Spherical Interpolated Convolutional Network with Distance-Feature Density for 3D Semantic Segmentation of Point Clouds
Shanghai Jiao Tong University（上海交通大学）；Beijing Advanced Innovation Center for Intelligent Robots and Systems（智能机器人与系统北京先进创新中心）；Beijing Institute of Technology（北京理工大学）；University of Cambridge（剑桥大学）
Guangming Wang, Yehui Yang, Huixin Zhang, Zhe Liu, Hesheng Wang
The semantic segmentation of point clouds is an important part of the environment perception for robots. However, it is difficult to directly adopt the traditional 3D convolution kernel to extract features from raw 3D point clouds because of the unstructured property of point clouds. In this paper, a spherical interpolated convolution operator is proposed to replace the traditional grid-shaped 3D convolution operator. This newly proposed feature extraction operator improves the accuracy of the network and reduces the parameters of the network. In addition, this paper analyzes the defect of point cloud interpolation methods based on the distance as the interpolation weight and proposes the self-learned distance-feature density by combining the distance and the feature correlation. The proposed method makes the feature extraction of spherical interpolated convolution network more rational and effective. The effectiveness of the proposed network is demonstrated on the 3D semantic segmentation task of point clouds. Experiments show that the proposed method achieves good performance on the ScanNet dataset and Paris-Lille-3D dataset.
We present a new and general framework for convolutional neural network operations on spherical (or omnidirectional) images. Our approach represents the surface as a graph of connected points that doesn't rely on a particular sampling strategy. Additionally, by using an interpolated version of SelectionConv, we can operate on the sphere while using existing 2D CNNs and their weights. Since our method leverages existing graph implementations, it is also fast and can be fine-tuned efficiently. Our method is also general enough to be applied to any surface type, even those that are topologically …
With the recent proliferation of consumer-grade 360° cameras, it is worth revisiting visual perception challenges with spherical cameras given the potential benefit of their global field of view. To this end we introduce a spherical convolutional hourglass network (SCHN) for the dense labeling on the sphere. The SCHN is invariant to camera orientation (lifting the usual requirement for `upright' panoramic images), and its design is scalable for larger practical datasets. Initial experiments show promising results on a spherical semantic segmentation task.
University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Applying convolutional neural networks to spherical images requires particular considerations. We look to the millennia of work on cartographic map projections to provide the tools to define an optimal representation of spherical images for the convolution operation. We propose a representation for deep spherical image inference based on the icosahedral Snyder equal-area (ISEA) projection, a projection onto a geodesic grid, and show that it vastly exceeds the state-of-the-art for convolution on spherical images, improving semantic segmentation results by 12.6%.
While 360° cameras offer tremendous new possibilities in vision, graphics, and augmented reality, the spherical images they produce make core feature extraction non-trivial. Convolutional neural networks (CNNs) trained on images from perspective cameras yield "flat" filters, yet 360° images cannot be projected to a single plane without significant distortion. A naive solution that repeatedly projects the viewing sphere to all tangent planes is accurate, but much too computationally intensive for real problems. We propose to learn a spherical convolutional network that translates a planar CNN t…
Point cloud is an important type of 3D representation. However, directly applying convolutions on point clouds is challenging due to the sparse, irregular and unordered data structure. In this paper, we propose a novel Interpolated Convolution operation, InterpConv, to tackle the point cloud feature learning and understanding problem. The key idea is to utilize a set of discrete kernel weights and interpolate point features to neighboring kernel-weight coordinates by an interpolation function for convolution. A normalization term is introduced to handle neighborhoods of different sparsity leve…
Accurate detection of lane and road markings is a task of great importance for intelligent vehicles. In existing approaches, the detection accuracy often degrades with the increasing distance. This is due to the fact that distant lane and road markings occupy a small number of pixels in the image, and scales of lane and road markings are inconsistent at various distances and perspectives. The Inverse Perspective Mapping (IPM) can be used to eliminate the perspective distortion, but the inherent interpolation can lead to artifacts especially around distant lane and road markings and thus has a …
Convolutional neural networks (CNNs) have been widely used in various vision tasks, e.g. image classification, semantic segmentation, etc. Unfortunately, standard 2D CNNs are not well suited for spherical signals such as panorama images or spherical projections, as the sphere is an unstructured grid. In this paper, we present Spherical Transformer which can transform spherical signals into vectors that can be directly processed by standard CNNs such that many well-designed CNNs architectures can be reused across tasks and datasets by pretraining. To this end, the proposed method first uses loc…
Omni-directional cameras have many advantages overconventional cameras in that they have a much wider field-of-view (FOV). Accordingly, several approaches have beenproposed recently to apply convolutional neural networks(CNNs) to omni-directional images for various visual tasks.However, most of them use image representations defined inthe Euclidean space after transforming the omni-directionalviews originally formed in the non-Euclidean space. Thistransformation leads to shape distortion due to nonuniformspatial resolving power and the loss of continuity. Theseeffects make existing convolution…
Efficient 3D affinely equivariant CNNs with adaptive fusion of augmented spherical Fourier-Bessel bases
School of Computer and Artificial Intelligence, Nanjing University of Finance and Economics（南京金融学院计算机与人工智能学院）；Interdisciplinary Center for Scientific Computing, Mannheim Institute for Intelligent Systems in Medicine, Medical Faculty Mannheim, Heidelberg University（科学计算交叉中心、医学智能系统研究所、曼海姆医学院、海德堡大学）；Computer Assisted Clinical Medicine, Mannheim Institute for Intelligent Systems in Medicine, Medical Faculty Mannheim, Heidelberg University（临床医学辅助计算机、医学智能系统研究所、曼海姆医学院、海德堡大学）；Department of Diagnostic and Interventional Radiology, University Hospital Bonn（诊断与介入放射科、波恩大学医院）；Interdisciplinary Center for Scientific Computing, Central Institute for Computer Engineering, CSZ Heidelberg Center for Model-Based AI, Data Analysis and Modeling in Medicine, Mannheim Institute for Intelligent Systems in Medicine, Medical Faculty Mannheim, Heidelberg University（科学计算交叉中心、计算机工程中央研究所、海德堡模型驱动AI中心、医学数据与建模中心、曼海姆医学智能系统研究所、曼海姆医学院、海德堡大学）
Semantic segmentation of 3D point cloud data is essential for enhanced high-level perception in autonomous platforms. Furthermore, given the increasing deployment of LiDAR sensors onboard of cars and drones, a special emphasis is also placed on non-computationally intensive algorithms that operate on mobile GPUs. Previous efficient state-of-the-art methods relied on 2D spherical projection of point clouds as input for 2D fully convolutional neural networks to balance the accuracy-speed trade-off. This paper introduces a novel approach for 3D point cloud semantic segmentation that exploits mult…
The Hong Kong University of Science and Technology（香港科技大学）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
In this paper, we propose PointSeg, a real-time end-to-end semantic segmentation method for road-objects based on spherical images. We take the spherical image, which is transformed from the 3D LiDAR point clouds, as input of the convolutional neural networks (CNNs) to predict the point-wise semantic map. To make PointSeg applicable on a mobile system, we build the model based on the light-weight network, SqueezeNet, with several improvements. It maintains a good balance between memory cost and prediction performance. Our model is trained on spherical images and label masks projected from the …
We propose a neural network for 3D point cloud processing that exploits `spherical' convolution kernels and octree partitioning of space. The proposed metric-based spherical kernels systematically quantize point neighborhoods to identify local geometric structures in data, while maintaining the properties of translation-invariance and asymmetry. The network architecture itself is guided by octree data structuring that takes full advantage of the sparse nature of irregular point clouds. We specify spherical kernels with the help of neurons in each layer that in turn are associated with spatial …
Kagenova Limited（Kagenova有限公司）；University College London (UCL)（伦敦大学学院）
No existing spherical convolutional neural network (CNN) framework is both computationally scalable and rotationally equivariant. Continuous approaches capture rotational equivariance but are often prohibitively computationally demanding. Discrete approaches offer more favorable computational performance but at the cost of equivariance. We develop a hybrid discrete-continuous (DISCO) group convolution that is simultaneously equivariant and computationally scalable to high-resolution. While our framework can be applied to any compact group, we specialize to the sphere. Our DISCO spherical convo…
Chalmers University of Technology（查尔姆斯理工大学）；Berlin Institute of Technology（柏林工业大学）；Berlin Institute for the Foundations of Learning and Data (BIFOLD)（柏林学习与数据基础研究所（BIFOLD））；University of Gothenburg（哥德堡大学）；Umeå University（于默奥大学）；Zenseact（Zenseact（智己汽车科技有限公司））
We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with an increasing amount of data augmentation. The chosen architectures can be considered baseline references for the respective design paradigms. Our models are trained and evaluated on single or multiple items from the MNIST or FashionMNIST dataset projected onto the sphere. For the task of image classification, which is inherently rotationally invariant, we f…
UC Berkeley（加州大学伯克利分校）；Stanford University（斯坦福大学）；Lawrence Berkeley Nat’l Lab（劳伦斯伯克利国家实验室）；Technical University of Munich（慕尼黑工业大学）
We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. To this end, we replace conventional convolution kernels with linear combinations of differential operators that are weighted by learnable parameters. Differential operators can be efficiently estimated on unstructured grids using one-ring neighbors, and learnable parameters can be optimized through standard back-propagation. As a result, we obtain extremely efficien…
Chalmers University of Technology（查尔姆斯理工大学）；Gothenburg University（哥德堡大学）；Umeå University（于默奥大学）；Zenseact
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using principal bundles with structure group $K$ and equivariant maps between sections of associated vector bundles. We also discuss group equivariant neural networks for homogeneous spaces $\mathcal{M}=G/K$, which are instead equivariant with respect to the global symmetry $G$ on $\mathcal{M}$. Group equivariant layers can be interpreted as intertwiners between ind…
Leveraging SO(3)-steerable convolutions for pose-robust semantic segmentation in 3D medical data
Support Center for Advanced Neuroimaging (SCAN), University Institute of Diagnostic and Interventional Neuroradiology, University of Bern, Inselspital, Bern University Hospital（高级神经影像支持中心（SCAN）、伯尔尼大学诊断与介入神经放射学研究所、伯尔尼大学、因塞尔斯皮塔尔医院、伯尔尼大学医院）；NVIDIA（英伟达）
We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations…
In this paper, we develop a general theoretical framework for constructing Haar-type tight framelets on any compact set with a hierarchical partition. In particular, we construct a novel area-regular hierarchical partition on the 2-sphere and establish its corresponding spherical Haar tight framelets with directionality. We conclude by evaluating and illustrating the effectiveness of our area-regular spherical Haar tight framelets in several denoising experiments. Furthermore, we propose a convolutional neural network (CNN) model for spherical signal denoising which employs the fast framelet d…
The presence of certain clinical dermoscopic features within a skin lesion may indicate melanoma, and automatically detecting these features may lead to more quantitative and reproducible diagnoses. We reformulate the task of classifying clinical dermoscopic features within superpixels as a segmentation problem, and propose a fully convolutional neural network to detect clinical dermoscopic features from dermoscopy skin lesion images. Our neural network architecture uses interpolated feature maps from several intermediate network layers, and addresses imbalanced labels by minimizing a negative…
Wuhan University（武汉大学）；Finnish Geospatial Research Institute（芬兰地理空间研究所）；Hubei University of Technology（湖北工业大学）
As an important technology in 3D mapping, autonomous driving, and robot navigation, LiDAR odometry is still a challenging task. Appropriate data structure and unsupervised deep learning are the keys to achieve an easy adjusted LiDAR odometry solution with high performance. Utilizing compact 2D structured spherical ring projection model and voxel model which preserves the original shape of input data, we propose a fully unsupervised Convolutional Auto-Encoder based LiDAR Odometry (CAE-LO) that detects interest points from spherical ring data using 2D CAE and extracts features from multi-resolut…
Zhejiang University（浙江大学）；Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies（阿里巴巴-浙江大学前沿技术联合研究院）；Hikvision Research Institute（海康威视研究院）
LiDAR sensor is essential to the perception system in autonomous vehicles and intelligent robots. To fulfill the real-time requirements in real-world applications, it is necessary to efficiently segment the LiDAR scans. Most of previous approaches directly project 3D point cloud onto the 2D spherical range image so that they can make use of the efficient 2D convolutional operations for image segmentation. Although having achieved the encouraging results, the neighborhood information is not well-preserved in the spherical projection. Moreover, the temporal information is not taken into consider…
In this paper, we explore an efficient variant of convolutional sparse coding with unit norm code vectors where reconstruction quality is evaluated using an inner product (cosine distance). To use these codes for discriminative classification, we describe a model we term Energy-Based Spherical Sparse Coding (EB-SSC) in which the hypothesized class label introduces a learned linear bias into the coding step. We evaluate and visualize performance of stacking this encoder to make a deep layered model for image classification.
Given a single RGB panorama, the goal of 3D layout reconstruction is to estimate the room layout by predicting the corners, floor boundary, and ceiling boundary. A common approach has been to use standard convolutional networks to predict the corners and boundaries, followed by post-processing to generate the 3D layout. However, the space-varying distortions in panoramic images are not compatible with the translational equivariance property of standard convolutions, thus degrading performance. Instead, we propose to use spherical convolutions. The resulting network, which we call OmniLayout pe…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；School of Electrical Engineering（电气工程学院）
With the advance in user-friendly and powerful video editing tools, anyone can easily manipulate videos without leaving prominent visual traces. Frame-rate up-conversion (FRUC), a representative temporal-domain operation, increases the motion continuity of videos with a lower frame-rate and is used by malicious counterfeiters in video tampering such as generating fake frame-rate video without improving the quality or mixing temporally spliced videos. FRUC is based on frame interpolation schemes and subtle artifacts that remain in interpolated frames are often difficult to distinguish. Hence, d…
Convolutional neural networks (CNNs) have become increasingly popular for solving a variety of computer vision tasks, ranging from image classification to image segmentation. Recently, autonomous vehicles have created a demand for depth information, which is often obtained using hardware sensors such as Light detection and ranging (LIDAR). Although it can provide precise distance measurements, most LIDARs are still far too expensive to sell in mass-produced consumer vehicles, which has motivated methods to generate depth information from commodity automotive sensors like cameras. In this paper…
University of Applied Sciences Western Switzerland (HES-SO)（瑞士西部应用科学大学）；CHUV（洛桑大学医院）；Harvard School of Engineering and Applied Sciences（哈佛工程与应用科学学院）
Locally Rotation Invariant (LRI) operators have shown great potential in biomedical texture analysis where patterns appear at random positions and orientations. LRI operators can be obtained by computing the responses to the discrete rotation of local descriptors, such as Local Binary Patterns (LBP) or the Scale Invariant Feature Transform (SIFT). Other strategies achieve this invariance using Laplacian of Gaussian or steerable wavelets for instance, preventing the introduction of sampling errors during the discretization of the rotations. In this work, we obtain LRI operators via the local pr…
School of Computer Science and Software Engineering（计算机科学与软件工程学院）；The University of Western Australia（西澳大学）
We propose an octree guided neural network architecture and spherical convolutional kernel for machine learning from arbitrary 3D point clouds. The network architecture capitalizes on the sparse nature of irregular point clouds, and hierarchically coarsens the data representation with space partitioning. At the same time, the proposed spherical kernels systematically quantize point neighborhoods to identify local geometric structures in the data, while maintaining the properties of translation-invariance and asymmetry. We specify spherical kernels with the help of network neurons that in turn …
The recent advances in deep learning indicate significant progress in the field of single image super-resolution. With the advent of these techniques, high-resolution image with high peak signal to noise ratio (PSNR) and excellent perceptual quality can be reconstructed. The major challenges associated with existing deep convolutional neural networks are their computational complexity and time; the increasing depth of the networks, often result in high space complexity. To alleviate these issues, we developed an innovative shallow residual feature representative network (SRFRN) that uses a bic…
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）；Massachusetts Institute of Technology（麻省理工学院）
Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and $SO(3)$ convolutions, researchers have recently developed deep learning methods better suited for classifying spherical images. These newly proposed convolutional layers naturally extend the notion of convolution to functions on the unit sphere $S^2$ and the group of rotations $SO(3)$ and these layers are equivariant to 3D rotations. In this paper, we consider th…
Swiss Data Science Center (SDSC)（瑞士数据科学中心）；EPFL（洛桑联邦理工学院）；ETH Zurich（苏黎世联邦理工学院）
Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning toolbox and have led to many breakthroughs in Artificial Intelligence. These networks have mostly been developed for regular Euclidean domains such as those supporting images, audio, or video. Because of their success, CNN-based methods are becoming increasingly popular in Cosmology. Cosmological data often comes as spherical maps, which make the use of the traditional CNNs more complicated. The commonly used pixelization scheme for spherical maps is the Hierarchical Equal Area isoLatitude Pixelisation (HEALPix). We pr…
Convolutional Neural Networks have revolutionized vision applications. There are image domains and representations, however, that cannot be handled by standard CNNs (e.g., spherical images, superpixels). Such data are usually processed using networks and algorithms specialized for each type. In this work, we show that it may not always be necessary to use specialized neural networks to operate on such spaces. Instead, we introduce a new structured graph convolution operator that can copy 2D convolution weights, transferring the capabilities of already trained traditional CNNs to our new graph …
Image2Flow: A hybrid image and graph convolutional neural network for rapid patient-specific pulmonary artery segmentation and CFD flow field calculation from 3D cardiac MRI data
Institute of Cardiovascular Science, University College London（伦敦大学学院心血管科学研究所）
Key Laboratory of Biomedical Engineering of Ministry of Education, Zhejiang University（浙江大学教育部生物医学工程重点实验室）；Department of Radiology and BRIC, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校放射科和BRIC（生物医学研究信息中心））；Department of Psychiatry, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校精神病学系）
Convolutional Neural Networks (CNNs) have been providing the state-of-the-art performance for learning-related problems involving 2D/3D images in Euclidean space. However, unlike in the Euclidean space, the shapes of many structures in medical imaging have a spherical topology in a manifold space, e.g., brain cortical or subcortical surfaces represented by triangular meshes, with large inter-subject and intrasubject variations in vertex number and local connectivity. Hence, there is no consistent neighborhood definition and thus no straightforward convolution/transposed convolution operations …
University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these two components, freeing the operation from the confines of the image grid and allowing the kernel to process any type of structured data. As a test case, we demonstrate its use by applying it to dense inference on spherical data. We perform an in-depth study of existing spherical image convolution methods and propose an improved sampling method for equirectang…
Singapore University of Technology and Design（新加坡科技设计大学）；The University of Tokyo（东京大学）；Hong Kong University of Science and Technology（香港科技大学）
Deep learning with 3D data has progressed significantly since the introduction of convolutional neural networks that can handle point order ambiguity in point cloud data. While being able to achieve good accuracies in various scene understanding tasks, previous methods often have low training speed and complex network architecture. In this paper, we address these problems by proposing an efficient end-to-end permutation invariant convolution for point cloud deep learning. Our simple yet effective convolution operator named ShellConv uses statistics from concentric spherical shells to define re…
This work aims to estimate 6Dof (6D) object pose in background clutter. Considering the strong occlusion and background noise, we propose to utilize the spatial structure for better tackling this challenging task. Observing that the 3D mesh can be naturally abstracted by a graph, we build the graph using 3D points as vertices and mesh connections as edges. We construct the corresponding mapping from 2D image features to 3D points for filling the graph and fusion of the 2D and 3D features. Afterward, a Graph Convolutional Network (GCN) is applied to help the feature exchange among objects' poin…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Facebook AI Research（Facebook人工智能研究院）
Ideally, 360° imagery could inherit the deep convolutional neural networks (CNNs) already trained with great success on perspective projection images. However, existing methods to transfer CNNs from perspective to spherical images introduce significant computational costs and/or degradations in accuracy. In this work, we present the Kernel Transformer Network (KTN). KTNs efficiently transfer convolution kernels from perspective images to the equirectangular projection of 360° images. Given a source CNN for perspective images as input, the KTN produces a function parameterized by a polar angle …
School of Computer Science and Engineering, Chung-Ang University（韩国中央大学计算机科学与工程学院）；Twelve Labs（Twelve Labs公司）
Using convolutional neural networks for 360images can induce sub-optimal performance due to distortions entailed by a planar projection. The distortion gets deteriorated when a rotation is applied to the 360image. Thus, many researches based on convolutions attempt to reduce the distortions to learn accurate representation. In contrast, we leverage the transformer architecture to solve image classification problems for 360images. Using the proposed transformer for 360images has two advantages. First, our method does not require the erroneous planar projection process by sampling pixels from th…
In this work, we exploit a depth estimation Fully Convolutional Residual Neural Network (FCRN) for in-air perspective images to estimate the depth of underwater perspective and omni-directional images. We train one conventional and one spherical FCRN for underwater perspective and omni-directional images, respectively. The spherical FCRN is derived from the perspective FCRN via a spherical longitude-latitude mapping. For that, the omni-directional camera is modeled as a sphere, while images captured by it are displayed in the longitude-latitude form. Due to the lack of underwater datasets, we …
Macquarie University（麦考瑞大学）；Australian Institute of Health Innovation（澳大利亚健康创新研究院）
Magnetic Resonance Imaging (MRI) is used in everyday clinical practice to assess brain tumors. Several automatic or semi-automatic segmentation algorithms have been introduced to segment brain tumors and achieve an expert-like accuracy. Deep Convolutional Neural Networks (DCNN) have recently shown very promising results, however, DCNN models are still far from achieving clinically meaningful results mainly because of the lack of generalization of the models. DCNN models need large annotated datasets to achieve good performance. Models are often optimized on the domain dataset on which they hav…
Georgia Institute of Technology（佐治亚理工学院）；Sandia National Laboratories（桑迪亚国家实验室）
Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional architecture for learning over concentric spherical feature maps, of which the single sphere representation is a special case. Our hierarchical architecture is based on alternatively learning to incorporate both intra-sphere and inter-sphere information. We show the applicability of our method for two different types of 3D inputs, mesh objects, which can be …
New York University Abu Dhabi（纽约大学阿布扎比分校）；Inception Institute of Artificial Intelligence（起源人工智能研究院）；New York University（纽约大学）
Analyzing the structure of proteins is a key part of understanding their functions and thus their role in biology at the molecular level. In addition, design new proteins in a methodical way is a major engineering challenge. In this work, we introduce a joint geometric-neural networks approach for comparing, deforming and generating 3D protein structures. Viewing protein structures as 3D open curves, we adopt the Square Root Velocity Function (SRVF) representation and leverage its suitable geometric properties along with Deep Residual Networks (ResNets) for a joint registration and comparison.…
Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D…
Convolutional neural networks (CNNs) constructed natively on the sphere have been developed recently and shown to be highly effective for the analysis of spherical data. While an efficient framework has been formulated, spherical CNNs are nevertheless highly computationally demanding; typically they cannot scale beyond spherical signals of thousands of pixels. We develop scattering networks constructed natively on the sphere that provide a powerful representational space for spherical data. Spherical scattering networks are computationally scalable and exhibit rotational equivariance, while th…
University of Manchester（曼彻斯特大学）；University of Sheffield（谢菲尔德大学）
High resolution diffusion MRI (dMRI) data is often constrained by limited scanning time in clinical settings, thus restricting the use of downstream analysis techniques that would otherwise be available. In this work we develop a 3D recurrent convolutional neural network (RCNN) capable of super-resolving dMRI volumes in the angular (q-space) domain. Our approach formulates the task of angular super-resolution as a patch-wise regression using a 3D autoencoder conditioned on target b-vectors. Within the network we use a convolutional long short term memory (ConvLSTM) cell to model the relationsh…
Macquarie University（麦考瑞大学）；Australian Institute of Health Innovation（澳大利亚健康创新研究院）
Pre-processing and Data Augmentation play an important role in Deep Convolutional Neural Networks (DCNN). Whereby several methods aim for standardization and augmentation of the dataset, we here propose a novel method aimed to feed DCNN with spherical space transformed input data that could better facilitate feature learning compared to standard Cartesian space images and volumes. In this work, the spherical coordinates transformation has been applied as a preprocessing method that, used in conjunction with normal MRI volumes, improves the accuracy of brain tumor segmentation and patient overa…
Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed that such models can generally be understood as performing convolutions with G-steerable kernels, that is, kernels that satisfy an equivariance constraint themselves. While the G-steerability constraint has been derived, it has to date only been solved for specific use cases - a general characterization of G-steerable kernel spaces is still missing. This wo…
FaceBook（脸书）；University of California, Berkeley（加州大学伯克利分校）；University of Florida（佛罗里达大学）
Convolutional neural networks have been highly successful in image-based learning tasks due to their translation equivariance property. Recent work has generalized the traditional convolutional layer of a convolutional neural network to non-Euclidean spaces and shown group equivariance of the generalized convolution operation. In this paper, we present a novel higher order Volterra convolutional neural network (VolterraNet) for data defined as samples of functions on Riemannian homogeneous spaces. Analagous to the result for traditional convolutions, we prove that the Volterra functional convo…
School of Computer and Information, Hefei University of Technology（合肥工业大学计算机与信息学院）；School of Electrical Engineering and Automation, Hefei University of Technology（合肥工业大学电气与自动化工程学院）；The University of Electro-Communications,Japan（日本电气通信大学）
Field of view (FoV) prediction is critical in 360-degree video multicast, which is a key component of the emerging Virtual Reality (VR) and Augmented Reality (AR) applications. Most of the current prediction methods combining saliency detection and FoV information neither take into account that the distortion of projected 360-degree videos can invalidate the weight sharing of traditional convolutional networks, nor do they adequately consider the difficulty of obtaining complete multi-user FoV information, which degrades the prediction performance. This paper proposes a spherical convolution-e…
Shanghai Jiao Tong University（上海交通大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
Pooling and unpooling are two essential operations in constructing hierarchical spherical convolutional neural networks (HS-CNNs) for comprehensive feature learning in the spherical domain. Most existing models employ downsampling-based pooling, which will inevitably incur information loss and cannot adapt to different spherical signals and tasks. Besides, the preserved information after pooling cannot be well restored by the subsequent unpooling to characterize the desirable features for a task. In this paper, we propose a novel framework of HS-CNNs with a lifting structure to learn adaptive …
University College London（伦敦大学学院）；Kagenova Limited（Kagenova有限公司）
This paper demonstrates spherical convolutional neural networks (S-CNN) offer distinct advantages over conventional fully-connected networks (FCN) at estimating scalar parameters of tissue microstructure from diffusion MRI (dMRI). Such microstructure parameters are valuable for identifying pathology and quantifying its extent. However, current clinical practice commonly acquires dMRI data consisting of only 6 diffusion weighted images (DWIs), limiting the accuracy and precision of estimated microstructure indices. Machine learning (ML) has been proposed to address this challenge. However, exis…
