Abstract—This paper describes a Bayesian framework for performing relational graph matching by discrete relaxation. Our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching. Broadly speaking there are two main aspects to this study. Firstly we focus on the issue of how relational inexactness may be quantified. We illustrate that several popular relational distance measures can be recovered as specific limiting cases of the Bayesian consistency measure. The second aspect of our comparison concerns the way in which structural inexactness is controlled. We investigate three different realizations of the matching process which draw on contrasting control models. The main conclusion of our study is that the active process of graph-editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter.

We propose a model-based approach to automated 3D extraction of buildings from aerial images. We focus on a reconstruction strategy that is not restricted to a small class of buildings. Therefore, we employ a generic modeling approach which relies on the well dened combination of building part models. Building parts are classied by their roof type.

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Hierarchical image structures are abundant in computer vision and have been used to encode part structure, scale spaces, and a variety of multiresolution features. In this paper, we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic graph (DAG) into a low-dimensional vector space. Based on a novel spectral characterization of a DAG, this topological signature allows us to efficiently retrieve a promising set of candidates from a database of models using a simple nearest-neighbor search. We establish the insensitivity of the signature to minor perturbation of graph structure due to noise, occlusion, or node split/merge. To accommodate large-scale occlusion, the DAG rooted at each nonleaf node of the query "votes" for model objects that share that "part," effectively accumulating local evidence in a model DAG's topological subspaces. We demonstrate the approach with a series of indexing experiments in the domain of view-based 3D object recognition using shock graphs.

In Pattern Recognition, the Graph Matching problem involves the matching of a sample data graph with the subgraph of a larger model graph where vertices and edges correspond to pattern parts and their relations. In this paper, we present Rulegraphs, a new method that combines the Graph Matching approach with Rule-Based approaches from Machine Learning. This new method reduces the cardinality of the (NP-Complete) Graph Matching problem by replacing model part, and their relational, attribute states by rules which depict attribute bounds and evidence for di erent classes. We show how rulegraphs, when combined with techniques for checking feature label-compatibilities, not only reduce the search space but also improve the uniqueness of the matching process.

Recently some fast methods (LAESA and TLAESA) have been proposed to find nearest neighbours in metric spaces. The average number of distances computed by these algorithms does not depend on the number of prototypes and they show linear space complexity. These results where obtained through a vast experimentation using only artificial data. In this paper, we corroborate this behaviour when applied to handwritten character recognition tasks. Moreover, we compare LAESA and TLAESA with some classical algorithms also working in metric spaces.

A typical content-based image retrieval (CBIR) system would need to handle the vagueness in the user queries as well as the inherent uncertainty in image representation, similarity measure, and relevance feedback. In this paper, we discuss how fuzzy set theory can be effectively used for this purpose and describe an image retrieval system called FIRST (Fuzzy Image Retrieval SysTem) which incorporates many of these ideas. FIRST can handle exemplar-based, graphical-sketch-based, as well as linguistic queries involving region labels, attributes, and spatial relations. FIRST uses Fuzzy Attributed Relational Graphs (FARGs) to represent images, where each node in the graph represents an image region and each edge represents a relation between two regions. The given query is converted to a FARG, and a low-complexity fuzzy graph matching algorithm is used to compare the query graph with the FARGs in the database. The use of an indexing scheme based on a leader clustering algorithm avoids an exhaustive search of the FARG database. We quantify the retrieval performance of the system in terms of several standard measures.

This paper presents a convergence analysis for the problem of consistent labelling using genetic search. The work builds on a recent empirical study of graph matching where we showed that a Bayesian consistency measure could be e$ciently optimised using a hybrid genetic search procedure which incorporated a hill-climbing step. In the present study we return to the algorithm and provide some theoretical justi"cation for its observed convergence behaviour. The novelty of the analysis is to demonstrate analytically that the hill-climbing step signi"cantly accelerates convergence, and that the convergence rate is polynomial in the size of the node-set of the graphs being matched. � 2000 Pattern Recognition

1 This paper briefly reviews the two currently dominant paradigms in machine learning - the connectionist network (CN) models and symbol processing (SP) systems; argues for the centrality of knowledge representation frameworks in learning; examines a range of representations in increasing order of complexity and measures of similarity or distance that are appropriate for each of them; introduces the notion of a generalized distance measure (GDM) and presents a class of GDM-based inductive learning algorithms (GDML). GDML are motivated by the need for an integration of symbol processing (SP) and connectionist network (CN) approaches to machine learning. GDM offer a natural generalization of the notion of distance or measure of mismatch used in a variety of pattern recognition techniques (e.g., k-nearest neighbor classifiers, neural networks using radial basis functions, and so on) to a range of structured representations such strings, trees, pyramids, association nets, conceptual graphs...

D building data is needed in many application areas. Besides the geometric description an increasing number of applications also demand thematic information about acquired buildings. We present a concept for the automatic extraction of buildings from aerial images. In contrast to other approaches generic building structures both are geometrically reconstructed and semantically classified. A component-based, parameterized building model is employed to control the reconstruction of buildings. This paper describes how geometric and semantic knowledge of buildings is propagated through the different aggregation levels of the building model. Furthermore, it is shown how rules and constraints are derived from the model and exploited at each stage of the reconstruction process. 1