A Theory of Dynamic Machine Vision and Computational Algorithms

华盛顿大学（Washington University） Bijoy K.Ghosh等研究人员证明了通过在四维空间中投影线性运动而得到的三维透视空间中的透视系统用Riccati动力系统表示，其投影系统又用Riccati动力系统表示，并研究了该Riccati动力系统的运动参数可辨识性。特别地，我们通过透视和正射影观测得到了关于Riccati动力系统可识别性的各种结果，并使用扩展卡尔曼滤波器进行了一些计算机模拟来说明所得到的结果。这些结果已经发表在IEEE自动控制汇刊上的一篇论文中（见下面的出版物列表中的第一篇论文）。此外，我们利用Kronecker标准形式的概念研究了透视图动力系统的参数估计问题，并获得了具有给定Kronecker指标集的透视图动力系统的参数化，并使用扩展卡尔曼滤波器进行了各种计算机模拟以验证我们方法的有效性。这些结果在2000年的美国控制会议上发表（见下面出版物列表中的第二篇论文）。此外，对透视线性系统的可观测性进行了研究，得到了一些重要的结果，并在2009年IEEE决策与控制会议（CDC2000）和2003年SICE动力系统理论研讨会（DST2000）上发表（见以下出版物列表中的第三篇和第五篇论文）。最后，对透视线性系统的观察者进行了研究，并获得了非常有趣的结果，这些结果在ISCIE随机系统及其应用国际研讨会（SSS2000）和SICE动力系统理论研讨会（DST2000）上发表（参见下面的出版物列表中的第四和第六篇论文）。

The investigators with Bijoy K.Ghosh of Washington University have shown that the perspective system in 3-dimensional perspective space obtained by projecting a linear motion in 4-dimensional space is represented by a Riccati dynamical system and its projected system is again represented by a Riccati dynamical system, and has studied the identifiability of motion parameters of such a Riccati dynamical system. In particular, we obtained various results on the identifiability of the Riccati dynamical system with perspective and orthographic observations, and performed some computer simulations using extended Kalman filters to illustrate the obtained results. These results have been published in a paper appeared in IEEE Transactions on Automatic Control (see the first paper in the publication list below).Further, we investigated the parameter estimation problem of perspective dynamical systems using a notion of Kronecker canonical form, and obtained the parameterization of a perspective dynamical system having a given set of Kronecker indices and performed various computer simulations using extended Kalman filters to check the usefulness of our approach. These results were presented at the American Control Conference in 2000 (see the second paper in the publication list below). Furthermore, the observability of perspective linear systems was studied, and some important results were obtained and were presented the 39^<th>IEEE Conference on Decision and Control (CDC2000) and the 23^<rd> SICE Symposium on Dynamical Systems Theory (DST2000)(See the third and fifth papers in the publication list below). Finally, observers for perspective linear systems were investigated and very interesting results were obtained, and those results were presented at the 32^<nd> ISCIE International Symposium on Stochastic Systems and Its Applications (SSS2000) and the 23^<rd> SICE Symposium on Dynamical Systems Theory (DST2000)(See the forth and sixth papers in the publication list below).