Convolution plays a crucial role in various applications in signal and image processing, analysis and recognition. It is also the main building block of convolution neural networks (CNNs). Designing appropriate convolution neural networks on manifold-structured point clouds can inherit and empower recent advances of CNNs to analyzing and processing point cloud data. However, one of the major challenges is to define a proper way to "sweep" filters through the point cloud as a natural generalization of the planar convolution and to reflect the point cloud's geometry at the same time. In this paper, we consider generalizing convolution by adapting parallel transport on the point cloud. Inspired by a triangulated surface based method [Stefan C. Schonsheck, Bin Dong, and Rongjie Lai, arXiv:1805.07857.], we propose the Narrow-Band Parallel Transport Convolution (NPTC) using a specifically defined connection on a voxelized narrow-band approximation of point cloud data. With that, we further propose a deep convolutional neural network based on NPTC (called NPTC-net) for point cloud classification and segmentation. Comprehensive experiments show that the proposed NPTC-net achieves similar or better results than current state-of-the-art methods on point clouds classification and segmentation.
There are mainly two types of point-based convolution. The first type is to combine the information of points directly. These methods can be formulated as where @math is a neighborhood of @math and kernel @math takes different forms in different methods. PointNet @cite_1 is an early attempt to extract features on point cloud. PointNet is a network structure without convolution, or alternatively we can interpret the convolution defined by PointNet has the simplest kernel @math where @math is the Kronecker-Delta. Various later works attempt to improve PointNet by choosing different forms of the kernel @math . For example, PointNet++ @cite_23 introduces a max pooling among local points, i.e. choosing kernel @math as an indicator function: @math . Pointcnn @cite_19 chooses @math where @math and @math are trainable variables with @math . DGCNN @cite_7 proposes an "edge convolution" that can be viewed as fixing @math and @math MLP @math , where MLP means the Multi-Layer Perceptron.
@cite_19 @cite_1 @cite_7 @cite_23
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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. 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. We present a simple and general framework for feature learning from point cloud. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids (e.g. images). However, point cloud are irregular and unordered, thus a direct convolving of kernels against the features associated with the points will result in deserting the shape information while being variant to the orders. To address these problems, we propose to learn a X-transformation from the input points, which is used for simultaneously weighting the input features associated with the points and permuting them into latent potentially canonical order. Then element-wise product and sum operations of typical convolution operator are applied on the X-transformed features. The proposed method is a generalization of typical CNNs into learning features from point cloud, thus we call it PointCNN. Experiments show that PointCNN achieves on par or better performance than state-of-the-art methods on multiple challenging benchmark datasets and tasks. 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 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 Convolutional Neural Networks (CNNs)-based methods for 3D hand pose estimation with depth cameras usually take 2D depth images as input and directly regress holistic 3D hand pose. Different from these methods, our proposed Point-to-Point Regression PointNet directly takes the 3D point cloud as input and outputs point-wise estimations, i.e., heat-maps and unit vector fields on the point cloud, representing the closeness and direction from every point in the point cloud to the hand joint. The point-wise estimations are used to infer 3D joint locations with weighted fusion. To better capture 3D spatial information in the point cloud, we apply a stacked network architecture for PointNet with intermediate supervision, which is trained end-to-end. Experiments show that our method can achieve outstanding results when compared with state-of-the-art methods on three challenging hand pose datasets. Conventional convolutional neural networks use either a linear or a nonlinear filter to extract features from an image patch (region) of spatial size @math (typically, @math is small and is equal to @math , e.g., @math is 5 or 7). Generally, the size of the filter is equal to the size @math of the input patch. We argue that the representational ability of equal-size strategy is not strong enough. To overcome the drawback, we propose to use subpatch filter whose spatial size @math is smaller than @math . The proposed subpatch filter consists of two subsequent filters. The first one is a linear filter of spatial size @math and is aimed at extracting features from spatial domain. The second one is of spatial size @math and is used for strengthening the connection between different input feature channels and for reducing the number of parameters. The subpatch filter convolves with the input patch and the resulting network is called a subpatch network. Taking the output of one subpatch network as input, we further repeat constructing subpatch networks until the output contains only one neuron in spatial domain. These subpatch networks form a new network called the cascaded subpatch network (CSNet). The feature layer generated by CSNet is called the csconv layer. For the whole input image, we construct a deep neural network by stacking a sequence of csconv layers. Experimental results on five benchmark data sets demonstrate the effectiveness and compactness of the proposed CSNet. For example, our CSNet reaches a test error of 5.68 on the CIFAR10 data set without model averaging. To the best of our knowledge, this is the best result ever obtained on the CIFAR10 data set. Convolution as inner product has been the founding basis of convolutional neural networks (CNNs) and the key to end-to-end visual representation learning. Benefiting from deeper architectures, recent CNNs have demonstrated increasingly strong representation abilities. Despite such improvement, the increased depth and larger parameter space have also led to challenges in properly training a network. In light of such challenges, we propose hyperspherical convolution (SphereConv), a novel learning framework that gives angular representations on hyperspheres. We introduce SphereNet, deep hyperspherical convolution networks that are distinct from conventional inner product based convolutional networks. In particular, SphereNet adopts SphereConv as its basic convolution operator and is supervised by generalized angular softmax loss - a natural loss formulation under SphereConv. We show that SphereNet can effectively encode discriminative representation and alleviate training difficulty, leading to easier optimization, faster convergence and comparable (even better) classification accuracy over convolutional counterparts. We also provide some theoretical insights for the advantages of learning on hyperspheres. In addition, we introduce the learnable SphereConv, i.e., a natural improvement over prefixed SphereConv, and SphereNorm, i.e., hyperspherical learning as a normalization method. Experiments have verified our conclusions. Convolutional Neural Networks (CNNs) with Bilinear Pooling, initially in their full form and later using compact representations, have yielded impressive performance gains on a wide range of visual tasks, including fine-grained visual categorization, visual question answering, face recognition, and description of texture and style. The key to their success lies in the spatially invariant modeling of pairwise (2nd order) feature interactions. In this work, we propose a general pooling framework that captures higher order interactions of features in the form of kernels. We demonstrate how to approximate kernels such as Gaussian RBF up to a given order using compact explicit feature maps in a parameter-free manner. Combined with CNNs, the composition of the kernel can be learned from data in an end-to-end fashion via error back-propagation. The proposed kernel pooling scheme is evaluated in terms of both kernel approximation error and visual recognition accuracy. Experimental evaluations demonstrate state-of-the-art performance on commonly used fine-grained recognition datasets. Convolutional neural network (CNN) has achieved the state-of-the-art performance in many different visual tasks. Learned from a large-scale training data set, CNN features are much more discriminative and accurate than the handcrafted features. Moreover, CNN features are also transferable among different domains. On the other hand, traditional dictionary-based features (such as BoW and spatial pyramid matching) contain much more local discriminative and structural information, which is implicitly embedded in the images. To further improve the performance, in this paper, we propose to combine CNN with dictionary-based models for scene recognition and visual domain adaptation (DA). Specifically, based on the well-tuned CNN models (e.g., AlexNet and VGG Net), two dictionary-based representations are further constructed, namely, mid-level local representation (MLR) and convolutional Fisher vector (CFV) representation. In MLR, an efficient two-stage clustering method, i.e., weighted spatial and feature space spectral clustering on the parts of a single image followed by clustering all representative parts of all images, is used to generate a class-mixture or a class-specific part dictionary. After that, the part dictionary is used to operate with the multiscale image inputs for generating mid-level representation. In CFV, a multiscale and scale-proportional Gaussian mixture model training strategy is utilized to generate Fisher vectors based on the last convolutional layer of CNN. By integrating the complementary information of MLR, CFV, and the CNN features of the fully connected layer, the state-of-the-art performance can be achieved on scene recognition and DA problems. An interested finding is that our proposed hybrid representation (from VGG net trained on ImageNet) is also complementary to GoogLeNet and or VGG-11 (trained on Place205) greatly. In this paper, we present a simple and modularized neural network architecture, named interleaved group convolutional neural networks (IGCNets). The main point lies in a novel building block, a pair of two successive interleaved group convolutions: primary group convolution and secondary group convolution. The two group convolutions are complementary: (i) the convolution on each partition in primary group convolution is a spatial convolution, while on each partition in secondary group convolution, the convolution is a point-wise convolution; (ii) the channels in the same secondary partition come from different primary partitions. We discuss one representative advantage: Wider than a regular convolution with the number of parameters and the computation complexity preserved. We also show that regular convolutions, group convolution with summation fusion, and the Xception block are special cases of interleaved group convolutions. Empirical results over standard benchmarks, CIFAR- @math , CIFAR- @math , SVHN and ImageNet demonstrate that our networks are more efficient in using parameters and computation complexity with similar or higher accuracy. Deep Convolutional Neural Networks (DCNNs) commonly use generic 'max-pooling' (MP) layers to extract deformation-invariant features, but we argue in favor of a more refined treatment. First, we introduce epitomic con-volution as a building block alternative to the common convolution-MP cascade of DCNNs; while having identical complexity to MP, Epitomic Convolution allows for pa-rameter sharing across different filters, resulting in faster convergence and better generalization. Second, we introduce a Multiple Instance Learning approach to explicitly accommodate global translation and scaling when training a DCNN exclusively with class labels. For this we rely on a 'patchwork' data structure that efficiently lays out all image scales and positions as candidates to a DCNN. Factoring global and local deformations allows a DCNN to 'focus its resources' on the treatment of non-rigid defor-mations and yields a substantial classification accuracy improvement. Third, further pursuing this idea, we develop an efficient DCNN sliding window object detector that employs explicit search over position, scale, and aspect ratio. We provide competitive image classification and localization results on the ImageNet dataset and object detection results on the Pascal VOC 2007 benchmark. Abstract We present a novel convolutional neural network (CNN) based pipeline which can effectively fuse multi-level information extracted from different intermediate layers generating hybrid convolutional features (HCF) for edge detection. Different from previous methods, the proposed method fuses multi-level information in a feature-map based manner. The produced hybrid convolutional features can be used to perform high-quality edge detection. The edge detector is also computationally efficient, because it detects edges in an image-to-image way without any post-processing. We evaluate the proposed method on three widely used datasets for edge detection including BSDS500, NYUD and Multicue, and also test the method on Pascal VOC’12 dataset for object contour detection. The results show that HCF achieves an improvement in performance over the state-of-the-art methods on all four datasets. On BSDS500 dataset, the efficient version of the proposed approach achieves ODS F-score of 0.804 with a speed of 22 fps and the high-accuracy version achieves ODS F-score of 0.814 with 11 fps . With the rapid development of Deep Convolutional Neural Networks (DCNNs), numerous works focus on designing better network architectures (i.e., AlexNet, VGG, Inception, ResNet and DenseNet etc.). Nevertheless, all these networks have the same characteristic: each convolutional layer is followed by an activation layer, a Rectified Linear Unit (ReLU) layer is the most used among them. In this work, we argue that the paired module with 1:1 convolution and ReLU ratio is not the best choice since it may result in poor generalization ability. Thus, we try to investigate the more suitable convolution and ReLU ratio for exploring the better network architectures. Specifically, inspired by Leaky ReLU, we focus on adopting the proportional module with N:M (N @math M) convolution and ReLU ratio to design the better networks. From the perspective of ensemble learning, Leaky ReLU can be considered as an ensemble of networks with different convolution and ReLU ratio. We find that the proportional module with N:M (N @math M) convolution and ReLU ratio can help networks acquire the better performance, through the analysis of a simple Leaky ReLU model. By utilizing the proportional module with N:M (N @math M) convolution and ReLU ratio, many popular networks can form more rich representations in models, since the N:M (N @math M) proportional module can utilize information more effectively. Furthermore, we apply this module in diverse DCNN models to explore whether is the N:M (N @math M) convolution and ReLU ratio indeed more effective. From our experimental results, we can find that such a simple yet effective method achieves better performance in different benchmarks with various network architectures and the experimental results verify that the superiority of the proportional module. 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. Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large-scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best-performing GNN architecture. In this paper, we present a simple and modularized neural network architecture, named interleaved group convolutional neural networks (IGCNets). The main point lies in a novel building block, a pair of two successive interleaved group convolutions: primary group convolution and secondary group convolution. The two group convolutions are complementary: (i) the convolution on each partition in primary group convolution is a spatial convolution, while on each partition in secondary group convolution, the convolution is a point-wise convolution; (ii) the channels in the same secondary partition come from different primary partitions. We discuss one representative advantage: Wider than a regular convolution with the number of parameters and the computation complexity preserved. We also show that regular convolutions, group convolution with summation fusion, and the Xception block are special cases of interleaved group convolutions. Empirical results over standard benchmarks, CIFAR-10, CIFAR-100, SVHN and ImageNet demonstrate that our networks are more efficient in using parameters and computation complexity with similar or higher accuracy. Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and causes issues. In this paper, we design a novel type of neural network that directly consumes point clouds and well respects the permutation invariance of points in the input. Our network, named PointNet, provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing. Though simple, PointNet is highly efficient and effective. Empirically, it shows strong performance on par or even better than state of the art. Theoretically, we provide analysis towards understanding of what the network has learnt and why the network is robust with respect to input perturbation and corruption. Deep convolutional neural networks (CNNs) have become a key element in the recent breakthrough of salient object detection. However, existing CNN-based methods are based on either patchwise (regionwise) training and inference or fully convolutional networks. Methods in the former category are generally time-consuming due to severe storage and computational redundancies among overlapping patches. To overcome this deficiency, methods in the second category attempt to directly map a raw input image to a predicted dense saliency map in a single network forward pass. Though being very efficient, it is arduous for these methods to detect salient objects of different scales or salient regions with weak semantic information. In this paper, we develop hybrid contrast-oriented deep neural networks to overcome the aforementioned limitations. Each of our deep networks is composed of two complementary components, including a fully convolutional stream for dense prediction and a segment-level spatial pooling stream for sparse saliency inference. We further propose an attentional module that learns weight maps for fusing the two saliency predictions from these two streams. A tailored alternate scheme is designed to train these deep networks by fine-tuning pretrained baseline models. Finally, a customized fully connected conditional random field model incorporating a salient contour feature embedding can be optionally applied as a postprocessing step to improve spatial coherence and contour positioning in the fused result from these two streams. Extensive experiments on six benchmark data sets demonstrate that our proposed model can significantly outperform the state of the art in terms of all popular evaluation metrics. Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and causes issues. In this paper, we design a novel type of neural network that directly consumes point clouds, which well respects the permutation invariance of points in the input. Our network, named PointNet, provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing. Though simple, PointNet is highly efficient and effective. Empirically, it shows strong performance on par or even better than state of the art. Theoretically, we provide analysis towards understanding of what the network has learnt and why the network is robust with respect to input perturbation and corruption.