Multi-class extension of B^3-Seg via a Dirichlet–Categorical model

Develop a Dirichlet–Categorical extension of the B^3-Seg framework to enable multi-class (multi-object) segmentation in 3D Gaussian Splatting scenes, integrating Dirichlet–Categorical updates into the analytic Expected Information Gain-driven active view selection pipeline under camera-free and training-free conditions.

Background

B^3-Seg formulates open-vocabulary 3DGS segmentation as sequential Beta–Bernoulli Bayesian updates with analytic Expected Information Gain (EIG) for active view selection. The method currently addresses binary foreground–background decisions, achieving few-second, camera-free, training-free performance with theoretical guarantees.

The authors indicate that many real-world applications involve multiple objects or semantic categories and note that the Bayesian framework naturally generalizes from Beta–Bernoulli to Dirichlet–Categorical. They explicitly state that this generalization and integration into the current EIG-based pipeline are left for future work.