Registering incomplete radar images using the EM algorithm

Simon Moss, Edwin R. Hancock

Abstract: This paper describes an application of the EM (expectation and maximisation) algorithm to the registration of incomplete millimetric radar images. The data used in this study consists of a series of non-overlapping radar sweeps. Our registration process aims to recover transformation parameters between the radar-data and a digital map. The tokens used in the matching process are fragmented line-segments extracted from the radar images which predominantly correspond to hedge-rows in the cartographic data. The EM technique models data uncertainty using Gaussian mixtures defined over the positions and orientations of the lines. The resulting weighted least-squares parameter estimation problem is solved using the Levenberg-Marquardt method. A sensitivity analysis reveals that the data-likelihood function is unimodal in the translation and scale parameters. In fact, the algorithm is only potentially sensitive to the choice of initial rotation parameter; this is attributable to local sub-optima in the log-likelihood function associated with π 2 orientation ambiguities in the map. By adopting Levenberg-Marquardt optimisation we reduce the local convergence difficulties posed by these local rotation maxima. The method is also demonstrated to be relatively insensitive to random measurement errors on the line-segments.