The Perspective System Theory in Machine Vision and Construction of Observers

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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.