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Observability/Identifiability of Rigid Motion under Perspective Projection

Soatto, Stefano and Perona, Pietro (1994) Observability/Identifiability of Rigid Motion under Perspective Projection. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1994.001

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Abstract

The "visual motion" problem consists of estimating the motion of an object viewed under projection. In this paper we address the feasibility of such a problem. We will show that the model which defines the visual motion problem for feature points in the euclidean 3D space lacks of both linear and local (weak) observability. The locally observable manifold is covered with three levels of lie differentiations. Indeed, by imposing metric constraints on the state-space, it is possible to reduce the set of indistinguishable states. We will then analyze a model for visual motion estimation in terms of identification of an Exterior Differential System, with the parameters living on a topological manifold, called the "essential manifold", which includes explicitly in its definition the forementioned metric constraints. We will show that rigid motion is globally observable/identifiable under perspective projection with zero level of lie differentiation under some general position conditions. Such conditions hold when the viewer does not move on a quadric surface containing all the visible points.


Item Type:Report or Paper (Technical Report)
Additional Information:Research funded by the California Institute of Technology, ONR grant N00014-93-1-0990 and an AT&T Foundation Special Purpose grant. This work is registered as CDS Technical Report CIT-CDS 94-001, California Institute of Technology, January 1994 - revised February 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. The authors wish to thank Prof. Ruggero Frezza and Prof. Giorgio Picci for their constant support, advice and directions. The discussions with Prof. Richard Murray, Michiel van Nieuwstadt and Andrea Mennucci were very helpful in understanding the geometric structure of the problem. The suggestions of Prof. J. K. Åström, Prof. John Doyle, Prof. Manfred Morari and Prof. Shankar Sastry were also very valuable.
Group:Control and Dynamical Systems Technical Reports
Subject Keywords:dynamic vision, motion estimation, nonlinear observability, implicit systems, exterior differential systems, differential algebraic equations
Record Number:CaltechCDSTR:1994.001
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1994.001
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:28069
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:06 Sep 2006
Last Modified:26 Dec 2012 14:29

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