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 equirectangular images. Then, we discuss the impact of data discretization when deriving a sampling function, highlighting drawbacks of the cube map representation for spherical data. Finally, we illustrate how mapped convolutions enable us to convolve directly on a mesh by projecting the spherical image onto a geodesic grid and training on the textured mesh. This method exceeds the state of the art for spherical depth estimation by nearly 17%. Our findings suggest that mapped convolutions can be instrumental in expanding the application scope of convolutional neural networks.
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 …
Point cloud analysis without pose priors is very challenging in real applications, as the orientations of point clouds are often unknown. In this paper, we propose a brand new point-set learning framework PRIN, namely, Pointwise Rotation-Invariant Network, focusing on rotation-invariant feature extraction in point clouds analysis. We construct spherical signals by Density Aware Adaptive Sampling to deal with distorted point distributions in spherical space. In addition, we propose Spherical Voxel Convolution and Point Re-sampling to extract rotation-invariant features for each point. Our netwo…
We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid CNN kernels, the spherical kernel maintains translation-invariance and asymmetry properties, where the former guarantees weight sharing among similar local structures in the data and the latter facilitates fine geometric learning. The proposed kernel is applied to graph neural networks without edge-dependent filter generation, making it computationally attrac…
Poznan University of Technology（波兹南理工大学）；Warsaw University of Technology（华沙理工大学）
The 3D LiDAR place recognition aims to estimate a coarse localization in a previously seen environment based on a single scan from a rotating 3D LiDAR sensor. The existing solutions to this problem include hand-crafted point cloud descriptors (e.g., ScanContext, M2DP, LiDAR IRIS) and deep learning-based solutions (e.g., PointNetVLAD, PCAN, LPDNet, DAGC, MinkLoc3D), which are often only evaluated on accumulated 2D scans from the Oxford RobotCar dataset. We introduce MinkLoc3D-SI, a sparse convolution-based solution that utilizes spherical coordinates of 3D points and processes the intensity of …
University of Bologna（博洛尼亚大学）；Vislab Srl - Ambarella Inc（Vislab Srl - 安霸公司）；University of Parma（帕尔马大学）
Generating dense point clouds from sparse raw data benefits downstream 3D understanding tasks, but existing models are limited to a fixed upsampling ratio or to a short range of integer values. In this paper, we present APU-SMOG, a Transformer-based model for Arbitrary Point cloud Upsampling (APU). The sparse input is firstly mapped to a Spherical Mixture of Gaussians (SMOG) distribution, from which an arbitrary number of points can be sampled. Then, these samples are fed as queries to the Transformer decoder, which maps them back to the target surface. Extensive qualitative and quantitative e…
RMIT University（皇家墨尔本理工大学）；University College London（伦敦大学学院）
In this paper, we present a robust spherical harmonics approach for the classification of point cloud-based objects. Spherical harmonics have been used for classification over the years, with several frameworks existing in the literature. These approaches use variety of spherical harmonics based descriptors to classify objects. We first investigated these frameworks robustness against data augmentation, such as outliers and noise, as it has not been studied before. Then we propose a spherical convolution neural network framework for robust object classification. The proposed framework uses the…
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 …
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 …
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%.
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…
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 …
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）
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 poi…
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 …
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…
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…
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…
Möbius transformations play an important role in both geometry and spherical image processing - they are the group of conformal automorphisms of 2D surfaces and the spherical equivalent of homographies. Here we present a novel, Möbius-equivariant spherical convolution operator which we call Möbius convolution, and with it, develop the foundations for Möbius-equivariant spherical CNNs. Our approach is based on a simple observation: to achieve equivariance, we only need to consider the lower-dimensional subgroup which transforms the positions of points as seen in the frames of their neighbors. T…
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…
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…
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…
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…
University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
In this work, we propose "tangent images," a spherical image representation that facilitates transferable and scalable $360^\circ$ computer vision. Inspired by techniques in cartography and computer graphics, we render a spherical image to a set of distortion-mitigated, locally-planar image grids tangent to a subdivided icosahedron. By varying the resolution of these grids independently of the subdivision level, we can effectively represent high resolution spherical images while still benefiting from the low-distortion icosahedral spherical approximation. We show that training standard convolu…
TU Wien（维也纳技术大学）；University of Technology Sydney（悉尼科技大学）
While object semantic understanding is essential for most service robotic tasks, 3D object classification is still an open problem. Learning from artificial 3D models alleviates the cost of annotation necessary to approach this problem, but most methods still struggle with the differences existing between artificial and real 3D data. We conjecture that the cause of those issue is the fact that many methods learn directly from point coordinates, instead of the shape, as the former is hard to center and to scale under variable occlusions reliably. We introduce spherical kernel point convolutions…
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…
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…
GRASP Laboratory（GRASP实验室）；University of Pennsylvania（宾夕法尼亚大学）；Google Research（谷歌研究院）
Learning equivariant representations is a promising way to reduce sample and model complexity and improve the generalization performance of deep neural networks. The spherical CNNs are successful examples, producing SO(3)-equivariant representations of spherical inputs. There are two main types of spherical CNNs. The first type lifts the inputs to functions on the rotation group SO(3) and applies convolutions on the group, which are computationally expensive since SO(3) has one extra dimension. The second type applies convolutions directly on the sphere, which are limited to zonal (isotropic) …
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…
Symmetry-Aware 9D Pose Estimation with Sim(3)-Consistent Feature and Spherical Inception Convolution
National Engineering Research Center for Robot Visual Perception and Control, School of Robotics and Artificial Intelligence, Hunan University（机器人视觉感知与控制国家工程研究中心，机器人与人工智能学院，湖南大学）；Beijing Spacecrafts, China Academy of Space Technology（北京航天器，中国航天科技研究院）；School of Computing and Information Systems, The University of Melbourne（计算与信息学院，墨尔本大学）
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…
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…
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…
Indian Institute of Technology Gandhinagar（印度理工学院甘地纳加尔分校）；Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）
The process of rendering high dynamic range (HDR) images to be viewed on conventional displays is called tone mapping. However, tone mapping introduces distortions in the final image which may lead to visual displeasure. To quantify these distortions, we introduce a novel no-reference quality assessment technique for these tone mapped images. This technique is composed of two stages. In the first stage, we employ a convolutional neural network (CNN) to generate quality aware maps (also known as distortion maps) from tone mapped images by training it with the ground truth distortion maps. In th…
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 …
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…
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…
With the development of Earth observation technology, very-high-resolution (VHR) image has become an important data source of change detection. Nowadays, deep learning methods have achieved conspicuous performance in the change detection of VHR images. Nonetheless, most of the existing change detection models based on deep learning require annotated training samples. In this paper, a novel unsupervised model called kernel principal component analysis (KPCA) convolution is proposed for extracting representative features from multi-temporal VHR images. Based on the KPCA convolution, an unsupervi…
Peking University（北京大学）；The Chinese University of Hong Kong（香港中文大学）；Pazhou Lab（琶洲实验室）
Spherical signals exist in many applications, e.g., planetary data, LiDAR scans and digitalization of 3D objects, calling for models that can process spherical data effectively. It does not perform well when simply projecting spherical data into the 2D plane and then using planar convolution neural networks (CNNs), because of the distortion from projection and ineffective translation equivariance. Actually, good principles of designing spherical CNNs are avoiding distortions and converting the shift equivariance property in planar CNNs to rotation equivariance in the spherical domain. In this …
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…
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Swiss Data Science Center (SDSC)（瑞士数据科学中心）
Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the sampled sphere, strikes a controllable balance between these two desiderata. This contribution is twofold. First, we study both theoretically and empirically how equivariance is affected by the underlying graph with respect to the number of vertices and neighbors. Second, we evaluate DeepSphere on relevant problems. Experiments show state-of-the-art performance and demonstrates the efficiency and flexibilit…
