Predicting the saliency map of a 360-degree video is the key for various downstream tasks, such as saliency-based compression and tile-based adaptive streaming. Besides static salient objects, the moving target will also contribute to the saliency map. Therefore, the joint exploitation of spherical spatio-temporal information is necessary for an accurate saliency prediction. The spherical spatial feature extraction, however, is hindered by the non-Euclidean geometric nature of spherical data, which imposes difficulty on direct extraction of the spatial features with traditional convolutional neural networks (CNNs). While the efficient exploitation of temporal correlation between these spherical spatial features remains another challenge, which requires the extraction of spherical optical flows for explicit motion information. To address these, in this paper, we first propose a spherical graph-based Farneback algorithm to extract the spherical optical flows directly in the sphere domain, by leveraging the GICOPix uniform sampling scheme. We then design a 3D separable graph convolutional network-based saliency prediction framework, named 360Spred, by taking both the spherical frames and spherical optical flows as input. The proposed 360Spred framework is based on the U-Net structure, with a 3D separable graph convolution (3DSGC) operator that directly extracts the visual and motion features in the sphere domain and exploits temporal correlation of both the high-level and low-level spatial features. Experimental results on two public datasets show that 360Spred can achieve a better performance than other baseline models in terms of the saliency prediction accuracy for 360-degree videos.

Viewers of 360-degree videos are provided with both visual modality to characterize their surrounding views and audio modality to indicate the sound direction. Though both modalities are important for saliency prediction, little work has been done by jointly exploiting them, which is mainly due to the lack of audio-visual saliency datasets and insufficient exploitation of the multi-modality. In this article, we first construct an audio-visual saliency dataset with 57 360-degree videos watched by 63 viewers. Through a deep analysis of the constructed dataset, we find that the human gaze can be attracted by the auditory cues, resulting in a more concentrated saliency map if the sound source's location is further provided. To jointly exploit the visual and audio features and their correlation, we further design a saliency prediction network for 360-degree videos (SVGC-AVA) based on spherical vector-based graph convolution and audio-visual attention. The proposed spherical vector-based graph convolution can process visual and audio features directly in the sphere domain, thus avoiding projection distortion incurred by traditional CNN-based predictors. In addition, the audio-visual attention scheme explores self-modal and cross-modal correlation for both modalities, which are further hierarchically processed with the U-Net's multi-scale structure of SVGC-AVA. Evaluations on both our and public datasets validate that SVGC-AVA can achieve higher prediction accuracy, both qualitatively and subjectively.

Learning a rotation-invariant (RI) representation is of significant importance for real-world point cloud segmentation that is perturbed by arbitrary rotations. Recent principal component analysis (PCA)-based methods provide an effective alternative to align point clouds and produce the RI representation under the preservation of global information. However, conventional PCA with 3-D coordinates cannot fully represent high-dimensional geometric structures like surfaces and curves and cannot uniformly align these structures for learning RI representation. In this paper, we propose a novel rotation-invariant method for point cloud segmentation, which leverages kernel PCA (KPCA) for aligning point clouds in a projected high-dimensional space via non-linear mapping and develops a Geometry-based Weighted Convolution (GWConv) to distinguish part boundaries during segmentation. Specifically, the KPCA produces a RI representation with polynomial kernels for effectively representing complicated geometric structures in point clouds. Moreover, the GWConv incorporates geometric structures into convolution and enhances neighboring points with similar geometry for fine-grained segmentation based on the RI representation. Experimental results demonstrate that the proposed method can achieve competitive performance with the state-of-the-arts and outperforms existing PCA-based methods in part segmentation on ShapeNet. Furthermore, it achieves evident performance gains on complicated 3-D shapes such as Earphone and Car and facilitates segmentation around the part boundaries.

Graph convolutional networks (GCNs) are widely adopted for spherical data processing, striking a balance between rotation equivariance and computation efficiency. However, current GCN-based approaches either apply radial filters with a fixed convolution kernel, or adopt attention schemes to learn a variable kernel based only on node features, which lack expressiveness and may suffer over-smoothing problem. To address this, in this paper, we propose a global-local attention-based spherical graph convolution (GlasGC) for spherical data representation. Specifically, the designed graph convolution includes a structure-enhanced local attention module to estimate the structure correlation efficiently based on topological characteristics of the given spherical graph. The structure correlation is then incorporated with the feature correlation to form the local attention that determines importance of a neighbor node to the center node. We also design a global attention module to obtain the importance scores of different nodes based on both node features and graph topology, which acts as a message-passing enhancer for informative nodes and can relieve the over-smoothing problem. Based on our proposed GlasGC, we design specific GlasGCNs for classification and semantic segmentation of spherical data. Empirical evaluations on these tasks demonstrate that our proposed GlasGCNs can generally achieve better classification and segmentation performance.

Convolutional neural networks (CNNs) designed for low-dimensional regular grids will unfortunately lead to non-optimal solutions for analyzing spherical images, due to their different geometrical properties from planar images. In this paper, we generalize the grid-based CNNs to a non-Euclidean space by taking into account the geometry of spherical surfaces and propose a Spherical Graph Convolutional Network (SGCN) to encode rotation equivariant representations. Specifically, we propose a spherical graph construction criterion showing that a graph needs to be regular by evenly covering the spherical surfaces in order to design a rotation equivariant graph convolutional layer. For the practical case where the perfectly regular graph does not exist, we design two quantitative measures to evaluate the degree of irregularity for a spherical graph. The Geodesic ICOsahedral Pixelation (GICOPix) is adopted to construct spherical graphs with the minimum degree of irregularity compared to the current popular pixelation schemes. In addition, we design a hierarchical pooling layer to keep the rotation-equivariance, followed by a transition layer to enforce the invariance to the rotations for spherical image classification. We evaluate the proposed graph convolutional layers with different pixelations schemes in terms of equivariance errors. We also assess the effectiveness of the proposed SGCN in fulfilling rotation-invariance by the invariance error of the transition layers and recognizing the spherical images and 3D objects.

The non-Euclidean geometry characteristic poses a challenge to the saliency prediction for 360-degree images. Since spherical data cannot be projected onto a single plane without distortion, existing saliency prediction methods based on traditional CNNs are inefficient. In this paper, we propose a saliency prediction framework for 360-degree images based on graph convolutional networks (SalGCN), which directly applies to the spherical graph signals. Specifically, we adopt the Geodesic ICOsahedral Pixelation (GICOPix) to construct a spherical graph signal from a spherical image in equirectangular projection (ERP) format. We then propose a graph saliency prediction network to directly extract the spherical features and generate the spherical graph saliency map, where we design an unpooling method suitable for spherical graph signals based on linear interpolation. The network training process is realized by modeling the node regression problem of the input and output spherical graph signals, where we further design a Kullback-Leibler (KL) divergence loss with sparse consistency to make the sparseness of the saliency map closer to the ground truth. Eventually, to obtain the ERP format saliency map for evaluation, we further propose a spherical crown-based (SCB) interpolation method to convert the output spherical graph saliency map into a saliency map in ERP format. Experiments show that our SalGCN can achieve comparable or even better saliency prediction performance both subjectively and objectively, with a much lower computation complexity.

Sending only the viewport of interest provides a solution for 360-degree video streaming under the current bandwidth-constrained infrastructure. To this end, the user viewport requires to be prefetched in advance by conducting viewport prediction. To more accurately capture the nonlinear and long-term dependent relation between the future and past viewports, we develop a single viewport prediction model using convolutional neural network (CNN), in which the pooling layers are dropped and more convolutional layers are added for stronger nonlinear fitting ability. Further, we design a viewport trajectory prediction model based on recurrent neural network (RNN) which learns long-term dependency in sequential viewports. Specially, it is capable to estimate future viewport trajectory and support variable-size prediction window with low complexity. Finally, a correlation filter-based viewport tracker (CFVT) is proposed to perform content-aware viewport prediction. The combination of the RNN and the CFVT through a fusion model enables them to complement each other which is validated by significant improvement in prediction accuracy.

How to balance the tradeoff between the user experience and bandwidth utilization emerges a critical challenge for multi-user 360-degree video adaptive streaming. This paper studies the server-side rate adaptation strategy for multiple users which are competing for the server bandwidth capacity. A tile visibility probability model is established, by which the tiles are classified into predicted, marginal and invisible types. A fine-grained rate adaptation problem is formulated as a nonlinear integer programming (NIP) problem, which aims at maximizing the video quality and navigation smoothness for multiple users. Thereafter, a steepest ascent algorithm with feasible starting point is developed to solve the proposed NIP problem in polynomial time. Finally, simulation results verify the performance of the proposed rate adaptation strategy.