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.

翻译：我们引入了一种增强型转置全连接加权（t-FCW）图表示，用于将点云嵌入度量空间。尽管原始t-FCW在点云分类任务中已展现出显著效果，但其有效性背后的机理及更广泛的应用潜力仍不明确。本研究分析了增强型与原始t-FCW有效性的关键属性，并设计了一种完全以增强型t-FCW作为特征提取器的网络架构。从可解释性角度出发，我们利用增强型t-FCW构建了用于分类、部件分割与语义分割的存储库。分析表明，增强型t-FCW继承自表面描述符的鲁棒性，并通过维度间关联实现可解释性。这些特性使得网络兼具高效性与可解释性——在NVIDIA RTX A5000 GPU上处理ModelNet40分类任务仅需约7秒。重要的是，增强型t-FCW既可作为轻量级独立基线模型，也可作为现有深度模型的即插即用补充模块。