Data-driven discovery of governing equations has kindled significant
interests in many science and engineering areas. Existing studies primarily
focus on uncovering equations that govern nonlinear dynamics based on direct
measurement of the system states (e.g., trajectories). Limited efforts have
been placed on distilling governing laws of dynamics directly from videos for
moving targets in a 3D space. To this end, we propose a vision-based approach
to automatically uncover governing equations of nonlinear dynamics for 3D
moving targets via raw videos recorded by a set of cameras. The approach is
composed of three key blocks: (1) a target tracking module that extracts plane
pixel motions of the moving target in each video, (2) a Rodrigues' rotation
formula-based coordinate transformation learning module that reconstructs the
3D coordinates with respect to a predefined reference point, and (3) a
spline-enhanced library-based sparse regressor that uncovers the underlying
governing law of dynamics. This framework is capable of effectively handling
the challenges associated with measurement data, e.g., noise in the video,
imprecise tracking of the target that causes data missing, etc. The efficacy of
our method has been demonstrated through multiple sets of synthetic videos
considering different nonlinear dynamics.

提议一种基于视觉的方法，通过一组摄像机记录的原始视频自动发现 3D 移动目标的非线性动力学方程，通过目标跟踪模块、坐标变换学习模块和增强曲线支持的稀疏回归器组成，该方法有效处理与视觉数据相关的挑战。