A Unified Non-Parametric and Interpretable Point Cloud Analysis via t-FCW Graph Representation

2026-05-14

AI Summary

This work addresses the lack of a unified, efficient, and interpretable non-parametric approach for point cloud analysis. The authors propose a framework based on an enhanced transposed fully connected weighting (t-FCW) graph representation that embeds point clouds into a metric space. They design a lightweight network relying solely on t-FCW as the feature extractor, augmented with a memory bank mechanism to perform both classification and segmentation tasks. The method combines the robustness of surface descriptors with the interpretability of dimensional relationships, enabling standalone deployment or seamless integration as a plug-in module to enhance existing models. On ModelNet40, it achieves classification in approximately 7 seconds using an NVIDIA RTX A5000 GPU, striking a remarkable balance among efficiency, performance, and interpretability.

Abstract

We introduce an empowered transposed Fully Connected Weighted (t-FCW) graph representation to embed point clouds into a metric space. While original t-FCW has shown promising results for point cloud classification, the reasons behind its effectiveness and its broader applicability remained unclear. In this work, we analyze the properties that make the empowered and original t-FCW effective and design a network that uses the empowered t-FCW exclusively as feature extractors. From an interpretability perspective, we build memory banks for classification, part segmentation, and semantic segmentation using the empowered t-FCW. Our analysis reveals that the empowered t-FCW inherits robustness from surface descriptors, provides interpretability through dimension-wise relations. These properties enable a highly efficient and interpretable network, which processes the ModelNet40 classification problem in approximately 7 seconds on an NVIDIA RTX A5000 GPU. Importantly, empowered t-FCW can function both as a lightweight standalone baseline and as a complementary plug-in to existing deep models.

Problem

• point cloud analysis
• interpretability
• non-parametric representation
• graph representation
• t-FCW

Innovation

• t-FCW graph
• non-parametric
• interpretable representation
• point cloud analysis
• surface descriptor