Gauges and gauge transformations for uncertainty description of geometric structure with indeterminacy
Journal Article, IEEE Transactions on Information Theory, Vol. 47, No. 5, pp. 2017 - 2028, July, 2001
Abstract
This paper presents a consistent theory for describing indeterminacy and uncertainty of 3-D reconstruction from a sequence of images. First, we give a group-theoretical analysis of gauges and gauge transformations. We then discuss how to evaluate the reliability of the solution that has indeterminacy and extend the Cramer-Rao lower bound to incorporate internal indeterminacy. We also introduce the free-gauge approach and define the normal form of a covariance matrix that is independent of particular gauges. Finally, we show simulated and real-image examples to illustrate the effect of gauge freedom on uncertainty description.
BibTeX
@article{Kanatani-2001-8276,author = {Kenichi Kanatani and Daniel D. Morris},
title = {Gauges and gauge transformations for uncertainty description of geometric structure with indeterminacy},
journal = {IEEE Transactions on Information Theory},
year = {2001},
month = {July},
volume = {47},
number = {5},
pages = {2017 - 2028},
keywords = {Lie group theory, gauge transformation, computer vision, uncertainty description, geometric indeterminacy, statistical estimation, Cramer-Rao lower bound},
}
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