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

TL;DR

This paper introduces Mahalanobis k-NN as a statistical approach to improve feature matching in point cloud registration, demonstrating enhanced accuracy and discriminative features in classification tasks.

Contribution

It presents a novel Mahalanobis k-NN method integrated with existing registration techniques, improving robustness and feature discriminability in point cloud analysis.

Findings

20% improvement in registration accuracy

Features from registration show discriminative power

Effective across multiple datasets and methods

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.