PROBE: Probabilistic Occupancy BEV Encoding with Analytical Translation Robustness for 3D Place Recognition

Abstract

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 $\ddot{I}{ƒ}_{\hat{I}}¸=\ddot{I}{ƒ}_t/r$ in $\mathcal{O}(R\cdot S)$ time. The primary parameter $\ddot{I}{ƒ}_t$ 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. The source code and supplementary materials are available at https://sites.google.com/view/probe-pr.

8 pages, 8 figures. Accepted for publication in IEEE Robotics and Automation Letters (RA-L). (c) 2026 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses