B³-Seg: Camera-Free, Training-Free 3DGS Segmentation via Analytic EIG and Beta

Overview

Interactive 3DGS segmentation without predefined cameras or retraining.

B³-Seg overview with camera-free view selection and Bayesian updates.

Problem

Existing methods rely on preset viewpoints, ground-truth labels, or costly retraining, which slows low-latency editing workflows.

Idea

Treat segmentation as Bayesian inference over per-Gaussian foreground probabilities and choose the next view by expected information gain.

Result

Fast, adaptive segmentation that matches supervised baselines while using only a handful of views.

Method

Active view selection with analytic EIG and fast Bayesian updates for camera-free 3DGS segmentation.

Overview of the camera-free pipeline: sample candidate views, score EIG, select the best, infer masks, and update Beta posteriors.

01

Initialize Beta Priors

Assign a Beta distribution to each Gaussian’s foreground probability and estimate an initial mask.

02

Sample Candidate Views

Uniformly sample camera candidates around the estimated object center to evaluate informativeness.

03

Compute EIG

Render once per view to estimate responsibilities and score Expected Information Gain.

04

Select + Update

Pick the best view, run Grounding DINO + SAM2 + CLIP, then update Beta parameters.

Theoretical Foundations

Bayesian reformulation and analytic EIG with greedy view selection guarantees.

Bayesian Reformulation

Each Gaussian $g_i$ has a latent label $y_i \in \\{0,1\\}$, with a Beta prior over the foreground probability $p_i$:

$$p_i \sim \mathrm{Beta}(a_i, b_i), \quad y_i \sim \mathrm{Bernoulli}(p_i)$$

Given a view $v$ and mask $M(v)$, per-Gaussian evidence is the sum of visibility-weighted responsibilities inside or outside the mask:

$$e_{i,1}(v) = \sum_{(j,k) \in I(v)} \alpha_i T_i \mathbb{I}[M_{j,k}(v)=1], \; e_{i,0}(v)=\sum_{(j,k) \in I(v)} \alpha_i T_i \mathbb{I}[M_{j,k}(v)=0]$$

By conjugacy, the posterior update is closed-form:

$$\mathrm{Beta}(a_i,b_i) \rightarrow \mathrm{Beta}(a_i + e_{i,1}(v),\; b_i + e_{i,0}(v))$$

Analytic EIG + Greedy Guarantee

To avoid running SAM2 on all candidates, we approximate counts using the current mean $m_i = a_i/(a_i+b_i)$ and compute Expected Information Gain:

$$\mathrm{EIG}(v)= \sum_i \Big[ H(\mathrm{Beta}(a_i,b_i)) - H(\mathrm{Beta}(a_i+\tilde e_{i,1}(v),\; b_i+\tilde e_{i,0}(v))) \Big]$$

We select the next view greedily:

$$v^* = \arg\max_v \mathrm{EIG}(v)$$

EIG is adaptive monotone and submodular, giving a greedy $(1 - 1/e)$ approximation to the optimal view-selection policy.

Information gain visualization used to score candidate views without running SAM2.

Results

Competitive 3D segmentation with far fewer views.

Qualitative segmentation across diverse scenes.

EIG-selected views and segmentation evolution

EIG-selected view sequence (left to right: RGB, SAM2 mask, Beta mean map) across iterations.

Quantitative comparison on LERF-Mask dataset.

360° segmentation results.

Qualitative results on 3DOVS dataset.

Qualitative results on LERF-Mask dataset.

Downloads

Swap in final links when ready.

Paper (PDF)

Main paper

Supplementary

Appendix

BibTeX

Update with the final citation entry.

@misc{kamata2026b3segcamerafreetrainingfree3dgs,
      title={B$^3$-Seg: Camera-Free, Training-Free 3DGS Segmentation via Analytic EIG and Beta-Bernoulli Bayesian Updates}, 
      author={Hiromichi Kamata and Samuel Arthur Munro and Fuminori Homma},
      year={2026},
      eprint={2602.17134},
      archivePrefix={arXiv},
      primaryClass={cs.CV},
      url={https://arxiv.org/abs/2602.17134}, 
}

B3-Seg Camera-Free, Training-Free 3DGS Segmentation via Analytic EIG and Beta–Bernoulli Bayesian Updates