Mahalanobis k-NN: A Statistical Lens for Robust Point-Cloud Registrations

TL;DR

This work tackles robust point-cloud registration under variable densities by introducing Mahalanobis k-NN as a statistical lens that builds surface-aware, covariance-informed neighborhoods. The method plugs into local-graph based registration pipelines, yielding two variants: MDCP and MDeepUME, and demonstrates state-of-the-art performance on ModelNet40, FAUST, and related benchmarks. It also shows that features learned for registration can be discriminative for few-shot classification, broadening the impact of registration-derived representations. The approach emphasizes surface structure and resilience to outliers and density imbalance, offering a practical, plug-and-play enhancement for learning-based 3D alignment.

Abstract

In this paper, we discuss Mahalanobis k-NN: A Statistical Lens designed to address the challenges of feature matching in learning-based point cloud registration when confronted with an arbitrary density of point clouds. We tackle this by adopting Mahalanobis k-NN's inherent property to capture the distribution of the local neighborhood and surficial geometry. Our method can be seamlessly integrated into any local-graph-based point cloud analysis method. In this paper, we focus on two distinct methodologies: Deep Closest Point (DCP) and Deep Universal Manifold Embedding (DeepUME). Our extensive benchmarking on the ModelNet40 and FAUST datasets highlights the efficacy of the proposed method in point cloud registration tasks. Moreover, we establish for the first time that the features acquired through point cloud registration inherently can possess discriminative capabilities. This is evident by a substantial improvement of about 20% in the average accuracy observed in the point cloud few-shot classification task, benchmarked on ModelNet40 and ScanObjectNN.

Figures (4)

• Figure 1: The visual supremacy of our proposed methodologies, MDCP-v1 and MDeepUME, becomes apparent in a point cloud registration, involving a target point cloud with only half the points compared to the source point cloud. In the visualization, regions highlighted in red illustrate the limited performance of DCP-v1DCP and DeepUMEDeepUME, while the regions highlighted in green demonstrate the resilience of the proposed Mahalanobis versions of DCP-v1DCP and DeepUMEDeepUME.
• Figure 2: Illustration highlights the distinction between the Red gradients representing Euclidean distance fields that capture spatial neighbors and the Blue gradients depicting Mahalanobis distance fields, which consider neighbors concerning the underlying data distribution. To further emphasize the point, we present the influence of both Euclidean and Mahalanobis k-NN on a chair point cloud. The black query point is surrounded by Euclidean neighbors shown in red points and Mahalanobis neighbors in blue points. The depiction clearly illustrates the impact of Mahalanobis distance, effectively capturing surficial points per the data distribution—vital for precise feature matching.
• Figure 3: Evaluation of Robustness for varied test cases. Both DCP-v1 DCP and proposed MDCP-v1 trained on ModelNet40 modelnet dataset. Our evaluation encompasses three distinct scenarios: 1) Evaluation on unseen data, specifically a man holding palms together from the FAUST FAUST dataset; 2) Assessment of low-density source point clouds, exemplified by an airplane; and 3) Examination of low-density target point clouds, illustrated by a chair. In our visual analysis, regions highlighted in red highlights the vulnerabilities observed in vanilla DCP-v1 DCP, while regions in green accentuate the pronounced efficacy demonstrated by the proposed MDCP-v1 over the conventional DCP-v1.
• Figure 4: We present a compelling demonstrations showcasing the surface awareness within the proposed MDCP-v1, in contrast to the Euclidean approach in DCP-v1DCP. Each row within the illustration corresponds to K values ranging from 2 to 5, effectively exemplifying the pronounced surficial awareness embodied by MDCP-v1. This surficial awareness is pivotal for robust point cloud registration tasks.