On Exploring PDE Modeling for Point Cloud Video Representation Learning

• URL: http://arxiv.org/abs/2404.04720v2
• Date: Wed, 29 May 2024 15:01:55 GMT
• Title: On Exploring PDE Modeling for Point Cloud Video Representation Learning
• Authors: Zhuoxu Huang, Zhenkun Fan, Tao Xu, Jungong Han,
• Abstract summary: We introduce Motion PointNet composed of a PointNet-like encoder and a PDE-solving module. Our Motion PointNet achieves an impressive accuracy of 97.52% on the MSRAction-3D dataset.
• Score: 48.02197741709501
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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).

Related papers

• Dynamic 3D Point Cloud Sequences as 2D Videos [81.46246338686478]
  3D point cloud sequences serve as one of the most common and practical representation modalities of real-world environments. We propose a novel generic representation called textitStructured Point Cloud Videos (SPCVs) SPCVs re-organizes a point cloud sequence as a 2D video with spatial smoothness and temporal consistency, where the pixel values correspond to the 3D coordinates of points.
  arXiv  Detail & Related papers  (2024-03-02T08:18:57Z)
• Learning Dynamic Point Cloud Compression via Hierarchical Inter-frame Block Matching [35.80653765524654]
  3D dynamic point cloud (DPC) compression relies on mining its temporal context. This paper proposes a learning-based DPC compression framework via hierarchical block-matching-based inter-prediction module.
  arXiv  Detail & Related papers  (2023-05-09T11:44:13Z)
• Implicit Neural Spatial Representations for Time-dependent PDEs [29.404161110513616]
  Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR.
  arXiv  Detail & Related papers  (2022-09-30T22:46:40Z)
• IDEA-Net: Dynamic 3D Point Cloud Interpolation via Deep Embedding Alignment [58.8330387551499]
  We formulate the problem as estimation of point-wise trajectories (i.e., smooth curves) We propose IDEA-Net, an end-to-end deep learning framework, which disentangles the problem under the assistance of the explicitly learned temporal consistency. We demonstrate the effectiveness of our method on various point cloud sequences and observe large improvement over state-of-the-art methods both quantitatively and visually.
  arXiv  Detail & Related papers  (2022-03-22T10:14:08Z)
• PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs [8.220908558735884]
  Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks (NNs) to solve PDEs as a basis for data-driven inverse analysis. We propose the novel physics-informed convolutional-recurrent learning architectures (PhyCRNet and PhCRyNet-s) for solving PDEs without any labeled data.
  arXiv  Detail & Related papers  (2021-06-26T22:22:19Z)
• Shape As Points: A Differentiable Poisson Solver [118.12466580918172]
  In this paper, we introduce a differentiable point-to-mesh layer using a differentiable formulation of Poisson Surface Reconstruction (PSR) The differentiable PSR layer allows us to efficiently and differentiably bridge the explicit 3D point representation with the 3D mesh via the implicit indicator field. Compared to neural implicit representations, our Shape-As-Points (SAP) model is more interpretable, lightweight, and accelerates inference time by one order of magnitude.
  arXiv  Detail & Related papers  (2021-06-07T09:28:38Z)
• CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations [72.4716073597902]
  We propose a method to learn object Canonical Point Cloud Representations of dynamically or moving objects. We demonstrate the effectiveness of our method on several applications including shape reconstruction, camera pose estimation, continuoustemporal sequence reconstruction, and correspondence estimation.
  arXiv  Detail & Related papers  (2020-08-06T17:58:48Z)
• Pseudo-LiDAR Point Cloud Interpolation Based on 3D Motion Representation and Spatial Supervision [68.35777836993212]
  We propose a Pseudo-LiDAR point cloud network to generate temporally and spatially high-quality point cloud sequences. By exploiting the scene flow between point clouds, the proposed network is able to learn a more accurate representation of the 3D spatial motion relationship.
  arXiv  Detail & Related papers  (2020-06-20T03:11:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.