Abstract—This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two real-world problems. The first involves the matching of different perspective views of 3.5-inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a line-scan sampling process. We complement these experiments with a sensitivity study based on synthetic data.

AbstractÐThis paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is to say, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions. Commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm. Our second contribution is to cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows us to efficiently recover correspondence matches using singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding methods. Index TermsÐInexact graph matching, EM algorithm, matrix factorization, mixture models, Delaunay triangulations. 1

I propose a learning algorithm for learning hierarchical models for object recognition. The model architecture is a compositional hierarchy that represents part-whole relationships: parts are described in the local context of substructures of the object. The focus of this report is learning hierarchical models from data, i.e. inducing the structure of model prototypes from observed exemplars of an object. At each node in the hierarchy, a probability distribution governing its parameters must be learned. The connections between nodes reflects the structure of the object. The formulation of substructures is encouraged such that their parts become conditionally independent. The resulting model can be interpreted as a Bayesian Belief Network and also is in many respects similar to the stochastic visual grammar described by Mjolsness. 1 INTRODUCTION Model-based object recognition solves the problem of invariant recognition by relying on stored prototypes at unit scale positioned at the ori...