Recherche de motifs fréquents dans une base de cartes combinatoires. (Frequent pattern discovery in combinatorial maps databases)

A combinatorial map is a topological model that can represent the subdivisions of space into cells and their adjacency relations in n dimensions. This data structure is increasingly used in image processing, but it still lacks tools for analysis. Our goal is to define new tools for combinatorial maps nD. We are particularly interested in the extraction of submaps in a database of maps. We define two combinatorial map signatures : the first one has a quadratic space complexity and may be used to decide of isomorphism with a new map in linear time whereas the second one has a linear space complexity and may be used to decide of isomorphism in quadratic time. They can be used for connected maps, non connected maps, labbeled maps or non labelled maps. These signatures can be used to efficiently search for a map in a database. Moreover, the search time does not depend on the number of maps in the database. Then, we formalize the problem of finding frequent submaps in a database of combinatorial nD maps. We implement two algorithms for solving this problem. The first algorithm extracts the submaps with a breadth-first search approach and the second uses a depth-first search approach. We compare the performance of these two algorithms on synthetic database of maps. Finally, we propose to use the frequent patterns in an image classification application. Each image is described by a map that is transformed into a vector representing the number of occurrences of frequent patterns. From these vectors, we use standard techniques of classification defined on vector spaces. We propose experiments in supervised and unsupervised classification on two images databases.