While event cameras offer immense potential for underwater SLAM, existing Time Surface (TS)-based methods prove highly unreliable when deployed underwater. Fluctuating camera velocities severely degrade TS imaging quality, while wide stereo baselines and repetitive underwater textures induce critical matching failures, frequently triggering system failure. To overcome these challenges, we develop the first high-accuracy event-based underwater stereo SLAM system. A structure-aware metric for TS is designed based on structure tensor coherence and gradients to quantitatively evaluate TS structural information density. By decoupling the optimal TS generation into two distinct stages based on system initialization, Bayesian Optimization(BO) first predicts an optimal prior TS sequentially before initialization while we set an asynchronous online local searching method periodically to obtain appropriate TS in real-time during the tracking stage. We use the prior disparity to guarantee precise data association and "latest-observation-first'' triangulation mechanism to realize stable triangulation. As a benchmark for these solutions and a resource for the community, we also contribute UWE, the first high-quality real-world underwater event dataset containing variable camera motions, complex textures and different trajectory features. Extensive evaluations on public datasets and UWE show the competitive accuracy performance of the proposed SLAM system compared to the state-of-the-art event-based method. The code and data will be open-sourced.

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