text: A number of problems can be formulated as prediction on graph-structured data. In this work, we generalize the convolution operator from regular grids to arbitrary graphs while avoiding the spectral domain, which allows us to handle graphs of varying size and connectivity. To move beyond a simple diffusion, filter weights are conditioned on the specific edge labels in the neighborhood of a vertex. Together with the proper choice of graph coarsening, we explore constructing deep neural networks for graph classification. In particular, we demonstrate the generality of our formulation in point cloud classification, where we set the new state of the art, and on a graph classification dataset, where we outperform other deep learning approaches. The source code is available at this https URL
  @cite_35: Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks (GCNN), a generalization of the convolutional networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of the filters and linear combination weights are optimization variables that are learned to minimize a task-specific cost function. We use GCNN to learn invariant shape features, allowing to achieve state-of-the-art performance in problems such as shape description, retrieval, and correspondence.
  @cite_12: In this paper, we tackle the labeling problem for 3D point clouds. We introduce a 3D point cloud labeling scheme based on 3D Convolutional Neural Network. Our approach minimizes the prior knowledge of the labeling problem and does not require a segmentation step or hand-crafted features as most previous approaches did. Particularly, we present solutions for large data handling during the training and testing process. Experiments performed on the urban point cloud dataset containing 7 categories of objects show the robustness of our approach.
  @cite_43: Robust object recognition is a crucial skill for robots operating autonomously in real world environments. Range sensors such as LiDAR and RGBD cameras are increasingly found in modern robotic systems, providing a rich source of 3D information that can aid in this task. However, many current systems do not fully utilize this information and have trouble efficiently dealing with large amounts of point cloud data. In this paper, we propose VoxNet, an architecture to tackle this problem by integrating a volumetric Occupancy Grid representation with a supervised 3D Convolutional Neural Network (3D CNN). We evaluate our approach on publicly available benchmarks using LiDAR, RGBD, and CAD data. VoxNet achieves accuracy beyond the state of the art while labeling hundreds of instances per second.
summary: * CNNs on Point Clouds and Meshes. There has been little work on deep learning on point clouds or meshes. Masci al @cite_35 define convolution over patch descriptors around every vertex of a 3D mesh using geodesic distances, formulated in a deep learning architecture. The only way of processing point clouds using deep learning has been to first voxelize them before feeding them to a 3D CNN, be it for classification @cite_43 or segmentation @cite_12 purposes. Instead, we regard point cloud as graphs in Euclidean space in this work.