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This article presents an improved method of 3D mesh modelsindexing for content-based retrieval in database withshape similarity and appearance queries. The approachis based on the Multiresolutional Reeb Graph matchingpresented in [1]. The original method only takes into accounttopological information what is often not sufficientfor effective matchings. Therefore we proposed to augmentthis graph with geometrical attributes. We also provide anew topological coherence condition to improve the graphmatching. Moreover 2D appearance attributes and 3D featuresare extracted and merged to improve the estimationof the similarity between models. Besides, all these newattributes are user-dependent as they can be weighted byvariable terms. We obtain a flexible multiresolutional andmulticriteria representation called Augmented Reeb Graph(ARG). Good preliminary results have been obtained ina shape-based matching framework compared to existingmethods based only on statistical measures. In addition,our study lead us to an innovative part matching schemebased on the same approach as our Augmented Reeb Graphmatching.