The Perspective System Theory in Machine Vision and Construction of Observers

机器视觉中的视角系统理论与观察者的构造

• 批准号: 13650497
• 负责人: INABA Hiroshi
• 金额: $ 2.24万
• 依托单位: Tokyo Denki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650497/
• 关键词: Perspective System; Nonlinear systems; Parameter Identification; Observer; Machine vision

The essential problem in dynamic machine vision is how to understand the motion of a moving rigid body and/or to determine any unknown parameters characterizing the motion and the shape of the body from knowledge of the associated optical flow. Perspective dynamical systems arise from describing mathematically such a dynamic vision problem, and in system theory terminology the essential problem in dynamic machine vision can be described as a problem of estimating any unknown state and/or identifying any unknown parameters of such a system based on its perspective observations.One of most simple dynamic machine vision problems is to estimate the state of the motion of a rigid body based on its perspective observations. In the present investigation, we introduce a generalized notion of perspective dynamical systems and a nonlinear observer of the Luenberger-type for such systems. And then we study the convergence problem of the nonlinear observer, in particular, it is shown that, under suitable conditions, including that System (1) is Lyapunov stable and satisfies some sort of detectability condition, it is possible to construct a nonlinear observer of the Luenberger-type whose estimation error converges exponentially to zero. Further, using some simple examples appearing in machine vision, numerical results are presented to illustrate the convergence of the proposed nonlinear observer. The numerical results show that the observer works quite well.The results obtained have been presented in various international conferences and some related work has been published in a qualified journal.

动态机器视觉中的基本问题是如何理解运动刚体的运动和/或根据相关的光流知识确定表征运动和物体形状的任何未知参数。透视动态系统源于对动态视觉问题的数学描述，在系统论术语中，动态机器视觉的基本问题可以描述为基于透视观测估计系统的任何未知状态和/或识别系统的任何未知参数的问题。在本研究中，我们引入了透视动力系统的广义概念和这类系统的Luenberger型非线性观测器。然后，我们研究了非线性观测器的收敛问题，特别地，证明了在适当的条件下，包括系统(1)是Lyapunov稳定的并且满足某种可检测性条件，可以构造估计误差指数收敛到零的Luenberger型非线性观测器。进一步，利用机器视觉中的一些简单例子，给出了数值结果来说明所提出的非线性观测器的收敛。数值结果表明，该观测器具有较好的工作性能，已在多个国际会议上发表，相关工作已发表在一本有资质的期刊上。

项目成果

R.Abdursul, H.Inaba: "Nonlinear observers for perspective time-varying linear systems"Proceedings of 2002 International Conference on Control, Automation and Systems. 1402-1406 (2002)

R.Abdursul、H.Inaba：“透视时变线性系统的非线性观察者”2002 年国际控制、自动化和系统会议论文集。

R. Abdursul and H. Inaba: "Nonlinear observers for perspective time-varying linear systems"Abstracts of the 4th SIAM Conference on Linear Algebra in Signals, Systems and Control. (2001)

R. Abdursul 和 H. Inaba：“透视时变线性系统的非线性观察者”第四届 SIAM 信号、系统和控制线性代数会议摘要。

H. Inaba and Rixat Abdursul: "A note on nonlinear observers of perspective linear systems"Abstracts of the International Linear Algebra Conference. 34 (2001)

H. Inaba 和 Rixat Abdursul：“关于透视线性系统的非线性观察者的说明”国际线性代数会议摘要。

R. Abdursul, H. Inaba: "Nonlinear observers for perspective time-varying linear systems"SLAM Conference on Linear Algebra in Signals, Systems and Control. (2001)

R. Abdursul、H. Inaba：“透视时变线性系统的非线性观察者”信号、系统和控制中的线性代数 SLAM 会议。

H. Inaba, R. Abdursul and S. Takahashi: "Doubly Coprime Representation of Linear Systems and Its Application to Simultaneous Stabilization"IMA Journal of Mathematical Control and Information. 20. 21-35 (2003)

H. Inaba、R. Abdursul 和 S. Takahashi：“线性系统的双重互质表示及其在同时稳定中的应用”IMA 数学控制与信息杂志。