Gauges and gauge transformations for uncertainty description of geometric structure with indeterminacy

Kenichi Kanatani and Daniel D. Morris
IEEE Transactions on Information Theory, Vol. 47, No. 5, July, 2001, pp. 2017--2028.


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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.

Keywords
Lie group theory, gauge transformation, computer vision, uncertainty description, geometric indeterminacy, statistical estimation, Cramer-Rao lower bound

Notes
Associated Project(s): Modeling by Videotape
Number of pages: 12

Text Reference
Kenichi Kanatani and Daniel D. Morris, "Gauges and gauge transformations for uncertainty description of geometric structure with indeterminacy," IEEE Transactions on Information Theory, Vol. 47, No. 5, July, 2001, pp. 2017--2028.

BibTeX Reference
@article{Morris_2001_3798,
   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",
   pages = "2017--2028",
   month = "July",
   year = "2001",
   volume = "47",
   number = "5",
}