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

TL;DR

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 against both handcrafted and supervised baselines.

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 $σ_θ= σ_t / r$ in $\mathcal{O}(R \times S)$ time. The primary parameter $σ_t$ represents the expected translational uncertainty in meters, a sensor-independent physical quantity allowing cross-sensor generalization without 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 against both handcrafted and supervised baselines. The source code and supplementary materials are available at https://sites.google.com/view/probe-pr.

Figures (6)

• Figure 1: PROBE encodes a LiDAR point cloud (top-left) into a probabilistic polar BEV grid. The binary occupancy mask $\bm{O}$ (top-right), Bernoulli mean $\mu$ (bottom-left), and per-cell uncertainty $\sigma$ (bottom-right) are computed via Jacobian-derived analytical marginalization. High-$\sigma$ boundary cells are automatically downweighted during matching.
• Figure 2: PROBE pipeline. (I) Descriptor generation: a BEV polar grid $\bm{G}$ is built with max-height encoding and occupancy mask $\bm{O}$. Analytical marginalization via the polar Jacobian produces per-cell Bernoulli occupancy $(\mu,\sigma)$. A rotation-invariant ring-mean key $\bm{k}\in\mathbb{R}^{2R}$ is formed for KD-tree pre-filtering. (II) Pairwise scoring: FFT-based rotation alignment on the max-height grids yields $\delta^*$; the query is circularly shifted to produce an aligned query, which is scored against the map via a shrinkage-regularized Bernoulli-KL Jaccard $\mathcal{J}_{KL}$. The final score fuses $\mathcal{J}_{KL}$ with the height cosine similarity $\mathcal{C}=\mathrm{CC}[\delta^*]$ multiplicatively: $S_{\text{PROBE}} = \mathcal{J}_{KL} \cdot \mathcal{C}$.
• Figure 3: Translation robustness: similarity under increasing lateral translation on KITTI-08 (averaged over 7 frames and 3 translation directions). SC (no augmentation) degrades fastest; SC++ mitigates this via discrete augmentation, producing a characteristic plateau. The Bernoulli-KL Jaccard $\mathcal{J}_{KL}$ is shown at three blur levels: without blur ($\sigma_t{=}0$, dashed), $\sigma_t{=}2$ m (proposed), and $\sigma_t{=}4$ m. Analytical marginalization transforms a brittle binary descriptor into a smoothly robust one.
• Figure 4: Average AUC over all single- and multi-session sequence pairs. Solid bars: single-session (16 sequences); hatched bars: multi-session (6 pairs).
• Figure 5: Single-session Precision-Recall curves (one representative sequence per dataset).