On Exploring PDE Modeling for Point Cloud Video Representation Learning

TL;DR

The paper reframes point cloud video representation learning as a PDE-solving problem and introduces Motion PointNet, a lightweight architecture combining a PointNet-like encoder with a PDE-solving module to model spatio-temporal correlations. It targets improved alignment and uniformity of spatial-temporal representations using a spectral PDE operator and a contrastive InfoNCE loss. Empirical results across MSRAction-3D, NTU RGB+D, and UTD-MHAD demonstrate state-of-the-art performance with minimal parameters (0.72M) and FLOPs (0.82G), notably achieving 97.52% on MSRAction-3D with 24-frame inputs. The work showcases the viability of PDE-inspired approaches for efficient 3D point cloud video understanding and suggests future expansion to segmentation, detection, and tracking tasks.

Abstract

Point cloud video representation learning is challenging due to complex structures and unordered spatial arrangement. Traditional methods struggle with frame-to-frame correlations and point-wise correspondence tracking. Recently, partial differential equations (PDE) have provided a new perspective in uniformly solving spatial-temporal data information within certain constraints. While tracking tangible point correspondence remains challenging, we propose to formalize point cloud video representation learning as a PDE-solving problem. Inspired by fluid analysis, where PDEs are used to solve the deformation of spatial shape over time, we employ PDE to solve the variations of spatial points affected by temporal information. By modeling spatial-temporal correlations, we aim to regularize spatial variations with temporal features, thereby enhancing representation learning in point cloud videos. We introduce Motion PointNet composed of a PointNet-like encoder and a PDE-solving module. Initially, we construct a lightweight yet effective encoder to model an initial state of the spatial variations. Subsequently, we develop our PDE-solving module in a parameterized latent space, tailored to address the spatio-temporal correlations inherent in point cloud video. The process of solving PDE is guided and refined by a contrastive learning structure, which is pivotal in reshaping the feature distribution, thereby optimizing the feature representation within point cloud video data. Remarkably, our Motion PointNet achieves an impressive accuracy of 97.52% on the MSRAction-3D dataset, surpassing the current state-of-the-art in all aspects while consuming minimal resources (only 0.72M parameters and 0.82G FLOPs).

Figures (5)

• Figure 1: Representations of MSRAction-3D test set on hypersphere. The temporal uniformity, spatial uniformity, and final logits uniformity are present in blue, red, and green, respectively. Feature vectors should ideally be uniformly distributed over a unit hypersphere. The uniformity demonstrates the integrity of the information in features.
• Figure 2: Overall architecture of our Motion PointNet. PointNet-like Encoder: Benefiting from the rolling operation, as the network goes deeper, features from the current frame are continually aggregated to the next frame, while also perceiving more spatial information with a larger spatial receptive field. PDE-solving module: We then further refine the motion information by formulating this process as solvable PDE. The PDE-solving module provides additional supervision of the backbone with a cross-dimension feature reconstruction target.
• Figure 3: Comparison between reconstruction target for (a) inner data distribution and (b) spatial-temporal correlation modeling.
• Figure 4: Visualization comparison between PointNet++ and our Motion PointNet. High response points are marked in orange, which are selected based on the magnitude of the feature response. We choose binary representation for clarity in visualization.
• Figure 5: Visualization of high feature response on MSRAction-3D dataset. High response points are marked in orange, which are selected based on the magnitude of the feature response. We choose binary representation for clarity in visualization.