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

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2 Author(s)
K. Kanatani ; Dept. of Comput. Sci., Gunma Univ., Japan ; D. D. Morris

This paper presents a consistent theory for describing indeterminacy and uncertainty of three-dimensional (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

Published in:

IEEE Transactions on Information Theory  (Volume:47 ,  Issue: 5 )