Interactive 3D Gaussian Splatting (3DGS) segmentation is essential for real-time editing of pre-reconstructed assets in film and game production. However, existing methods rely on predefined camera viewpoints, ground-truth labels, or costly retraining, making them impractical for low-latency use. We propose B$^3$-Seg (Beta-Bernoulli Bayesian Segmentation for 3DGS), a fast and theoretically grounded method for open-vocabulary 3DGS segmentation under camera-free and training-free conditions. Our approach reformulates segmentation as sequential Beta-Bernoulli Bayesian updates and actively selects the next view via analytic Expected Information Gain (EIG). This Bayesian formulation guarantees the adaptive monotonicity and submodularity of EIG, which produces a greedy $(1{-}1/e)$ approximation to the optimal view sampling policy. Experiments on multiple datasets show that B$^3$-Seg achieves competitive results to high-cost supervised methods while operating end-to-end segmentation within a few seconds. The results demonstrate that B$^3$-Seg enables practical, interactive 3DGS segmentation with provable information efficiency.

翻译：交互式3D高斯溅射（3DGS）分割对于电影和游戏制作中预重建资源的实时编辑至关重要。然而，现有方法依赖于预定义的相机视角、真实标注标签或代价高昂的重新训练，使其难以适用于低延迟场景。我们提出B$^3$-Seg（面向3DGS的Beta-Bernoulli贝叶斯分割），这是一种在免相机、免训练条件下实现开放词汇3DGS分割的快速且理论完备的方法。我们的方法将分割重新表述为顺序Beta-Bernoulli贝叶斯更新过程，并通过解析期望信息增益（EIG）主动选择下一视角。该贝叶斯框架保证了EIG的自适应单调性和子模性，从而产生对最优视角采样策略的贪心$(1{-}1/e)$近似。在多个数据集上的实验表明，B$^3$-Seg在实现端到端分割仅需数秒的同时，达到了与高成本监督方法相竞争的结果。实验证明B$^3$-Seg能够以可证明的信息效率实现实用、交互式的3DGS分割。