The Perspective System Theory in Machine Vision and Construction of Observers

动态机器视觉的基本问题是如何理解运动刚体的运动和/或从相关光流的知识中确定表征运动和物体形状的任何未知参数。视角动态系统产生于对这样一个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被描述为基于其视角观察估计任何未知状态和/或识别任何未知参数的问题。最简单的动态机器视觉问题之一是基于其视角观察来估计刚体的运动状态。在目前的研究中，我们引入了透视图动力系统的广义概念和这种系统的luenberger型非线性观测器。然后研究了非线性观测器的收敛问题，特别是在适当的条件下，包括系统(1)是Lyapunov稳定并满足某种可探测条件，可以构造估计误差指数收敛于零的luenberger型非线性观测器。通过机器视觉中出现的一些简单例子，给出了数值结果来说明所提出的非线性观测器的收敛性。数值结果表明，该观测器工作良好。所取得的成果已在各种国际会议上发表，一些相关工作已在一本合格的期刊上发表。

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.