FACT: Multinomial Misalignment Classification for Point Cloud Registration

TL;DR

FACT addresses the problem of assessing the quality of registered lidar point clouds (PC misalignment) by predicting a multinomial misalignment class, enabling finer quality assessment and uncertainty estimation. It combines local geometric features, Sinkhorn divergence from optimal transport, and co-visibility cues within a Point Transformer backbone, trained with a regression-by-classification loss that blends cross-entropy and Wasserstein terms $\mathcal{L}(y,p)=\tfrac{1}{2}\mathcal{L}_{CE}(y,p)+\tfrac{1}{2}\mathcal{L}_{W^1}(y,p)$. The method is validated on synthetic CorAl-style perturbations and on real registrations from nuScenes (ICP) and KITTI (GeoTransformer), outperforming the CorAl baseline and standard metrics in predicting misalignment and enabling practical map correction. This multinomial, uncertainty-aware output supports targeted re-registration and self-supervised learning in large-scale 3D mapping pipelines. The authors also release code for replication.

Abstract

We present FACT, a method for predicting alignment quality (i.e., registration error) of registered lidar point cloud pairs. This is useful e.g. for quality assurance of large, automatically registered 3D models. FACT extracts local features from a registered pair and processes them with a point transformer-based network to predict a misalignment class. We generalize prior work that study binary alignment classification of registration errors, by recasting it as multinomial misalignment classification. To achieve this, we introduce a custom regression-by-classification loss function that combines the cross-entropy and Wasserstein losses, and demonstrate that it outperforms both direct regression and prior binary classification. FACT successfully classifies point-cloud pairs registered with both the classical ICP and GeoTransformer, while other choices, such as standard point-cloud-quality metrics and registration residuals are shown to be poor choices for predicting misalignment. On a synthetically perturbed point-cloud task introduced by the CorAl method, we show that FACT achieves substantially better performance than CorAl. Finally, we demonstrate how FACT can assist experts in correcting misaligned point-cloud maps. Our code is available at https://github.com/LudvigDillen/FACT_for_PCMC.

Figures (11)

• Figure 1: Two examples of point clouds registrations from nuScenes nuscenes. Left: a correctly aligned pair; right: a misaligned pair (see red box). FACT easily finds the error class of the synthetically perturbed pairs. This paper proposes a method for predicting the quality (registration error) of a given point cloud alignment, both for synthetic errors, as shown here, and real registered point clouds pairs.
• Figure 2: Method overview: A pair of registered point clouds are passed through preprocessing, feature extraction, and then a classifier that predicts the misalignment class. Key aspects of the corresponding modules are provided below the boxes. The image below the preprocessing box shows three points and their spherically flipped counterparts.
• Figure 3: Regression-by-classification
• Figure 4: Regression
• Figure 6: Chamfer distance, Hausdorff distance, and Sinkhorn divergence vs. the registration error ($\epsilon$) for 850 nuScenes point cloud pairs registered with ICP-p2l.