Simon Moss

Registering incomplete radar images using the EM algorithm

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.

Multiple line-template matching with the EM algorithm

Abstract This paper shows how multiple shape hypotheses can be used to recognise complex line patterns using the expectation-maximisation algorithm. The idea underpinning this work is to construct a mixture distribution for an observed configuration of line segments over a space of hypothesised shape models. According to the EM framework each model is represented by a set of maximum likelihood registration parameters together with a set of matching probabilities. These two pieces of information are iteratively updated so as to maximise the expected data likelihood over the space of model-data associations. This architecture can be viewed as providing simultaneous shape registration and hypothesis verification. We illustrate the effectiveness of the recognition strategy by studying the registration of noisy radar data against a database of alternative cartographic maps for different locations.

A mixture model for pose clustering

This paper describes a structural method for object alignment by pose clustering. The idea underlying pose clustering is to decompose the objects under consideration into k-tuples of primitive parts. By bringing pairs of k-tuples into correspondence, sets of alignment parameters are estimated. The global alignment corresponds to the set of parameters with maximum votes. The work reported here oAers two novel contributions. Firstly, we impose structural constraints on the arrangement of the k-tuples of primitives used for pose clustering. This limits problems of combinatorial nature and eases the search for consistent pose clusters. Secondly, we use the EM algorithm to estimate maximum likelihood alignment parameters. Here we fit a mixture model to the set of transformation parameter votes. We control the order of the underlying mixture model using a minimum description length criterion. The new alignment method is illustrated on the matching of optical and radar images of aerial scenes. ” 1999 Published by Elsevier Science B.V. All rights reserved.

Pose clustering with density estimation and structural constraints

This paper describes a statistical framework for object alignment by pose clustering. The idea underlying pose clustering is to transform the alignment process from the image domain to that of the appropriate transformation parameters. It commence by taking k-tuples from the primitive-sets for the model and the data. The size of the k-tuples is such that there are sufficient measurements available to estimate the full-set of transformation parameters. By pairing each k-tuple in the model and each k-tuple in the data, a set of transformation parameter estimates or alignment votes is accumulated. The work reported here draws on three ideas. Firstly, we estimate maximum likelihood alignment parameters by using the the EM algorithm to fit a mixture model to the set of transformation parameter votes. Secondly, we control the order of the underlying structure model using a minimum description length criterion. Finally, we limit problems of combinatorial background by imposing structural constraints on the k-tuples.

Registering multiple cartographic models with the hierarchical mixture of experts algorithm

This paper describes an application of the hierarchical mixture of experts algorithm (HME) to the registration of multiple cartographic models to noisy radar data. According to the HME algorithm each model is represented by a set of maximum likelihood registration parameters together with a set of matching probabilities. This architecture can be viewed as providing simultaneous registration and hypothesis verification. The maps in the cartographic data-base compete to account for radar data through the imposed probability normalisation. The resulting matching algorithm can be regarded as a generic tool for model retrieval from a database. Our evaluation on radar images illustrates some of the characteristics of the algorithm. Our main conclusions are that the method is both robust to added image noise and poor initialisation.

Registering Incomplete Radar Images using the EM Algorithm.

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.

Structural Constraints for Pose Clustering

This paper describes a structural method for object alignment by pose clustering. The idea underlying pose clustering is to decompose the objects under consideration into k-tuples of primitive parts. By bringing pairs of k-tuples into correspondence, sets of alignment parameters are estimated. The global alignment corresponds to the set of parameters with maximum votes. The work reported here offers two novel contributions. Firstly, we impose structural constraints on the arrangement of the k-tuples of primitives used for pose clustering. This limits problems of combinatorial background and eases the search for consistent pose clusters. Secondly, we use the EM algorithm to estimate maximum likelihood alignment parameters. Here we fit a mixture model to the set of transformation parameter votes. We control the order of the underlying mixture model using a minimum description length criterion.

Cartographic matching with millimetre radar images

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 nonoverlapping 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 date-likelihood function is unimodal in the translation and scale parameters. In-fact the algorithm is only sensitive to the choice of initial rotation parameter; this is attributable to local suboptima in the log-likelihood function associated with /spl pi//3 orientation ambiguities in the map. The method is also demonstrated to be relatively insensitive to random measurement errors on the line-segments.

Image Registration with Shape Mixtures

This paper describes how mixtures of Gussins be used for multiple shape template registration . The EM algorithm is applied to the shape mixture model to compute both maximum likelihood registration parameters together with set of a posteriori matching probabilities. This architecture can be viewed as providing simultaneous registration and hypothesis verification. The different templates compete to account for data through the imposed probability normalisation. Based on a sensitivity study, our main conclusions are the method is both robust to added noise and poor initialisation.

Alignment and correspondence using Markov chain Monte Carlo

Describes a Markov chain Monte Carlo (MCMC) method for token matching. We commence by constructing a graphical model in which the roles of token correspondence and token alignment are made explicit. According to this model the Markov chain represents the conditional dependencies between the alignment parameters and the correspondence assignments. Through a process of Monte Carlo sampling we recover both alignment parameters and correspondence assignments so as to maximise the joint data likelihood. An important feature of our method is the way in which the alignment parameter distribution is sampled. We do this by selecting k-tuples of tokens. The size of the k-tuples is sufficient to determine the alignment parameters when token correspondence is known. In this way we generate an alignment parameter distribution which can be sampled by MCMC.