TUGS: Physics-based Compact Representation of Underwater Scenes by Tensorized Gaussian

TL;DR

This work addresses the challenge of underwater 3D reconstruction by integrating a physics-based underwater image formation model with a compact, tensorized Gaussian representation. The proposed Tensorized Underwater Gaussian Splatting (TUGS) leverages CP tensor decomposition to represent both scene geometry and the water medium through tensorized Gaussians, coupled with an Adaptive Medium Estimation (AME) module to simulate attenuation and backscatter during rendering. Key contributions include (i) a parameter-efficient representation that reduces the typical 3DGS parameter load by roughly 60–85%, (ii) an AME-based rendering pipeline that explicitly models water effects without extra Gaussian primitives, (iii) a tensorized densification strategy and a dedicated underwater loss to improve reconstruction accuracy under constrained resources, and (iv) extensive experiments showing TUGS achieves higher rendering speeds (106 FPS) and substantially lower memory usage (21 MB) than SeaThru-NeRF (383 MB) while maintaining or improving reconstruction quality. The approach enables memory-efficient, high-fidelity underwater scene reconstruction, with practical impact for resource-limited underwater robotics and UAVs.

Abstract

Underwater 3D scene reconstruction is crucial for undewater robotic perception and navigation. However, the task is significantly challenged by the complex interplay between light propagation, water medium, and object surfaces, with existing methods unable to model their interactions accurately. Additionally, expensive training and rendering costs limit their practical application in underwater robotic systems. Therefore, we propose Tensorized Underwater Gaussian Splatting (TUGS), which can effectively solve the modeling challenges of the complex interactions between object geometries and water media while achieving significant parameter reduction. TUGS employs lightweight tensorized higher-order Gaussians with a physics-based underwater Adaptive Medium Estimation (AME) module, enabling accurate simulation of both light attenuation and backscatter effects in underwater environments. Compared to other NeRF-based and GS-based methods designed for underwater, TUGS is able to render high-quality underwater images with faster rendering speeds and less memory usage. Extensive experiments on real-world underwater datasets have demonstrated that TUGS can efficiently achieve superior reconstruction quality using a limited number of parameters, making it particularly suitable for memory-constrained underwater UAV applications

Figures (5)

• Figure 1: SeaThru-NeRF SeaThruNeRF_2023_CVPR, 3DGS 3DGS_2023_TOG, and the proposed method TUGS are trained on the Curaçao scene of SeaThru-NeRF dataset. It can be seen that our model achieves the best PNSR with a size of only 21 MB.
• Figure 2: TUGS models the underwater object and the water medium by using different mode-1 slices of a high-order tensorized Gaussian $\mathcal{G}$, and simultaneously represents them using the mode factors $[\mathbf{U}^1 \text{, }\mathbf{U}^2 \text{, }\mathbf{U}^3]$, reducing the parameter count by approximately 60-85% compared to 3DGS 3DGS_2023_TOG (in \ref{['sub:TensorizedGaussians']}). When synthesizing images, TUGS renders the medium Gaussian as a light attenuation and backscatter image through the Adaptive Medium Estimation (AME) model and blends it with the restoration image from the object Gaussian through the underwater image formation model for the final output (in \ref{['sub:AdaptiveMediumEstimation']}). CP is the CP decomposition CP_C_1970CP_P_1970 and TDS stand for Tensorized Densification Strategies in \ref{['sub:tds']}.
• Figure 3: Novel view rendering comparisons in SeaThru-NeRF dataset SeaThruNeRF_2023_CVPR. We adjusted the image brightness of two highlighted regions in row 4 and the green highlighted region in row 6 with the same settings for more visual comparisons of the different methods.
• Figure 4: Synthesizing novel views in a foggy environment.
• Figure 5: Novel view synthesis without water media in the SeaThru NeRF dataset SeaThruNeRF_2023_CVPR. TUGS restores the underlying colors of the scene more vividly and foreground details are clearer.