We present PROBE (PRobabilistic Occupancy BEV Encoding), a learning-free LiDAR place recognition descriptor that models each BEV cell's occupancy as a Bernoulli random variable. Rather than relying on discrete point-cloud perturbations, PROBE analytically marginalizes over continuous Cartesian translations via the polar Jacobian, yielding a distance-adaptive angular uncertainty σ_θ = σ_t / r in O(R·S) time. The primary parameter σ_t represents the expected translational uncertainty in meters, a sensor-independent physical quantity that enhances cross-sensor generalization while reducing the need for extensive per-dataset tuning. Pairwise similarity combines a Bernoulli-KL Jaccard with exponential uncertainty gating and FFT-based height cosine similarity for rotation alignment. Evaluated on four datasets spanning four diverse LiDAR types, PROBE achieves the highest accuracy among handcrafted descriptors in multi-session evaluation and competitive single-session performance relative to both handcrafted and supervised baselines.

Main Contributions:

1. Analytical Marginalization via Polar Jacobian: We replace computationally expensive discrete point-cloud perturbations with a closed-form probabilistic model. By applying a Jacobian-derived adaptive 1D spatial blur, we analytically marginalize continuous Cartesian translations into a single BEV grid in O(R·S) time, yielding a distance-adaptive angular uncertainty (σ_θ = σ_t / r) and eliminating the need for generating multiple virtual views.

2. Bernoulli-KL Jaccard with Uncertainty Gating: A pairwise scoring mechanism that smooths each cell's occupancy toward an uninformative prior proportionally to its uncertainty, computes symmetric KL divergence, and downweights high-σ cells via exponential gating. This replaces the standard binary Jaccard with a divergence measure that distinguishes stable structures from viewpoint-sensitive boundaries.

3. Cross-sensor generalization with a single physically-grounded parameter: The primary parameter σ_t represents the expected translational uncertainty in meters, a sensor-independent physical quantity that generalizes to unseen sensors and environments while reducing the need for extensive per-dataset tuning, as validated across 22 sequence configurations spanning four LiDAR types (KITTI, HeLiPR, NCLT, ComplexUrban).

@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}

}