This paper proposes a novel approach to recognize object categories in point clouds. By quantizing 3D SURF local descriptors, computed on partial 3D shapes extracted from the point clouds, a vocabulary of 3D visual words is generated. Using this codebook, we build a Bag-of-Words representation in 3D, which is used in conjunction with a SVM classification machinery. We also introduce the 3D Spatial Pyramid Matching Kernel, which works by partitioning a working volume into fine sub-volumes, and computing a hierarchical weighted sum of histogram intersections at each level of the pyramid structure. With the aim of increasing both the classification accuracy and the computational efficiency of the kernel, we propose selective hierarchical volume decomposition strategies, based on representative and discriminative (sub-)volume selection processes, which drastically reduce the pyramid to consider. Results on the challenging large-scale RGB-D object dataset show that our kernels signifi...