Paving the Way for Point Cloud Video Representation Learning Using A PDE Model

2026-05-31

AI Summary

This work addresses the challenge of spatiotemporal modeling in point cloud videos, where capturing dynamic associations across unordered point sets remains difficult. It introduces partial differential equations (PDEs) into point cloud video representation learning for the first time, proposing MotionPDE—a lightweight, plug-and-play module that integrates physical priors with self-supervised contrastive learning to refine the PDE solving process. This approach effectively enhances spatiotemporal feature representations while maintaining low computational overhead. Evaluated across multiple downstream tasks, MotionPDE consistently boosts the performance of existing backbone models, demonstrating strong generalization and adaptability.

Abstract

Investigating spatial-temporal correlations, specifically how spatial points vary over time, is crucial for understanding point cloud videos. Traditional methods, particularly flow-based techniques, struggle with these correlations due to the unordered spatial arrangement of sequential point cloud data. To address this challenge, we propose a novel approach that regularizes spatial-temporal correlation learning by formulating the problem as a solvable Partial Differential Equation (PDE). While PDEs have long been effective in the physical domain, their application to novel sequential data like point cloud video remains underexplored. Inspired by fluid analysis, we construct a simplified PDE, and the process of solving PDE is guided and refined by a contrastive learning structure between the temporal embeddings and the spatial embeddings. With this extra supervision, our method, named MotionPDE, serves as an effective, plug-and-play enhancement module for existing backbone models, adding minimal computational overhead and parameters. Capitalizing on the contrastive learning process, we delve deeper into the self-supervised capabilities of MotionPDE, yielding promising results that underscore its utility and adaptability in point cloud video data interpretation. The code repo with trained checkpoints will be available at https://github.com/zhh6425/motionpde.git for facilitating future research.

Problem

• point cloud video
• spatial-temporal correlation
• unordered data
• representation learning

Innovation

• Point Cloud Video
• Partial Differential Equation (PDE)
• Contrastive Learning
• Self-supervised Learning
• Spatio-temporal Modeling