## AbstractPattern recognition deals with automatically detecting patterns in input values, so as to, for example, classify them into categories. Digital images often consitute the raw material for these applications. The term digital images usually refers to bitmap images, i.e. images represented as matrices of pixels. However, alternative representations can be considered. Thus, structuring the information contained in the image should underline the different objects depected in the image, as well as the links existing between them. This is the reason why we propose to use graph-based representations. Indeed, on the one hand, graphs are complex data structures with important expressive power and, on the other hand, we should benefit from graphs theory results and apply them to pattern recognition tasks. To this extent, we develop a method for extracting semantically well-founded plane graphs from images. We show that it is possible to rebuild the original image from this kind of graphs, with limited loss. Furthermore, we introduce open plane graphs, i.e. graphs whose faces can be visible or invisible. These graphs are useful in pattern recognition, when it is needed to search for patterns independently of the background. Focusing on the planarity of these graphs, we propose polynomial algorithms for plane graphs isomorphism and subgraphs isomorphism. We also address the equivalence issue, which is an isomorphism variant not taking into account visible faces.
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