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

2024-09-10

arXiv.org

AI Summary

To address the poor robustness of point cloud registration caused by non-uniform point density and the underutilization of registration features in downstream tasks, this paper proposes a Mahalanobis-distance-based k-nearest-neighbor modeling method that explicitly captures both the statistical distribution and surface geometric structure of local neighborhoods. We first reveal that features learned by registration networks exhibit strong discriminability; leveraging this insight, we design a plug-and-play module to transfer these features to few-shot point cloud classification. Our approach seamlessly integrates into mainstream registration architectures (e.g., DCP, DeepUME), achieving significant improvements in registration accuracy on ModelNet40 and FAUST. In few-shot classification on ModelNet40 and ScanObjectNN, it boosts average accuracy by approximately 20%. The core innovation lies in reformulating registration as geometry-aware statistical modeling and enabling joint feature optimization across registration and classification tasks.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Multi-modal Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Point Cloud Registration
• Accuracy Improvement
• Classification Enhancement

Innovation

• Mahalanobis k-NN
• Point Cloud Registration
• Accuracy Improvement