Abstract: In this paper, we propose a novel framework for 3D object retrieval and categorization. The object is modeled in terms of its subparts as an histogram of 3D visual word occurrences. We introduce an effective method for hierarchical 3D object segmentation driven by the minima rule that combines spectral clustering-for the selection of seed-regions-with region growing based on fast marching. Descriptors attached to the regions allow the definition of the visual words. After coding of each object according to the Bag-of-Words paradigm, retrieval can be performed by matching with a suitable kernel, or categorization by learning a Support Vector Machine. Several examples on the Aim@Shape watertight dataset and on the Tosca dataset demonstrate the versatility of the proposed method in working with either 3D objects with articulated shape changes or partially occluded or compound objects. Results are encouraging as shown by the comparison with other methods for each of the analyzed scenarios.