This paper presents SO-Net, a permutation invariant architecture for deep learning with orderless point clouds. The SO-Net models the spatial distribution of point cloud by building a Self-Organizing Map (SOM). Based on the SOM, SO-Net performs hierarchical feature extraction on individual points and SOM nodes, and ultimately represents the input point cloud by a single feature vector. The receptive field of the network can be systematically adjusted by conducting point-to-node k nearest neighbor search. In recognition tasks such as point cloud reconstruction, classification, object part segmentation and shape retrieval, our proposed network demonstrates performance that is similar with or better than state-of-the-art approaches. In addition, the training speed is significantly faster than existing point cloud recognition networks because of the parallelizability and simplicity of the proposed architecture. Our code is available at the project website.1
We present O-CNN, an Octree-based Convolutional Neural Network (CNN) for 3D shape analysis. Built upon the octree representation of 3D shapes, our method takes the average normal vectors of a 3D model sampled in the finest leaf octants as input and performs 3D CNN operations on the octants occupied by the 3D shape surface. We design a novel octree data structure to efficiently store the octant information and CNN features into the graphics memory and execute the entire O-CNN training and evaluation on the GPU. O-CNN supports various CNN structures and works for 3D shapes in different representations. By restraining the computations on the octants occupied by 3D surfaces, the memory and computational costs of the O-CNN grow quadratically as the depth of the octree increases, which makes the 3D CNN feasible for high-resolution 3D models. We compare the performance of the O-CNN with other existing 3D CNN solutions and demonstrate the efficiency and efficacy of O-CNN in three shape analysis tasks, including object classification, shape retrieval, and shape segmentation. We present OctNet, a representation for deep learning with sparse 3D data. In contrast to existing models, our representation enables 3D convolutional networks which are both deep and high resolution. Towards this goal, we exploit the sparsity in the input data to hierarchically partition the space using a set of unbalanced octrees where each leaf node stores a pooled feature representation. This allows to focus memory allocation and computation to the relevant dense regions and enables deeper networks without compromising resolution. We demonstrate the utility of our OctNet representation by analyzing the impact of resolution on several 3D tasks including 3D object classification, orientation estimation and point cloud labeling. We present a new deep learning architecture (called Kd-network) that is designed for 3D model recognition tasks and works with unstructured point clouds. The new architecture performs multiplicative transformations and share parameters of these transformations according to the subdivisions of the point clouds imposed onto them by Kd-trees. Unlike the currently dominant convolutional architectures that usually require rasterization on uniform two-dimensional or three-dimensional grids, Kd-networks do not rely on such grids in any way and therefore avoid poor scaling behaviour. In a series of experiments with popular shape recognition benchmarks, Kd-networks demonstrate competitive performance in a number of shape recognition tasks such as shape classification, shape retrieval and shape part segmentation.