Convolutional Neural Networks (CNNs) achieve impressive performance in a wide variety of fields. Their success benefited from a massive boost when very deep CNN models were able to be reliably trained. Despite their merits, CNNs fail to properly address problems with non-Euclidean data. To overcome this challenge, Graph Convolutional Networks (GCNs) build graphs to represent non-Euclidean data, borrow concepts from CNNs, and apply them in training. GCNs show promising results, but they are usually limited to very shallow models due to the vanishing gradient problem. As a result, most state-of-the-art GCN models are no deeper than 3 or 4 layers. In this work, we present new ways to successfully train very deep GCNs. We do this by borrowing concepts from CNNs, specifically residual dense connections and dilated convolutions, and adapting them to GCN architectures. Extensive experiments show the positive effect of these deep GCN frameworks. Finally, we use these new concepts to build a very deep 56-layer GCN, and show how it significantly boosts performance (+3.7 mIoU over state-of-the-art) in the task of point cloud semantic segmentation. We believe that the community can greatly benefit from this work, as it opens up many opportunities for advancing GCN-based research.
GCNs are a perfect candidate for point cloud processing. Point cloud data poses a representational challenge, given its unstructured nature. Several attempts in creating structure from 3D data exist by either representing the 3D data with multiple 2D views @cite_43 @cite_49 @cite_14 @cite_47 , or by voxelization @cite_1 @cite_37 @cite_9 @cite_7 . More recent work focuses on directly processing unordered point cloud representations @cite_56 @cite_18 @cite_45 @cite_3 @cite_6 . The recent method by Wang al @cite_35 applies GCNs to point clouds. In particular, they propose a dynamic edge convolution algorithm for semantic segmentation of point clouds. The algorithm dynamically computes node adjacency at each graph layer using the distance between point features. This work demonstrates the potential of GCNs for point cloud related applications and beats the state-of-the-art in the task of point cloud segmentation. Unlike most other works, does not rely on RNNs or complex point aggregation methods.
@cite_35 @cite_37 @cite_14 @cite_18 @cite_7 @cite_9 @cite_1 @cite_3 @cite_56 @cite_6 @cite_43 @cite_45 @cite_49 @cite_47
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Semantic segmentation of 3D unstructured point clouds remains an open research problem. Recent works predict semantic labels of 3D points by virtue of neural networks but take limited context knowledge into consideration. In this paper, a novel end-to-end approach for unstructured point cloud semantic segmentation, named 3P-RNN, is proposed to exploit the inherent contextual features. First the efficient pointwise pyramid pooling module is investigated to capture local structures at various densities by taking multi-scale neighborhood into account. Then the two-direction hierarchical recurrent neural networks (RNNs) are utilized to explore long-range spatial dependencies. Each recurrent layer takes as input the local features derived from unrolled cells and sweeps the 3D space along two directions successively to integrate structure knowledge. On challenging indoor and outdoor 3D datasets, the proposed framework demonstrates robust performance superior to state-of-the-arts. 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. 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. 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. Point clouds are an efficient data format for 3D data. However, existing 3D segmentation methods for point clouds either do not model local dependencies [21] or require added computations [14, 23]. This work presents a novel 3D segmentation framework, RSNet1, to efficiently model local structures in point clouds. The key component of the RSNet is a lightweight local dependency module. It is a combination of a novel slice pooling layer, Recurrent Neural Network (RNN) layers, and a slice unpooling layer. The slice pooling layer is designed to project features of unordered points onto an ordered sequence of feature vectors so that traditional end-to-end learning algorithms (RNNs) can be applied. The performance of RSNet is validated by comprehensive experiments on the S3DIS[1], ScanNet[3], and ShapeNet [34] datasets. In its simplest form, RSNets surpass all previous state-of-the-art methods on these benchmarks. And comparisons against previous state-of-the-art methods [21, 23] demonstrate the efficiency of RSNets. We present an algorithm for registration between a large-scale point cloud and a close-proximity scanned point cloud, providing a localization solution that is fully independent of prior information about the initial positions of the two point cloud coordinate systems. The algorithm, denoted LORAX, selects super-points&#x2013;local subsets of points&#x2013;and describes the geometric structure of each with a low-dimensional descriptor. These descriptors are then used to infer potential matching regions for an efficient coarse registration process, followed by a fine-tuning stage. The set of super-points is selected by covering the point clouds with overlapping spheres, and then filtering out those of low-quality or nonsalient regions. The descriptors are computed using state-of-the-art unsupervised machine learning, utilizing the technology of deep neural network based auto-encoders. Abstract This novel framework provides a strong alternative to the common practice of using manually designed key-point descriptors for coarse point cloud registration. Utilizing super-points instead of key-points allows the available geometrical data to be better exploited to find the correct transformation. Encoding local 3D geometric structures using a deep neural network auto-encoder instead of traditional descriptors continues the trend seen in other computer vision applications and indeed leads to superior results. The algorithm is tested on challenging point cloud registration datasets, and its advantages over previous approaches as well as its robustness to density changes, noise, and missing data are shown. 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. This paper reports a novel mutual information (MI) based algorithm for automatic registration of unstructured 3D point clouds comprised of co-registered 3D lidar and camera imagery. The proposed method provides a robust and principled framework for fusing the complementary information obtained from these two different sensing modalities. High-dimensional features are extracted from a training set of textured point clouds (scans) and hierarchical k-means clustering is used to quantize these features into a set of codewords. Using this codebook, any new scan can be represented as a collection of codewords. Under the correct rigid-body transformation aligning two overlapping scans, the MI between the codewords present in the scans is maximized. We apply a James-Stein-type shrinkage estimator to estimate the true MI from the marginal and joint histograms of the codewords extracted from the scans. Experimental results using scans obtained by a vehicle equipped with a 3D laser scanner and an omnidirectional camera are used to validate the robustness of the proposed algorithm over a wide range of initial conditions. We also show that the proposed method works well with 3D data alone. 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. 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. 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 In this paper, we present a robust global approach for point cloud registration from uniformly sampled points. Based on eigenvalues and normals computed from multiple scales, we design fast descriptors to extract local structures of these points. The eigenvalue-based descriptor is effective at finding seed matches with low precision using nearest neighbor search. Generally, recovering the transformation from matches with low precision is rather challenging. Therefore, we introduce a mechanism named correspondence propagation to aggregate each seed match into a set of numerous matches. With these sets of matches, multiple transformations between point clouds are computed. A quality function formulated from distance errors is used to identify the best transformation and fulfill a coarse alignment of the point clouds. Finally, we refine the alignment result with the trimmed iterative closest point algorithm. The proposed approach can be applied to register point clouds with significant or limited overlaps and small or large transformations. More encouragingly, it is rather efficient and very robust to noise. A comparison to traditional descriptor-based methods and other global algorithms demonstrates the fine performance of the proposed approach. We also show its promising application in large-scale reconstruction with the scans of two real scenes. In addition, the proposed approach can be used to register low-resolution point clouds captured by Kinect as well. We present multiresolution tree-structured networks to process point clouds for 3D shape understanding and generation tasks. Our network represents a 3D shape as a set of locality-preserving 1D ordered list of points at multiple resolutions. This allows efficient feed-forward processing through 1D convolutions, coarse-to-fine analysis through a multi-grid architecture, and it leads to faster convergence and small memory footprint during training. The proposed tree-structured encoders can be used to classify shapes and outperform existing point-based architectures on shape classification benchmarks, while tree-structured decoders can be used for generating point clouds directly and they outperform existing approaches for image-to-shape inference tasks learned using the ShapeNet dataset. Our model also allows unsupervised learning of point-cloud based shapes by using a variational autoencoder, leading to higher-quality generated shapes. 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 http: www.merl.com research license#KCNet