# FACT: Multinomial Misalignment Classification for Point Cloud Registration

arXiv: https://arxiv.org/abs/2504.06627 · HTML: https://mlsanity.com/paper/2504.06627/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 9 Apr 2025.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion](https://mlsanity.com/paper/2111.12702/) (2021)
- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [Efficient Continuous-Time SLAM for 3D Lidar-Based Online Mapping](https://mlsanity.com/paper/1810.06802/) (2018)
- [CorAl -- Are the point clouds Correctly Aligned?](https://mlsanity.com/paper/2109.09820/) (2021)
- [Using proper divergence functions to evaluate climate models](https://mlsanity.com/paper/1301.5927/) (2013)
- [Hinge-Wasserstein: Estimating Multimodal Aleatoric Uncertainty in Regression Tasks](https://mlsanity.com/paper/2306.00560/) (2023)
- [Empir3D : A Framework for Multi-Dimensional Point Cloud Assessment](https://mlsanity.com/paper/2306.03660/) (2023)

## Built on by (most cited first, 1 of 1)

- [MATTER: Multiscale Attention for Registration Error Regression](https://mlsanity.com/paper/2509.12924/) (2025)

## Abstract (arXiv)

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.