On the Exact Linearization of Structure From Motion

Soatto, Stefano and Perona, Pietro (1994) On the Exact Linearization of Structure From Motion. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechCDSTR:1994.011]

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Abstract

The estimation of structure from motion has been a central task of computational vision over the last decade. As it is very well known, the problem is nonlinear due to the perspective nature of the measurements. One may ask at this point: does there exist a clever choice of coordinates which simplifies the estimation task? In particular, since "linearity" is a coordinate-dependent notion, is there a choice of coordinates such that the problem of estimating structure from motion becomes linear? In this paper we prove that the answer to the above question is no. An immediate consequence is that all choices of coordinates representations are structurally equivalent, in the sense that, at the current state of understanding of nonlinear estimation, none of them has an advantage based on geometric properties; instead, the difference between them is based purely on computational (numerical) ground. A further consequence of our result is the legitimation of the use of local linearization-based techniques (such as the Extended Kalman Filter) for estimating structure from known motion.

EPrint Type:	Monograph (Technical Report)
Additional Information:	Research funded by the California Institute of Technology, a scholarship from the University of Padova and a fellowship from the "A. Gini" Foundation. This work is registered as Technical Report CIT-CDS 94-018, California Institute of Technology, May 1994 We wish to thank Prof. Ruggero Frezza and Prof. Giorgio Picci for their constant support and advice, Prof. Richard Murray and Prof. Shankar Sastry for their observations and useful suggestions. Also discussions with Michiel van Nieuwstadt and Andrea Mennucci were helpful.
Uncontrolled Keywords:	Structure From Motion, nonlinear estimation, observer linearization
Subjects:	All Records
ID Code:	102
Deposited By:	Caltech Library System
Deposited On:	13 September 2006
Unique Identifier:	CaltechCDSTR:1994.011
Official Persistent URL:	http://resolver.caltech.edu/CaltechCDSTR:1994.011
Usage Policy:	You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.

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