arXiv subjects

Hong Zhang

Publications and source records attributed to Hong Zhang.

At least 271 records · Page 15Linked to original sources

arXiv2019

Prescribed $Q$-curvature flow on closed manifolds of even dimension

On a closed Riemannian manifold $(M,g_0)$ of even dimension $n \geqslant 4$, the well-known prescribed $Q$-curvature problem asks whether or not there is a metric $g$ comformal to $g_0$ such that its $Q$-curvature, associated with the GJMS operator $\mathbf P_g$, is equal to a given function $f$. Letting $g = e^{2u}g_0$, this problem is equivalent to solving \[ \mathbf P_{g_0} u+Q_{g_0} = f e^{nu}, \] where $Q_{g_0}$ denotes the $Q$-curvature of $g_0$. The primary objective of the paper is to introduce the following negative gradient flow of the time dependent metric $g(t)$ conformal to $g_0$, \[ \frac{\partial g (t)}{\partial t}= -2\Big(Q_{g (t)} - \frac{\int_M f Q_{g(t)} dμ_{g(t)} }{\int_M f^2 dμ_{g(t)} }f \Big)g(t) \quad \text{ for } t >0, \] to study the problem of prescribing $Q$-curvature. Since $\int_M Q_g dμ_g$ is conformally invariant, our analysis depends on the size of $\int_M Q_{g_0} dμ_{g_0}$, which is assumed to satisfy \[ \int_M Q_0 dμ_{g_0} \ne k (n-1)! \, {\rm vol}(\mathbb S^n) \quad \text{ for all } \; k = 2,3,... \] The paper is twofold. First, we identify suitable conditions on $f$ such that the gradient flow defined as above is defined to all time and convergent, as time goes to infinity, sequentially or uniformly. Second, we show that various existence theorems for prescribed $Q$-curvature problem can be derived from the convergence of the flow.

math.AP↗

arXiv2019

Mass and energy conservative high order diagonally implicit Runge--Kutta schemes for nonlinear Schrödinger equation in one and two dimensions

We present and analyze a series of conservative diagonally implicit Runge--Kutta schemes for the nonlinear Schrödiner equation. With the application of the newly developed invariant energy quadratization approach, these schemes possess not only high accuracy , high order convergence (up to fifth order) and efficiency due to diagonally implicity but also mass and energy conservative properties. Both theoretical analysis and numerical experiments of one- and two-dimensional dynamics are carried out to verify the invariant conservative properties, convergence orders and longtime simulation stability.

math.NA↗

arXiv2019

Stability Analysis of Interface Conditions for Ocean-Atmosphere Coupling

In this paper we analyze the stability of different coupling strategies for multidomain PDEs that arise in general circulation models used in climate simulations. We focus on fully coupled ocean-atmosphere models that are needed to represent and understand the complicated interactions of these two systems, becoming increasingly important in climate change assessment in recent years. Numerical stability issues typically arise because of different time-stepping strategies applied to the coupled PDE system. In particular, the contributing factors include using large time steps, lack of accurate interface flux, and singe-iteration coupling. We investigate the stability of the coupled ocean-atmosphere models for various interface conditions such as the Dirichlet-Neumann condition and the bulk interface condition, which is unique to climate modeling. By analyzing a simplified model, we demonstrate how the parameterization of the bulk condition and other numerical and physical parameters affect the coupling stability.

math.NA↗

arXiv2019

Part-level Car Parsing and Reconstruction from Single Street View

Part information has been shown to be resistant to occlusions and viewpoint changes, which is beneficial for various vision-related tasks. However, we found very limited work in car pose estimation and reconstruction from street views leveraging the part information. There are two major contributions in this paper. Firstly, we make the first attempt to build a framework to simultaneously estimate shape, translation, orientation, and semantic parts of cars in 3D space from a single street view. As it is labor-intensive to annotate semantic parts on real street views, we propose a specific approach to implicitly transfer part features from synthesized images to real street views. For pose and shape estimation, we propose a novel network structure that utilizes both part features and 3D losses. Secondly, we are the first to construct a high-quality dataset that contains 348 different car models with physical dimensions and part-level annotations based on global and local deformations. Given these models, we further generate 60K synthesized images with randomization of orientation, illumination, occlusion, and texture. Our results demonstrate that our part segmentation performance is significantly improved after applying our implicit transfer approach. Our network for pose and shape estimation achieves the state-of-the-art performance on the ApolloCar3D dataset and outperforms 3D-RCNN and DeepMANTA by 12.57 and 8.91 percentage points in terms of mean A3DP-Abs.

cs.CV↗

arXiv2019

Improved Techniques for Training Adaptive Deep Networks

Adaptive inference is a promising technique to improve the computational efficiency of deep models at test time. In contrast to static models which use the same computation graph for all instances, adaptive networks can dynamically adjust their structure conditioned on each input. While existing research on adaptive inference mainly focuses on designing more advanced architectures, this paper investigates how to train such networks more effectively. Specifically, we consider a typical adaptive deep network with multiple intermediate classifiers. We present three techniques to improve its training efficacy from two aspects: 1) a Gradient Equilibrium algorithm to resolve the conflict of learning of different classifiers; 2) an Inline Subnetwork Collaboration approach and a One-for-all Knowledge Distillation algorithm to enhance the collaboration among classifiers. On multiple datasets (CIFAR-10, CIFAR-100 and ImageNet), we show that the proposed approach consistently leads to further improved efficiency on top of state-of-the-art adaptive deep networks.

cs.CV↗

arXiv2019

On generalized Piterbarg-Berman function

This paper aims to evaluate the Piterbarg-Berman function given by $$\mathcal{P\!B}_α^h(x, E) = \int_\mathbb{R}e^z\mathbb{P} \left\{{\int_E \mathbb{I}\left(\sqrt2B_α(t) - |t|^α- h(t) - z>0 \right) {\text{d}} t > x} \right\} {\text{d}} z,\quad x\in[0, {mes}(E)],$$ with $h$ a drift function and $B_α$ a fractional Brownian motion (fBm) with Hurst index $α/2\in(0,1]$, i.e., a mean zero Gaussian process with continuous sample paths and covariance function \begin{align*} {\mathrm{Cov}}(B_α(s), B_α(t)) = \frac12 (|s|^α+ |t|^α- |s-t|^α). \end{align*} This note specifies its explicit expression for the fBms with $α=1$ and $2$ when the drift function $h(t)=ct^α, c>0$ and $E=\mathbb{R}_+\cup\{0\}$. For the Gaussian distribution $B_2$, we investigate $\mathcal{P\!B}_2^h(x, E)$ with general drift functions $h(t)$ such that $h(t)+t^2$ being convex or concave, and finite interval $E=[a,b]$. Typical examples of $\mathcal{P\!B}_2^h(x, E)$ with $h(t)=c|t|^λ-t^2$ and several bounds of $\mathcal{P\!B}_α^h(x, E)$ are discussed. Numerical studies are carried out to illustrate all the findings. Keywords: Piterbarg-Berman function; sojourn time; fractional Brownian motion; drift function

math.ST↗

arXiv2019

Semi-Supervised Monocular Depth Estimation with Left-Right Consistency Using Deep Neural Network

There has been tremendous research progress in estimating the depth of a scene from a monocular camera image. Existing methods for single-image depth prediction are exclusively based on deep neural networks, and their training can be unsupervised using stereo image pairs, supervised using LiDAR point clouds, or semi-supervised using both stereo and LiDAR. In general, semi-supervised training is preferred as it does not suffer from the weaknesses of either supervised training, resulting from the difference in the cameras and the LiDARs field of view, or unsupervised training, resulting from the poor depth accuracy that can be recovered from a stereo pair. In this paper, we present our research in single image depth prediction using semi-supervised training that outperforms the state-of-the-art. We achieve this through a loss function that explicitly exploits left-right consistency in a stereo reconstruction, which has not been adopted in previous semi-supervised training. In addition, we describe the correct use of ground truth depth derived from LiDAR that can significantly reduce prediction error. The performance of our depth prediction model is evaluated on popular datasets, and the importance of each aspect of our semi-supervised training approach is demonstrated through experimental results. Our deep neural network model has been made publicly available.

cs.CV↗

arXiv2019

Lightweight Monocular Depth Estimation Model by Joint End-to-End Filter pruning

Convolutional neural networks (CNNs) have emerged as the state-of-the-art in multiple vision tasks including depth estimation. However, memory and computing power requirements remain as challenges to be tackled in these models. Monocular depth estimation has significant use in robotics and virtual reality that requires deployment on low-end devices. Training a small model from scratch results in a significant drop in accuracy and it does not benefit from pre-trained large models. Motivated by the literature of model pruning, we propose a lightweight monocular depth model obtained from a large trained model. This is achieved by removing the least important features with a novel joint end-to-end filter pruning. We propose to learn a binary mask for each filter to decide whether to drop the filter or not. These masks are trained jointly to exploit relations between filters at different layers as well as redundancy within the same layer. We show that we can achieve around 5x compression rate with small drop in accuracy on the KITTI driving dataset. We also show that masking can improve accuracy over the baseline with fewer parameters, even without enforcing compression loss.

cs.CV↗

arXiv2019

Moving Object Detection under Discontinuous Change in Illumination Using Tensor Low-Rank and Invariant Sparse Decomposition

Although low-rank and sparse decomposition based methods have been successfully applied to the problem of moving object detection using structured sparsity-inducing norms, they are still vulnerable to significant illumination changes that arise in certain applications. We are interested in moving object detection in applications involving time-lapse image sequences for which current methods mistakenly group moving objects and illumination changes into foreground. Our method relies on the multilinear (tensor) data low-rank and sparse decomposition framework to address the weaknesses of existing methods. The key to our proposed method is to create first a set of prior maps that can characterize the changes in the image sequence due to illumination. We show that they can be detected by a k-support norm. To deal with concurrent, two types of changes, we employ two regularization terms, one for detecting moving objects and the other for accounting for illumination changes, in the tensor low-rank and sparse decomposition formulation. Through comprehensive experiments using challenging datasets, we show that our method demonstrates a remarkable ability to detect moving objects under discontinuous change in illumination, and outperforms the state-of-the-art solutions to this challenging problem.

cs.CV↗

arXiv2019

Bubbling of the prescribed $Q$-curvature equation on $4$-manifolds in the null case

Analog to the classical result of Kazdan-Warner for the existence of solutions to the prescribed Gaussian curvature equation on compact 2-manifolds without boundary, it is widely known that if $(M,g_0)$ is a closed 4-manifold with zero $Q$-curvature and if $f$ is any non-constant, smooth, sign-changing function with $\int_M f dμ_{{\it g}_0} <0$, then there exists at least one solution $u$ to the prescribed $Q$-curvature equation \[ \mathbf{P}_{g_0} u = f e^{4u}, \] where $\mathbf{P}_{g_0}$ is the Paneitz operator which is positive with kernel consisting of constant functions. In this paper, we fix a non-constant smooth function $f_0$ with \[ \max_{x\in M}f_0(x)=0, \quad \int_M f_0 dμ_{{\it g}_0} <0 \] and consider a family of prescribed $Q$-curvature equations \[ \mathbf{P}_{g_0} u=(f_0+λ)e^{4u}, \] where $λ>0$ is a suitably small constant. A solution to the equation above can be obtained from a minimizer $u_λ$ of certain energy functional associated to the equation. Firstly, we prove that the minimizer $u_λ$ exhibits bubbling phenomenon in a certain limit regime as $λ\searrow 0$. Then, we show that the analogous phenomenon occurs in the context of $Q$-curvature flow.

math.AP↗

arXiv2019

Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts

We obtain Dini and Schauder type estimates for concave fully nonlinear nonlocal parabolic equations of order $σ\in (0,2)$ with rough and non-symmetric kernels, and drift terms. We also study such linear equations with only measurable coefficients in the time variable, and obtain Dini type estimates in the spacial variable. This is a continuation of the work [10, 11] by the first and last authors.

math.AP↗

arXiv2019

Human Pose Estimation with Spatial Contextual Information

We explore the importance of spatial contextual information in human pose estimation. Most state-of-the-art pose networks are trained in a multi-stage manner and produce several auxiliary predictions for deep supervision. With this principle, we present two conceptually simple and yet computational efficient modules, namely Cascade Prediction Fusion (CPF) and Pose Graph Neural Network (PGNN), to exploit underlying contextual information. Cascade prediction fusion accumulates prediction maps from previous stages to extract informative signals. The resulting maps also function as a prior to guide prediction at following stages. To promote spatial correlation among joints, our PGNN learns a structured representation of human pose as a graph. Direct message passing between different joints is enabled and spatial relation is captured. These two modules require very limited computational complexity. Experimental results demonstrate that our method consistently outperforms previous methods on MPII and LSP benchmark.

cs.CV↗

arXiv2018

Axion Stars

The particle that makes up the dark matter of the universe could be an axion or axion-like particle. A collection of axions can condense into a bound Bose-Einstein condensate called an axion star. It is possible that a significant fraction of the axion dark matter is in the form of axion stars. This would make some efforts to identify the axion as the dark matter particle more challenging, but it would also open up new possibilities. We summarize the basic properties of isolated axion stars, which can be gravitationally bound or bound by self-interactions. Axions are naturally described by a relativistic field theory with a real scalar field, but low-energy axions can be described more simply by a classical nonrelativistic effective field theory with a complex scalar field.

hep-ph↗

arXiv2018

CNN-SVO: Improving the Mapping in Semi-Direct Visual Odometry Using Single-Image Depth Prediction

Reliable feature correspondence between frames is a critical step in visual odometry (VO) and visual simultaneous localization and mapping (V-SLAM) algorithms. In comparison with existing VO and V-SLAM algorithms, semi-direct visual odometry (SVO) has two main advantages that lead to state-of-the-art frame rate camera motion estimation: direct pixel correspondence and efficient implementation of probabilistic mapping method. This paper improves the SVO mapping by initializing the mean and the variance of the depth at a feature location according to the depth prediction from a single-image depth prediction network. By significantly reducing the depth uncertainty of the initialized map point (i.e., small variance centred about the depth prediction), the benefits are twofold: reliable feature correspondence between views and fast convergence to the true depth in order to create new map points. We evaluate our method with two outdoor datasets: KITTI dataset and Oxford Robotcar dataset. The experimental results indicate that the improved SVO mapping results in increased robustness and camera tracking accuracy.

cs.CV↗

arXiv2018

Towards A Deep Insight into Landmark-based Visual Place Recognition: Methodology and Practice

In this paper, we address the problem of landmark-based visual place recognition. In the state-of-the-art method, accurate object proposal algorithms are first leveraged for generating a set of local regions containing particular landmarks with high confidence. Then, these candidate regions are represented by deep features and pairwise matching is performed in an exhaustive manner for the similarity measure. Despite its success, conventional object proposal methods usually produce massive landmark-dependent image patches exhibiting significant distribution variance in scale and overlap. As a result, the inconsistency in landmark distributions tends to produce biased similarity between pairwise images yielding the suboptimal performance. In order to gain an insight into the landmark-based place recognition scheme, we conduct a comprehensive study in which the influence of landmark scales and the proportion of overlap on the recognition performance is explored. More specifically, we thoroughly study the exhaustive search based landmark matching mechanism, and thus derive three-fold important observations in terms of the beneficial effect of specific landmark generation strategies. Inspired by the above observations, a simple yet effective dense sampling based scheme is presented for accurate place recognition in this paper. Different from the conventional object proposal strategy, we generate local landmarks of multiple scales with uniform distribution from entire image by dense sampling, and subsequently perform multi-scale fusion on the densely sampled landmarks for similarity measure. The experimental results on three challenging datasets demonstrate that the recognition performance can be significantly improved by our efficient method in which the landmarks are appropriately produced for accurate pairwise matching.

cs.RO↗

arXiv2018

Terahertz Spin Transfer Torque Oscillator Based on a Synthetic Antiferromagnet

Bloch-Bloembergen-Slonczewski equation is adopted to simulate magnetization dynamics in spin-valve based spin-transfer torque oscillator with synthetic antiferromagnet acting as a free magnetic layer. High frequency up to the terahertz scale is predicted in synthetic antiferromagnet spin-transfer torque oscillator with no external magnetic field if the following requirements are fulfilled: antiferromagnetic coupling between synthetic antiferromagnetic layers is sufficiently strong, and the thickness of top (bottom) layer of synthetic antiferromagnet is sufficiently thick (thin) to achieve a wide current density window for the high oscillation frequency. Additionally, the transverse relaxation time of the free magnetic layer should be sufficiently larger compared with the longitudinal relaxation time. Otherwise, stable oscillation cannot be sustained or scenarios similar to regular spin valve-based spin-transfer torque oscillator with relatively low frequency will occur. Our calculations pave a new way for exploring THz spintronics devices.

physics.app-ph↗

arXiv2018

Discriminative multi-view Privileged Information learning for image re-ranking

Conventional multi-view re-ranking methods usually perform asymmetrical matching between the region of interest (ROI) in the query image and the whole target image for similarity computation. Due to the inconsistency in the visual appearance, this practice tends to degrade the retrieval accuracy particularly when the image ROI, which is usually interpreted as the image objectness, accounts for a smaller region in the image. Since Privileged Information (PI), which can be viewed as the image prior, enables well characterizing the image objectness, we are aiming at leveraging PI for further improving the performance of the multi-view re-ranking accuracy in this paper. Towards this end, we propose a discriminative multi-view re-ranking approach in which both the original global image visual contents and the local auxiliary PI features are simultaneously integrated into a unified training framework for generating the latent subspaces with sufficient discriminating power. For the on-the-fly re-ranking, since the multi-view PI features are unavailable, we only project the original multi-view image representations onto the latent subspace, and thus the re-ranking can be achieved by computing and sorting the distances from the multi-view embeddings to the separating hyperplane. Extensive experimental evaluations on the two public benchmarks Oxford5k and Paris6k reveal our approach provides further performance boost for accurate image re-ranking, whilst the comparative study demonstrates the advantage of our method against other multi-view re-ranking methods.

cs.CV↗

arXiv2018

Submap-based Pose-graph Visual SLAM: A Robust Visual Exploration and Localization System

For VSLAM (Visual Simultaneous Localization and Mapping), localization is a challenging task, especially for some challenging situations: textureless frames, motion blur, etc.. To build a robust exploration and localization system in a given space or environment, a submap-based VSLAM system is proposed in this paper. Our system uses a submap back-end and a visual front-end. The main advantage of our system is its robustness with respect to tracking failure, a common problem in current VSLAM algorithms. The robustness of our system is compared with the state-of-the-art in terms of average tracking percentage. The precision of our system is also evaluated in terms of ATE (absolute trajectory error) RMSE (root mean square error) comparing the state-of-the-art. The ability of our system in solving the `kidnapped' problem is demonstrated. Our system can improve the robustness of visual localization in challenging situations.

cs.RO↗