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Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold

Soatto, Stefano and Frezza, Ruggero and Perona, Pietro (1994) Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1994.004

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Abstract

We formulate the problem of estimating the motion of a rigid object viewed under perspective projection as the identification of a dynamic model in Exterior Differential form with parameters on a topological manifold. We first describe a general method for recursive identification of nonlinear implicit systems using prediction error criteria. The parameters are allowed to move slowly on some topological (not necessarily smooth) manifold. The basic recursion is solved in two different ways: one is based on a simple extension of the traditional Kalman Filter to nonlinear and implicit measurement constraints, the other may be regarded as a generalized "Gauss-Newton" iteration, akin to traditional Recursive Prediction Error Method techniques in linear identification. A derivation of the "Implicit Extended Kalman Filter" (IEKF) is reported in the appendix. The ID framework is then applied to solving the visual motion problem: it indeed is possible to characterize it in terms of identification of an Exterior Differential System with parameters living on a C0 topological manifold, called the "essential manifold". We consider two alternative estimation paradigms. The first is in the local coordinates of the essential manifold: we estimate the state of a nonlinear implicit model on a linear space. The second is obtained by a linear update on the (linear) embedding space followed by a projection onto the essential manifold. These schemes proved successful in performing the motion estimation task, as we show in experiments on real and noisy synthetic image sequences.


Item Type:Report or Paper (Technical Report)
Additional Information:Research funded by the California Institute of Technology, an AT&T Foundation Special Purpose grant, ONR grant N0014-93-1-0990 and grant ASI-RS-103 from the Italian Space Agency. This work is registered as Technical Report CIT-CDS 94-004, California Institute of Technology, 1994. Submitted to the invited session on "Dynamic Vision, System Theoretical Methods and Control Applications" at the 33rd IEEE conf. on Decision and Control, Florida, 1994. We wish to thank Prof. J.K. Åström for his discussions on implicit Kalman filtering, Prof. Richard Murray and Prof. Shankar Sastry for their observations and useful suggestions. Also discussions with Michiel van Nieuwstadt and Andrea Mennucci were helpful, as well as the suggestions of Prof. John Doyle and Prof. Manfred Morari.
Group:Control and Dynamical Systems Technical Reports
Subject Keywords:Dynamic vision, motion estimation, nonlinear identification, estimation on manifolds, Exterior Differential Systems, Differential Algebraic Equations
Record Number:CaltechCDSTR:1994.004
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1994.004
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28068
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:06 Sep 2006
Last Modified:26 Dec 2012 14:29

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