Calibrated and Efficient Sampling-Free Confidence Estimation for LiDAR Scene Semantic Segmentation

TL;DR

The paper tackles the need for well-calibrated, reliable confidence estimates in LiDAR-based 3D semantic segmentation for safety-critical autonomous systems. It introduces a sampling-free method that models per-class logits as Gaussians and defines confidence as $P(X_1 \geq \max_{i\geq 2} X_i)$, deriving a closed-form lower bound $\prod_{i=2}^C \Phi_{1i}$ to quantify confidence without Monte Carlo sampling. Empirical results on SemanticKITTI and nuScenes with SalsaNext and RangeViT show the approach achieves accurate calibration (ACE substantially lower than MCP and temperature scaling) and produces underconfident predictions that favor safety. The method delivers significant inference-time speedups over sampling-based approaches (about 15–18× faster) with modest computational overhead, and its calibration improves further when combined with epistemic uncertainty models like deep ensembles or MC dropout. These findings support practical deployment of calibrated, uncertainty-aware LiDAR perception for real-time autonomous driving, with robust performance across architectures and datasets.

Abstract

Reliable deep learning models require not only accurate predictions but also well-calibrated confidence estimates to ensure dependable uncertainty estimation. This is crucial in safety-critical applications like autonomous driving, which depend on rapid and precise semantic segmentation of LiDAR point clouds for real-time 3D scene understanding. In this work, we introduce a sampling-free approach for estimating well-calibrated confidence values for classification tasks, achieving alignment with true classification accuracy and significantly reducing inference time compared to sampling-based methods. Our evaluation using the Adaptive Calibration Error (ACE) metric for LiDAR semantic segmentation shows that our approach maintains well-calibrated confidence values while achieving increased processing speed compared to a sampling baseline. Additionally, reliability diagrams reveal that our method produces underconfidence rather than overconfident predictions, an advantage for safety-critical applications. Our sampling-free approach offers well-calibrated and time-efficient predictions for LiDAR scene semantic segmentation.

Figures (7)

• Figure 1: Comparison of confidence estimation methods: (a) Scatter plot shows minimal difference between exact and sampling-free confidences; (b) Reliability diagram indicates our method produces slightly underconfident predictions compared to baselines.
• Figure 2: Reliability diagrams comparing calibration of our method against temperature scaling (TS) and uncalibrated (MCP) models on SemanticKITTI validation set using SalsaNext and RangeViT. Our method shows better calibration (closer to perfect calibration).
• Figure 3: Qualitative comparison of uncertainty maps from the logit-sampling baseline and our sampling-free method (a-d). Both align with misclassifications, but our method shows higher uncertainty in error-prone regions, reflecting more underconfident estimation. Uncertainty maps are compared to those from temperature scaling and an uncalibrated model (e-h), which has not detected those misclassifications as high-uncertainty regions. outlier,car,road,sidewalk,building,fence,vegetation,trunk,terrain,pole,traffic-sign.
• Figure 4: Illustration for three classes $X\sim \mathcal{N}(\mu_a=4, \sigma_a^2=1)$, $Y\sim \mathcal{N}(\mu_b=1, \sigma_b^2=1)$, and $Z\sim \mathcal{N}(\mu_c=-1, \sigma_c^2=4^2)$. As $\mu_a > \mu_b, \mu_c$, class A (rightmost peak) will be the predicted class. The pairwise confidences are $P(X>Y)=0.9831$ and $P(X>Z)=0.8874$ (so although $\mu_c<\mu_b$, it is more likely to confuse A with C than A with B, due to the large $\sigma_c$). The lower bound is $P(X>Y)\cdot P(X>Z)=0.8723$, whereas the exact value is $P(X>Y, Z)=0.8740 \geq 0.8723$, as expected.
• Figure 5: Example of significant uncertainty arising from the confusion between the sidewalk and the street. The misclassified region (dashed red box) is labeled as a sidewalk in the ground truth but is also traversed by vehicles, causing overlapping classifications of street and sidewalk, which results in high uncertainty. Classes are represented with corresponding colors: outlier,parking,car,road,sidewalk,building,fence,vegetation,trunk,terrain,pole,traffic-sign.