation and Measurement · 2025
In this paper, we propose Lambertian Tensor Radiance Field Lambertian-TRF, a novel approach for fast dense 3D reconstruction of underwater objects using multibeam imaging sonar. Due to the sonar’s large vertical aperture, the intensity of each pixel is determined by the volumetric occupancy within a fan-shaped area, while the pixel of visual images is determined by the occupancy along a segment. Therefore, existing Neural Radiance Field (NeRF) methods often require hours to reconstruct underwater scenes using sonar images. To address this challenge, we leverage Lambert’s cosine law in the rendering model by utilizing iso-density surfaces. The novel rendering model significantly reduces the complexities of the volumetric density and intensity models employed in NeRF methods. Additionally, we replace multi-layer perceptrons with Tensor Radiance Fields (TRFs) to model volumetric density and intensity, represented as two distinct sets of vectors based on CANDECOMP/PARAFAC (CP) decomposition. To further enhance reconstruction efficiency, we introduce a space carving loss function, alongside the conventional rendering and smoothness losses, which accelerates convergence. Extensive experiments have been conducted on numerical simulations and the datasets collected from a laboratory tank. The results demonstrate that Lambertian-TRF is over 10 times faster than the existing approach Neusis, producing reconstructions of comparable quality.