A Theory of Dynamic Machine Vision and Computational Algorithms

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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).