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

2026-07-22

AI Summary

This work addresses the challenge of accurately and efficiently modeling continuous deformations of deformable objects, a task where existing methods often sacrifice either precision or real-time performance due to reliance on discrete time steps or high computational costs. The authors propose a novel 4D continuous deformation modeling framework based on Neural Ordinary Differential Equations (Neural ODEs), which maps 3D point clouds and physical conditions into a unified latent space to enable efficient and temporally continuous dynamics simulation. This approach represents the first extension of Neural ODEs to 4D motion modeling of deformable objects, demonstrating strong generalization to unseen shapes and physical parameters, as well as superior interpolation and extrapolation capabilities. Experiments show significant improvements in prediction accuracy under unseen physical configurations, successful transfer to real-world 3D capture data, and the release of code and datasets to support further research.

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. 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.

Problem

• continuous 4D motion
• shape deformation
• deformable objects
• real-time modeling
• temporal continuity

Innovation

• Neural ODEs
• continuous 4D deformation
• point cloud dynamics
• latent space modeling
• real-time shape deformation