JEVIS

Joint Entropy Estimation in 3DGS via Visibility Field
for Active Mapping

Dhruv Ahuja* Shangjie Xue*† Jesse Dill Panagiotis Tsiotras Frank Dellaert Danfei Xu

Georgia Institute of Technology

*Equal Contribution   †Project Lead

TL;DR

JEVIS is a principled framework for quantifying the expected information gain of multiple planned views in 3DGS through joint entropy estimation that accounts for cross-view dependencies, enabling long-horizon and multi-agent active mapping.

Abstract

Active mapping requires planning observations that maximally reduce uncertainty about an unknown scene. Recent methods have substantially improved uncertainty quantification in 3D Gaussian Splatting (3DGS) by explicitly modeling visibility, assigning higher uncertainty to unobserved regions. However, these methods estimate the entropy of a single image observation and therefore primarily support myopic next-best-view selection. Practical deployments instead require estimating the joint entropy of multiple observations, such as views along a long-horizon trajectory or viewpoints assigned across a team of robots. In these settings, different views can observe common unseen regions of the scene, and the correlation between their observations is not negligible. To this end, we present Joint Entropy estimation in 3DGS via VISibility field (JEVIS), a theoretically grounded framework for quantifying the expected information gain of multiple planned observations in 3DGS through joint entropy estimation. By leveraging a maximum-likelihood observation (MLO) approximation, JEVIS efficiently estimates joint entropy across multiple views. We evaluate JEVIS in long-horizon single-agent and multi-agent active mapping across diverse indoor and space-robotics environments. Results show that JEVIS more accurately captures joint uncertainty and produces higher-fidelity reconstructions than existing methods.

Contributions

  1. We estimate the joint entropy of planned 3DGS observations to guide long-horizon active mapping.
  2. We extend the formulation to multi-robot planning, offering, to our knowledge, the first information-theoretic approach to long-horizon multi-agent active mapping with radiance fields.
  3. Across indoor and space environments, JEVIS improves reconstruction quality over baselines in single- and multi-agent settings.

Method

Active mapping step: from the scene and the current 3DGS with its training views, JEVIS scores candidate paths using the uncertainty maps and synthesized views of their planned views; the agent executes the path with the highest joint entropy as the next best trajectory.
JEVIS scores candidate trajectories by their estimated joint observation entropy. The agent executes the highest-scoring trajectory and updates the 3DGS reconstruction with the acquired observations.
Candidate trajectory scoring (JEVIS): a visibility field built from the 3DGS and training views is used to evaluate each planned view of the candidate trajectory in turn (UAR), the visibility field is updated after each view, and the per-view entropies are summed into the trajectory's joint entropy.
JEVIS builds a visibility field (VF) from the trained 3DGS model and training poses. For each candidate trajectory, uncertainty aware rasterization (UAR) estimates each view’s entropy, while UpdateVF incorporates preceding planned poses into the VF before subsequent views are scored. These updates discount uncertainty shared across views. Summing the resulting conditional entropies estimates the trajectory’s joint entropy. Trajectories can be of arbitrary length.

Results

Entropy Estimation Qualitative Results

The candidate trajectory extends from observed into unseen regions, with substantial overlap between planned views. JEVIS sums each view’s entropy conditioned on preceding views to obtain the trajectory’s joint entropy, discounting previously covered regions. GAVIS scores views independently and double-counts overlap. JEVIS’s uncertainty maps more closely match ground-truth visibility.
The candidate trajectory circles the spacecraft and revisits an earlier viewpoint. JEVIS sums each view’s entropy conditioned on preceding views to obtain the trajectory’s joint entropy, discounting the revisited region. GAVIS scores views independently and double-counts overlap. JEVIS’s uncertainty maps more closely match ground-truth visibility.

Active Mapping Qualitative Results

JEVIS explores new regions along its trajectory, while the baselines repeatedly observe previously seen areas.
JEVIS agents explore complementary regions in parallel, whereas baseline agents follow largely overlapping trajectories.

Multi-Agent Active Mapping Quantitative Results

Metrics span view synthesis quality (PSNR, SSIM, LPIPS), mesh reconstruction quality (CR: completion ratio), visibility area (VIS), and uncertainty quantification time (TUQ: ms). Multi-agent runs use 3 agents and half as many planning steps as single-agent runs. All axes are normalized so that farther from the center is better.

BibTeX

@article{ahuja2026jevis,
  title     = {JEVIS: Joint Entropy Estimation in 3DGS via Visibility Field for Active Mapping},
  author    = {Ahuja, Dhruv and Xue, Shangjie and Dill, Jesse and Tsiotras, Panagiotis and Dellaert, Frank and Xu, Danfei},
  journal   = {arXiv preprint arXiv:xxxx.xxxxx},
  year      = {2026}
}

@inproceedings{xue2026gavis,
  title     = {Uncertainty-driven 3D Gaussian Splatting Active Mapping via Anisotropic Visibility Field},
  author    = {Xue, Shangjie and Dill, Jesse and Ahuja, Dhruv and Dellaert, Frank and Tsiotras, Panagiotis and Xu, Danfei},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
  year      = {2026}
}

@inproceedings{xue2024nvf,
  title     = {Neural Visibility Field for Uncertainty-Driven Active Mapping},
  author    = {Xue, Shangjie and Dill, Jesse and Mathur, Pranay and Dellaert, Frank and Tsiotras, Panagiotis and Xu, Danfei},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
  pages     = {18122--18132},
  year      = {2024}
}