Point-FCW: Transposed-FCW Graph Representation for Point Cloud Classification Using TDA

Dual challenges of computational efficiency and representation effectiveness exist in processing point clouds. Inspired by the TDA (Topological Data Analysis), we propose to convert the point cloud to a transposed fully connected and weighted (t-FCW) graph in order to significantly decrease the computational complexity in the following processing steps. We design a TDA pipeline called Point-FCW with a series of vectorization techniques for the 3D object point cloud feature extraction, which is plugged into the non-parametric classification head. Our experimental results demonstrate that Point-FCW achieves 75.28% accuracy on the ModelNet40 dataset with 512 points, providing a tiny, consistent, and effective representation for TDA. Furthermore, when integrated with the state-of-the-art non-parametric network Point-NN, the mixture model performs better, with an improvement of 4.47% in the OBJ-BG split of the ScanObjectNN dataset. Similarly, when integrating Point-FCW into the parametric network, PointMLP yields a performance improvement of 3.54% in the PB-T50-RS split of the ScanObjectNN dataset. The proposed Point-FCW can serve as a complementary enhancement feature when integrated into the Point-NN and PointMLP models. Moreover, the t-FCW graph representation can be efficiently converted at a rate of 3739 samples/second.