PROBE: Probabilistic Occupancy BEV Encoding

Official Python Implementation of PROBE

Paper arXiv Website

PROBE: Probabilistic Occupancy BEV Encoding with Analytical Translation Robustness for 3D Place Recognition
Jinseop Lee, Byoungho Lee, Gichul Yoo
IEEE Robotics and Automation Letters (RA-L), 2026
DOI: 10.1109/LRA.2026.3703245

PROBE is a lightweight, learning-free probabilistic descriptor for LiDAR place recognition. It models each Bird's-Eye-View (BEV) cell's occupancy as a Bernoulli random variable.

By analytically marginalizing over continuous Cartesian translations via the polar Jacobian, PROBE replaces standard heuristic spatial sampling with a closed-form probabilistic model. This yields a single deterministic descriptor with a per-cell distance-adaptive angular uncertainty $\sigma_\theta$. The framework is computationally efficient ($O(R \times S)$ time) and generalizes to unseen, heterogeneous sensor platforms via a single, physically-motivated parameter ($\sigma_t$).

PROBE Pipeline

1. Analytical Marginalization via Polar Jacobian: Computes continuous translation marginalization directly in the polar distribution domain instead of augmenting views.
2. Robust Bernoulli-KL Jaccard Scoring ($\mathcal{J}_{KL}$): Replaces standard binary Jaccard matching with a shrinkage mechanism that downweights viewpoint-sensitive boundary cells according to their local uncertainty $\sigma$.
3. Sensor Generalization without Tuning: We use the translation uncertainty parameter $\sigma_t = 2.0$ m. Derived from the physical translation model, this single parameter applies unchanged across diverse sensors (Ouster OS2-128, Velodyne HDL-64 / HDL-32 / VLP-16) and platforms without per-dataset hyperparameter tuning.

The full pipeline (mirrored in probe/probe.py, with paper cross-references) proceeds in six steps:

1. BEV polar grid construction — max-height encoding into an $R \times S$ grid (Sec. III-A).
2. Jacobian-derived adaptive blur — marginalize continuous translations into per-cell Bernoulli occupancy $(\mu, \sigma)$ (Sec. III-B):
   • Angular blur $\sigma_\theta = \sigma_t / (r \cdot \Delta\theta)$, distance-adaptive (Eq. 5)
   • Radial blur $\sigma_r = \sigma_t / \Delta r$, uniform (Eq. 6)
3. Ring-mean retrieval key — rotation-invariant key $\mathbf{k} = [\bar{\mathbf{G}} ,|, \bar{\boldsymbol{\mu}}]$ for KD-tree pre-filtering (Sec. III-C, Eq. 9).
4. FFT rotation alignment — height cross-correlation yields the heading $\delta^*$ (Sec. III-D.1) and cosine similarity $\mathcal{C}$ (Sec. III-D.3).
5. Bernoulli-KL Jaccard — shrinkage-regularized symmetric KL over the soft union gives $\mathcal{J}_{KL}$ (Sec. III-D.2).
6. Evidence fusion — the PROBE similarity is $S = \mathcal{J}_{KL} \cdot \mathcal{C}, \quad d = 1 - S$ (Eq. 16).

Online place recognition with PROBE — query scans matched against a prior map.

Requirements:

• Python 3.8+
• numpy
• scipy

pip install -r requirements.txt

Or install the package (recommended, enables the from probe import ... import anywhere):

pip install -e .

The descriptor generation is fully isolated inside PROBENode within probe/probe.py. A runnable version of the snippet below is available at examples/demo.py. For the full place-recognition pipeline (KD-tree pre-filter over the retrieval keys, followed by full-score re-ranking, as in the paper), see examples/retrieval_demo.py.

import numpy as np
from probe import PROBENode, compute_score
# 1. Load an N x 3 (or N x 4) point cloud frame
# (Example dummy point cloud data representing two sequential frames)
pc_map = np.random.rand(100000, 3) * 50.0
pc_query = pc_map + np.array([0.5, 0.2, 0.0]) # slight translation
# 2. Extract PROBE Descriptors
# (Generates Expected Occupancy Probability mu, Uncertainty sigma, and Height Grid)
# sigma_t sets the translation uncertainty threshold (Default: 2.0m)
node_m = PROBENode(pc_map, sigma_t=2.0)
node_q = PROBENode(pc_query, sigma_t=2.0)
# 3. Compute Similarity Distance for Place Recognition (0 = Exact Match, 1 = Max Distance)
distance = compute_score(node_m, node_q)
print(f"PROBE Distance: {distance:.4f}")

PROBE-descriptor/
├── probe/
│ ├── __init__.py # Public API (PROBENode, compute_score)
│ └── probe.py # Core PROBENode class and scoring algorithms
├── examples/
│ ├── demo.py # Minimal pairwise scoring example
│ └── retrieval_demo.py # Full retrieval: KD-tree pre-filter + re-ranking
├── assets/ # Hero figure and demo GIFs
├── pyproject.toml
├── requirements.txt
├── LICENSE
└── README.md

If you use PROBE in your research, please cite our paper:

@article{lee2026probe,
 title={PROBE: Probabilistic Occupancy BEV Encoding with Analytical Translation Robustness for 3D Place Recognition},
 author={Lee, Jinseop and Lee, Byoungho and Yoo, Gichul},
 journal={IEEE Robotics and Automation Letters},
 pages={1--8},
 year={2026},
 publisher={IEEE},
 doi={10.1109/LRA.2026.3703245}
}

Released under the BSD 3-Clause License. © 2026 Jinseop Lee.