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. Semantic parsing of large-scale 3D point clouds is an important research topic in computer vision and remote sensing fields. Most existing approaches utilize hand-crafted features for each modality independently and combine them in a heuristic manner. They often fail to consider the consistency and complementary information among features adequately, which makes them difficult to capture high-level semantic structures. The features learned by most of the current deep learning methods can obtain high-quality image classification results. However, these methods are hard to be applied to recognize 3D point clouds due to unorganized distribution and various point density of data. In this paper, we propose a 3DCNN-DQN-RNN method which fuses the 3D convolutional neural network (CNN), Deep Q-Network (DQN) and Residual recurrent neural network (RNN)for an efficient semantic parsing of large-scale 3D point clouds. In our method, an eye window under control of the 3D CNN and DQN can localize and segment the points of the object's class efficiently. The 3D CNN and Residual RNN further extract robust and discriminative features of the points in the eye window, and thus greatly enhance the parsing accuracy of large-scale point clouds. Our method provides an automatic process that maps the raw data to the classification results. It also integrates object localization, segmentation and classification into one framework. Experimental results demonstrate that the proposed method outperforms the state-of-the-art point cloud classification methods. Point clouds provide a flexible and scalable geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. Hence, the design of intelligent computational models that act directly on point clouds is critical, especially when efficiency considerations or noise preclude the possibility of expensive denoising and meshing procedures. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent overwhelming success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to the point cloud world. To this end, we propose a new neural network module dubbed EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv is differentiable and can be plugged into existing architectures. Compared to existing modules operating largely in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked or recurrently applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. Beyond proposing this module, we provide extensive evaluation and analysis revealing that EdgeConv captures and exploits fine-grained geometric properties of point clouds. The proposed approach achieves state-of-the-art performance on standard benchmarks including ModelNet40 and S3DIS. Graph convolutional neural networks (Graph-CNNs) extend traditional CNNs to handle data that is supported on a graph. Major challenges when working with data on graphs are that the support set (the vertices of the graph) do not typically have a natural ordering, and in general, the topology of the graph is not regular (i.e., vertices do not all have the same number of neighbors). Thus, Graph-CNNs have huge potential to deal with 3D point cloud data which has been obtained from sampling a manifold. In this paper we develop a Graph-CNN for classifying 3D point cloud data, called PointGCN1. The architecture combines localized graph convolutions with two types of graph downsampling operations (also known as pooling). By the effective exploration of the point cloud local structure using the Graph-CNN, the proposed architecture achieves competitive performance on the 3D object classification benchmark ModelNet, and our architecture is more stable than competing schemes. Recent deep networks that directly handle points in a point set, e.g., PointNet, have been state-of-the-art for supervised semantic learning tasks on point clouds such as classification and segmentation. In this work, a novel end-to-end deep auto-encoder is proposed to address unsupervised learning challenges on point clouds. On the encoder side, a graph-based enhancement is enforced to promote local structures on top of PointNet. Then, a novel folding-based approach is proposed in the decoder, which folds a 2D grid onto the underlying 3D object surface of a point cloud. The proposed decoder only uses about 7 parameters of a decoder with fully-connected neural networks, yet leads to a more discriminative representation that achieves higher linear SVM classification accuracy than the benchmark. In addition, the proposed decoder structure is shown, in theory, to be a generic architecture that is able to reconstruct an arbitrary point cloud from a 2D grid. Finally, this folding-based decoder is interpretable since the reconstruction could be viewed as a fine granular warping from the 2D grid to the point cloud surface. Deep neural networks have enjoyed remarkable success for various vision tasks, however it remains challenging to apply CNNs to domains lacking a regular underlying structures such as 3D point clouds. Towards this we propose a novel convolutional architecture, termed SpiderCNN, to efficiently extract geometric features from point clouds. SpiderCNN is comprised of units called SpiderConv, which extend convolutional operations from regular grids to irregular point sets that can be embedded in ( R ^n ), by parametrizing a family of convolutional filters. We design the filter as a product of a simple step function that captures local geodesic information and a Taylor polynomial that ensures the expressiveness. SpiderCNN inherits the multi-scale hierarchical architecture from classical CNNs, which allows it to extract semantic deep features. Experiments on ModelNet40 demonstrate that SpiderCNN achieves state-of-the-art accuracy (92.4 ) on standard benchmarks, and shows competitive performance on segmentation task. Recent deep networks that directly handle points in a point set, e.g., PointNet, have been state-of-the-art for supervised learning tasks on point clouds such as classification and segmentation. In this work, a novel end-to-end deep auto-encoder is proposed to address unsupervised learning challenges on point clouds. On the encoder side, a graph-based enhancement is enforced to promote local structures on top of PointNet. Then, a novel folding-based decoder deforms a canonical 2D grid onto the underlying 3D object surface of a point cloud, achieving low reconstruction errors even for objects with delicate structures. The proposed decoder only uses about 7 parameters of a decoder with fully-connected neural networks, yet leads to a more discriminative representation that achieves higher linear SVM classification accuracy than the benchmark. In addition, the proposed decoder structure is shown, in theory, to be a generic architecture that is able to reconstruct an arbitrary point cloud from a 2D grid. Our code is available at http: www.merl.com research license#FoldingNet This paper presents Point Convolutional Neural Networks (PCNN): a novel framework for applying convolutional neural networks to point clouds. The framework consists of two operators: extension and restriction, mapping point cloud functions to volumetric functions and vise-versa. A point cloud convolution is defined by pull-back of the Euclidean volumetric convolution via an extension-restriction mechanism. The point cloud convolution is computationally efficient, invariant to the order of points in the point cloud, robust to different samplings and varying densities, and translation invariant, that is the same convolution kernel is used at all points. PCNN generalizes image CNNs and allows readily adapting their architectures to the point cloud setting. Evaluation of PCNN on three central point cloud learning benchmarks convincingly outperform competing point cloud learning methods, and the vast majority of methods working with more informative shape representations such as surfaces and or normals. Accurate detection of objects in 3D point clouds is a central problem in many applications, such as autonomous navigation, housekeeping robots, and augmented virtual reality. To interface a highly sparse LiDAR point cloud with a region proposal network (RPN), most existing efforts have focused on hand-crafted feature representations, for example, a bird's eye view projection. In this work, we remove the need of manual feature engineering for 3D point clouds and propose VoxelNet, a generic 3D detection network that unifies feature extraction and bounding box prediction into a single stage, end-to-end trainable deep network. Specifically, VoxelNet divides a point cloud into equally spaced 3D voxels and transforms a group of points within each voxel into a unified feature representation through the newly introduced voxel feature encoding (VFE) layer. In this way, the point cloud is encoded as a descriptive volumetric representation, which is then connected to a RPN to generate detections. Experiments on the KITTI car detection benchmark show that VoxelNet outperforms the state-of-the-art LiDAR based 3D detection methods by a large margin. Furthermore, our network learns an effective discriminative representation of objects with various geometries, leading to encouraging results in 3D detection of pedestrians and cyclists, based on only LiDAR. Deep learning with 3D data such as reconstructed point clouds and CAD models has received great research interests recently. However, the capability of using point clouds with convolutional neural network has been so far not fully explored. In this paper, we present a convolutional neural network for semantic segmentation and object recognition with 3D point clouds. At the core of our network is point-wise convolution, a new convolution operator that can be applied at each point of a point cloud. Our fully convolutional network design, while being surprisingly simple to implement, can yield competitive accuracy in both semantic segmentation and object recognition task. Unlike images which are represented in regular dense grids, 3D point clouds are irregular and unordered, hence applying convolution on them can be difficult. In this paper, we extend the dynamic filter to a new convolution operation, named PointConv. PointConv can be applied on point clouds to build deep convolutional networks. We treat convolution kernels as nonlinear functions of the local coordinates of 3D points comprised of weight and density functions. With respect to a given point, the weight functions are learned with multi-layer perceptron networks and density functions through kernel density estimation. The most important contribution of this work is a novel reformulation proposed for efficiently computing the weight functions, which allowed us to dramatically scale up the network and significantly improve its performance. The learned convolution kernel can be used to compute translation-invariant and permutation-invariant convolution on any point set in the 3D space. Besides, PointConv can also be used as deconvolution operators to propagate features from a subsampled point cloud back to its original resolution. Experiments on ModelNet40, ShapeNet, and ScanNet show that deep convolutional neural networks built on PointConv are able to achieve state-of-the-art on challenging semantic segmentation benchmarks on 3D point clouds. Besides, our experiments converting CIFAR-10 into a point cloud showed that networks built on PointConv can match the performance of convolutional networks in 2D images of a similar structure. We present a novel approach to learning a point-wise, meaningful embedding for point-clouds in an unsupervised manner, through the use of neural-networks. The domain of point-cloud processing via neural-networks is rapidly evolving, with novel architectures and applications frequently emerging. Within this field of research, the availability and plethora of unlabeled point-clouds as well as their possible applications make finding ways of characterizing this type of data appealing. Though significant advancement was achieved in the realm of unsupervised learning, its adaptation to the point-cloud representation is not trivial. Previous research focuses on the embedding of entire point-clouds representing an object in a meaningful manner. We present a deep learning framework to learn point-wise description from a set of shapes without supervision. Our approach leverages self-supervision to define a relevant loss function to learn rich per-point features. We train a neural-network with objectives based on context derived directly from the raw data, with no added annotation. We use local structures of point-clouds to incorporate geometric information into each point's latent representation. In addition to using local geometric information, we encourage adjacent points to have similar representations and vice-versa, creating a smoother, more descriptive representation. We demonstrate the ability of our method to capture meaningful point-wise features through three applications. By clustering the learned embedding space, we perform unsupervised part-segmentation on point clouds. By calculating euclidean distance in the latent space we derive semantic point-analogies. Finally, by retrieving nearest-neighbors in our learned latent space we present meaningful point-correspondence within and among point-clouds. Abstract There is an increasing interest in applying deep learning to 3D mesh segmentation. We observe that 1) existing feature-based techniques are often slow or sensitive to feature resizing, 2) there are minimal comparative studies and 3) techniques often suffer from reproducibility issue. This study contributes in two ways. First, we propose a novel convolutional neural network (CNN) for mesh segmentation. It uses 1D data, filters and a multi-branch architecture for separate training of multi-scale features. Together with a novel way of computing conformal factor (CF), our technique clearly out-performs existing work. Secondly, we publicly provide implementations of several deep learning techniques, namely, neural networks (NNs), autoencoders (AEs) and CNNs, whose architectures are at least two layers deep. The significance of this study is that it proposes a robust form of CF, offers a novel and accurate CNN technique, and a comprehensive study of several deep learning techniques for baseline comparison. We propose a deep neural network for supervised learning on neuroanatomical shapes. The network directly operates on raw point clouds without the need for mesh processing or the identification of point correspondences, as spatial transformer networks map the data to a canonical space. Instead of relying on hand-crafted shape descriptors, an optimal representation is learned in the end-to-end training stage of the network. The proposed network consists of multiple branches, so that features for multiple structures are learned simultaneously. We demonstrate the performance of our method on two applications: (i) the prediction of Alzheimer's disease and mild cognitive impairment and (ii) the regression of the brain age. Finally, we visualize the important parts of the anatomy for the prediction by adapting the occlusion method to point clouds. We present PPFNet - Point Pair Feature NETwork for deeply learning a globally informed 3D local feature descriptor to find correspondences in unorganized point clouds. PPFNet learns local descriptors on pure geometry and is highly aware of the global context, an important cue in deep learning. Our 3D representation is computed as a collection of point-pair-features combined with the points and normals within a local vicinity. Our permutation invariant network design is inspired by PointNet and sets PPFNet to be ordering-free. As opposed to voxelization, our method is able to consume raw point clouds to exploit the full sparsity. PPFNet uses a novel N-tuple loss and architecture injecting the global information naturally into the local descriptor. It shows that context awareness also boosts the local feature representation. Qualitative and quantitative evaluations of our network suggest increased recall, improved robustness and invariance as well as a vital step in the 3D descriptor extraction performance. Unlike on images, semantic learning on 3D point clouds using a deep network is challenging due to the naturally unordered data structure. Among existing works, PointNet has achieved promising results by directly learning on point sets. However, it does not take full advantage of a point's local neighborhood that contains fine-grained structural information which turns out to be helpful towards better semantic learning. In this regard, we present two new operations to improve PointNet with a more efficient exploitation of local structures. The first one focuses on local 3D geometric structures. In analogy to a convolution kernel for images, we define a point-set kernel as a set of learnable 3D points that jointly respond to a set of neighboring data points according to their geometric affinities measured by kernel correlation, adapted from a similar technique for point cloud registration. The second one exploits local high-dimensional feature structures by recursive feature aggregation on a nearest-neighbor-graph computed from 3D positions. Experiments show that our network can efficiently capture local information and robustly achieve better performances on major datasets. Our code is available at this http URL We present a new deep learning architecture (called Kdnetwork) that is designed for 3D model recognition tasks and works with unstructured point clouds. The new architecture performs multiplicative transformations and shares parameters of these transformations according to the subdivisions of the point clouds imposed onto them by kdtrees. Unlike the currently dominant convolutional architectures that usually require rasterization on uniform twodimensional or three-dimensional grids, Kd-networks do not rely on such grids in any way and therefore avoid poor scaling behavior. 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. 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.