用神经微分方程建模物体变形的连续4D动态，无需离散时间步。
ODeform: Learning Continuous 4D Motion for Shape Deformation with Neural ODEs
- 将点云与物理参数映射到统一隐空间，通过求解ODE实现连续变形建模。
- 在未见物理参数下预测精度优于基线方法，支持真实物体形状迁移。
- 适合需要实时连续动力学模拟的机器人操控与视觉任务。
连续物体变形建模对计算机视觉和机器人任务（如操作与仿真）至关重要。现有方法依赖学习模型或物理仿真器，但通常采用离散时间步或计算开销过大，难以实时应用。本文提出ODeform，是神经常微分方程（Neural ODEs）在3D空间可变形物体连续4D动态中的新扩展。该方法将3D点云与物理条件（如材料属性）映射至统一隐空间，通过求解所得常微分方程，以连续流形式建模变形过程，避免离散时间步的同时保持高效计算。我们在未见物理参数配置下评估该方法，结果显示运动预测精度优于基线。实验还证明其能成功迁移至真实捕获的新型3D物体，并实现有效插值与外推。代码与数据将公开。
原文摘要 · Abstract (English)
Modeling continuous object deformation is important for many computer vision and robotics tasks, such as manipulation and simulation. Existing approaches rely on learning-based methods or physics simulators to model shape deformations. However, these approaches either use discrete time steps or are too computationally intensive for real-time applications. We present ODeform, a novel extension of Neural Ordinary Differential Equations to continuous 4D dynamics of deformable objects in 3D space. Our method transforms 3D point clouds and physical conditions (like material properties) into a unified latent space. By solving the resulting ordinary differential equations over time, we model deformations as continuous flows within this learned embedding, eliminating the need for discrete time steps while maintaining computational efficiency. We evaluate our approach on unseen physical parameter configurations, showing improved motion prediction accuracy over baseline methods. Our experiments further demonstrate a successful transfer to real 3D captured objects with novel shapes, along with effective interpolation and extrapolation of the learned dynamics. Our code and data will be made publicly available.
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