A Non-Parametric Framework for Dynamic Point Cloud Classification Using Optimal Transport-Based Embeddings

Dynamic point clouds, time-varying collections of unordered 3D points, exhibit complex variability arising from two distinct sources: spatial deformation of the permutation-invariant point configuration at each instant, and temporal variation of trajectories across time. Existing approaches to dynamic point cloud recognition predominantly rely on deep learning architectures that capture these variations through large numbers of learnable parameters and GPU-dependent optimization, posing practical challenges in resource-constrained settings. In this work, we propose a completely non-parametric framework for dynamic point cloud classification grounded in optimal transport theory. Linear Optimal Transport (LOT) resolves spatial permutation ambiguity by mapping each unordered point cloud to a canonical Euclidean representation, while the Cumulative Distribution Transform (CDT) encodes per-joint temporal signals into a representation where temporal variability becomes more tractable. Together, these embeddings capture the full dynamic structure in a space suitable to linear analysis, where each class is modeled as a low-dimensional subspace and classification is performed by nearest subspace assignment, requiring no gradient-based optimization, no learnable parameters, and no GPU at either training or inference time. Evaluated on KIMORE, UI-PRMD, MSR-Action3D, and NTU RGB+D against eight competitive parametric baselines, the proposed framework achieves competitive classification performance while requiring no learnable parameters or GPU-based optimization. It also maintains substantially lower floating point operations (FLOPs) and very low CPU inference latency, making it a strong candidate for resource-constrained deployment.