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

TL;DR

This paper introduces an interpretable, non-parametric point cloud analysis method using empowered t-FCW graph representation, enhancing robustness and efficiency for classification and segmentation tasks.

Contribution

It develops an empowered t-FCW-based network that is both highly interpretable and efficient, applicable as a standalone or plug-in model for point cloud analysis.

Findings

Efficient processing of ModelNet40 classification in ~7 seconds.

Empowered t-FCW inherits robustness from surface descriptors.

Provides interpretability through dimension-wise relations.

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.