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This work presents an improved method of 3D mesh models indexing for content-based retrieval in database with shape similarity and appearance queries. The approach is based on the multiresolutional Reeb graph matching presented by Hilaga et al. (2001). The original method only takes into account topological information what is often not sufficient for effective matchings. Therefore we proposed to augment this graph with geometrical attributes. We also provide a new topological coherence condition to improve the graph matching. Moreover 2D appearance attributes and 3D features are extracted and merged to improve the estimation of the similarity between models. Besides, all these new attributes are user-dependent as they can be weighted by variable terms. We obtain a flexible multiresolutional and multicriteria representation called augmented Reeb graph (ARG). Good preliminary results have been obtained in a shape-based matching framework compared to existing methods based only on statistical measures. In addition, our study lead us to an innovative part matching scheme based on the same approach as our augmented Reeb graph matching.