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
* 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.
@cite_35 @cite_12 @cite_43
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One challenge that remains open in 3D deep learning is how to efficiently represent 3D data to feed deep networks. Recent works have relied on volumetric or point cloud representations, but such approaches suffer from a number of issues such as computational complexity, unordered data, and lack of finer geometry. This paper demonstrates that a mesh representation (i.e. vertices and faces to form polygonal surfaces) is able to capture fine-grained geometry for 3D reconstruction tasks. A mesh however is also unstructured data similar to point clouds. We address this problem by proposing a learning framework to infer the parameters of a compact mesh representation rather than learning from the mesh itself. This compact representation encodes a mesh using free-form deformation and a sparse linear combination of models allowing us to reconstruct 3D meshes from single images. In contrast to prior work, we do not rely on silhouettes and landmarks to perform 3D reconstruction. We evaluate our method on synthetic and real-world datasets with very promising results. Our framework efficiently reconstructs 3D objects in a low-dimensional way while preserving its important geometrical aspects. 3D data such as point clouds and meshes are becoming more and more available. The goal of this paper is to obtain 3D object and scene classification and semantic segmentation. Because point clouds have irregular formats, most of the existing methods convert the 3D data into multiple 2D projection images or 3D voxel grids. These representations are suited as input of conventional CNNs but they either ignore the underlying 3D geometrical structure or are constrained by data sparsity and computational complexity. Therefore, recent methods encode the coordinates of each point cloud to certain high dimensional features to cover the 3D space. However, by their design, these models are not able to sufficiently capture the local patterns. In this paper, we propose a method that directly uses point clouds as input and exploits the implicit space partition of k-d tree structure to learn the local contextual information and aggregate features at different scales hierarchically. Extensive experiments on challenging benchmarks show that our proposed model properly captures the local patterns to provide discriminative point set features. For the task of 3D scene semantic segmentation, our method outperforms the state-of-the-art on the challenging Stanford Large-Scale 3D Indoor Spaces Dataset(S3DIS) by a large margin. We propose an end-to-end deep learning architecture that produces a 3D shape in triangular mesh from a single color image. Limited by the nature of deep neural network, previous methods usually represent a 3D shape in volume or point cloud, and it is non-trivial to convert them to the more ready-to-use mesh model. Unlike the existing methods, our network represents 3D mesh in a graph-based convolutional neural network and produces correct geometry by progressively deforming an ellipsoid, leveraging perceptual features extracted from the input image. We adopt a coarse-to-fine strategy to make the whole deformation procedure stable, and define various of mesh related losses to capture properties of different levels to guarantee visually appealing and physically accurate 3D geometry. Extensive experiments show that our method not only qualitatively produces mesh model with better details, but also achieves higher 3D shape estimation accuracy compared to the state-of-the-art.