Image Recognition With Graph Matching Using Estimation of Distribution Algorithms Endika Bengoetxea a , Pedro Larra ˜ naga b , Isabelle Bloch c and Aymeric Perchant c a Department of Computer Architecture and Technology, University of the Basque Country, San Sebastian, Spain b Department of Computer Science and Artificial Intelligence, University of the Basque Country, San Sebastian, Spain c Department of Signal and Image Processing, Ecole Nationale Sup´ erieure des T´ el´ ecommunications, CNRS URA 820, Paris, France Abstract. The use of graph matching techniques in pattern recognition is increasing due to the versatility of representing knowledge in the form of graphs. However, the size of the graphs as well as the number of attributes they contain can be too high in some domains. This happens for instance in image recognition, where structures of an image to be recognized need to be matched with a model defined as a graph. Due to this fact, graph matching can also be regarded as a combinatorial optimization problem with constraints and it can be solved with evolutionary computation techniques such as Genetic Algorithms (GAs) or Estimation of Distribution Algorithms (EDAs). This work proposes the use of EDAs, both in the discrete and continuous domains, in order to face the graph matching problem. As an example, a particular inexact graph matching problem applied to recognition of brain structures is shown. 1 Introduction Graphs are used to represent structural information in domains such as image interpretation and pattern recognition. For instance, graph matching techniques are often used for structural recognition of images: the model (which can be an atlas or a map depending on the application) is represented in the form of a graph, where each node contains information for a particular structure and arcs contain information about relationships between structures; a data graph is generated from the images to be analyzed and contains similar information. Graph matching techniques are then used to determine which structure in the model corresponds to each of the structures in a given image. Several techniques have been applied to graph matching, including combinatorial optimization [1], relaxation [2,3], EM algorithm [4], and evolutionary computation techniques such as Genetic Algorithms (GAs) [5]. This work proposes the use of Estimation Distribution Algorithms (EDAs) in both the discrete and continuous domains, showing the potential of this new evolutionary computation approach among traditional ones such as GAs. 2 Estimation Distribution Algorithms EDAs [6,7] are non-deterministic, stochastic heuristic search strategies within the evolutionary computation ap- proaches, where a number of solutions or individuals are created every generation evolving once and again until a satisfactory solution is achieved. The main characteristic of EDAs comparing to other evolutionary search strate- gies is that the evolution from a generation to the next is done by estimating the probability distribution of the fittest individuals, and afterwards by sampling the induced model. In EDAs, the individuals are not said to contain genes, but variables which dependencies have to be analyzed. Furthermore, while in other evolutionary computation heuristics the interrelations between the variables forming the individuals are considered implicitly (i.e. building block hypothesis), in EDAs the interrelations are expressed explicitly through a probability distribution estimated from the selected individuals of the previous generation. The latter constitutes the hardest task to perform. We distinguish four main steps in the EDA approach: 1. At the beginning, the first population of individuals is generated, usually by assuming an uniform distribution (either discrete or continuous) on each variable, and evaluating each of the individuals. 2. Secondly, a number ( ) of individuals are selected, usually the fittest ones. endika,pedro @si.ehu.es, Isabelle.Bloch, perchant @tsi.enst.fr