ODeform: Learning Continuous 4D Motion for Shape Deformation with Neural ODEs

ODeform：利用神经常微分方程（Neural ODEs）学习形状变形的连续 4D 运动

Abstract: 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.

摘要： 对连续物体变形进行建模对于许多计算机视觉和机器人任务（如操作和仿真）至关重要。现有的方法主要依赖于基于学习的方法或物理模拟器来建模形状变形。然而，这些方法要么使用离散的时间步长，要么计算过于密集，难以满足实时应用的需求。

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.

我们提出了 ODeform，这是将神经常微分方程（Neural ODEs）扩展到 3D 空间中可变形物体连续 4D 动力学的一种新颖方法。我们的方法将 3D 点云和物理条件（如材料属性）转换为统一的潜在空间。通过随时间求解所得的常微分方程，我们将变形建模为该学习嵌入空间内的连续流，从而在保持计算效率的同时，消除了对离散时间步长的需求。

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.

我们在未见过的物理参数配置上评估了我们的方法，结果显示其运动预测精度优于基准方法。我们的实验进一步证明了该方法能够成功迁移到具有新颖形状的真实 3D 捕获物体上，并能对学习到的动力学进行有效的插值和外推。我们的代码和数据将向公众开放。

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Paper Details:

• Authors: Yordanka Velikova, Mahdi Saleh, Liming Kuang, Benjamin Busam
• Subject: Computer Vision and Pattern Recognition (cs.CV)
• arXiv ID: 2607.20670
• Submission Date: 22 Jul 2026

论文详情：

• 作者： Yordanka Velikova, Mahdi Saleh, Liming Kuang, Benjamin Busam
• 学科： 计算机视觉与模式识别 (cs.CV)
• arXiv ID： 2607.20670
• 提交日期： 2026年7月22日