Vision-based Discovery of Nonlinear Dynamics for 3D Moving Target
Zitong Zhang, Yang Liu, Hao Sun
TL;DR
This paper introduces a vision-based method to automatically discover the governing equations of nonlinear 3D moving targets directly from raw video data, addressing challenges like noise and missing data in measurements.
Contribution
It presents a novel framework combining target tracking, coordinate transformation, and sparse regression to uncover nonlinear dynamics from videos, which was not previously explored.
Findings
Successfully applied to synthetic videos with various nonlinear dynamics
Effectively handles noisy and incomplete measurement data
Demonstrates accurate discovery of governing equations from raw video data
Abstract
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,…
Peer Reviews
Decision·ICLR 2024 Conference Withdrawn Submission
The paper boast of proposing first approach to discover the equations of dynamics for moving target while using the 2D data. The presented results demonstrate superior performance of the approach when compared to the baseline. While the paper lacks crucial information and is technically dense, it is generally well written.
- The paper rely to a great extent on figure 1 but the proposed methodology has not been explained well either in the figure or in the text. A lot of focus has been given to finding out the noisy 3D tracks from calibrated camera rigs - where I don't see any novelty. Vet little any attention has been given to actual spline driven fitting of reconstructed track and learning the equation parameters. I find that many of the notations in figure 1 still remain undescribed and the paper jumps from writ
- The general problem was clearly discussed. - Apart from some sections, generally, was easy to follow and understand the setup of the research questions.
- Relatively poor organization: - For example, some of the vital information are introduced early on, in Figure 1, and only referred and discussed in section 3.3. One has to referee to the formula in the figure to follow the discussion, although it was brief. - Insufficient experimental results: - One of the main claimed contributions of the paper is the estimation of dynamics from data, collected using multiple cameras. None of the experimental results include such dataset. Infact all
1) The paper is well written and organized. 2) The proposed method is well designed and well detailed. 3) Experiments are well conducted and convincing.
The paper will be sometimes hard to read for a novice.
General equations on the 3D motion dynamics are determined from video data of moving objects.
Only results from synthetic data are provided. Even though some test results with additive noise are presented, they cannot replace experiments with real data, where additional factors such as changes in illumination and localization errors may take place. These are crucial to determine the applicability of the proposed methodology to videos captured from the real world. The good theoretical analysis of the geometrical issues invloved in the proposed model, need to be assessed with real data.
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Taxonomy
TopicsAdvanced Vision and Imaging · Image and Object Detection Techniques
MethodsSparse Evolutionary Training · Focus