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

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 CramerRao 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.