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

This paper presents a consistent theory for describing indeterminacy and un certainty of three-dimensional (3-D) reconstruction from a sequence of imag es. First, we give a group-theoretical analysis of gauges and gauge transfo rmations. We then discuss how to evaluate the reliability of the solution t hat has indeterminacy and extend the Cramer-Rao lower bound to incorporate internal indeterminacy, We also introduce the free-gauge approach and defin e the normal form of a covariance matrix that is independent of particular gauges, Finally, we show simulated and real-image examples to illustrate th e effect of gauge freedom on uncertainty description.