In this paper we propose a novel framework for 3D object categorization. The object is modeled it in terms of its sub-parts 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. The front propagation is driven by local geometry features, namely the Shape Index. Finally, after the coding of each object according to the Bag-of-Words paradigm, a Support Vector Machine is learnt to classify different objects categories. Several examples on two different datasets are shown which evidence the effectiveness of the proposed framework.