arXiv subjects

Feng Zhou

Publications and source records attributed to Feng Zhou.

At least 217 records · Page 12Linked to original sources

arXiv2019

On Gaussian curvature equations in $\mathbb{R}^2$ with prescribed non-positive curvature

The purpose of this paper is to study the solutions of $$ Δu +K(x) e^{2u}=0 \quad{\rm in}\;\; \mathbb{R}^2 $$ with $K\le 0$. We introduce the following quantity: $$α_p(K)=\sup\left\{α\in \mathbb{R}:\, \int_{\mathbb{R}^2} |K(x)|^p(1+|x|)^{2αp+2(p-1)} dx<+\infty\right\}, \quad \forall\; p \ge 1.$$ Under the assumption $({\mathbb H}_1)$: $α_p(K)> -\infty$ for some $p>1$ and $α_1(K) > 0$, we show that for any $0 < α< α_1(K)$, there is a unique solution $u_α$ with $u_α(x) = α\ln |x|+ c_α+o\big(|x|^{-\frac{2β}{1+2β}} \big)$ at infinity and $β\in (0,\,α_1(K)-α)$. Furthermore, we show an example $K_0 \leq 0$ such that $α_p(K_0) = -\infty$ for any $p>1$ and $α_1(K_0) > 0$, for which we study the asymptotic behavior of solutions. In particular, we prove the existence of a solution $u_*$ such that $u_* -α_*\ln|x| = O(1)$ at infinity for some $α_* > 0$, but who does not converge to a constant at infinity. This example exhibits a new phenomenon of solutions with logarithmic growth and non-uniform behavior at infinity.

math.AP↗

arXiv2018

Nonexistence of Positive Supersolution to a Class of Semilinear Elliptic Equations and Systems in an Exterior Domain

In this paper, we primarily consider the following semilinear elliptic equation \begin{eqnarray*} \arraycolsep=1pt\left\{ \begin{array}{lll} \displaystyle -Δu= h(x,u)\quad \ &{\rm in}\ Ω,\\[1.5mm] \phantom{ -Δ} \displaystyle u\ge 0\qquad &{\rm on}\ \partialΩ, \end{array}\right. \end{eqnarray*} where $Ω$ is an exterior domain in $R^N$ with $N\ge 3$, and derive optimal nonexistence results of positive supersolution. Our argument is based on a nonexistence result of positive supersolution of a linear elliptic problem with Hardy potential. We also establish sharp nonexistence results of positive supersolution to an elliptic system.

math.AP↗

arXiv2018

3D Pose Estimation for Fine-Grained Object Categories

Existing object pose estimation datasets are related to generic object types and there is so far no dataset for fine-grained object categories. In this work, we introduce a new large dataset to benchmark pose estimation for fine-grained objects, thanks to the availability of both 2D and 3D fine-grained data recently. Specifically, we augment two popular fine-grained recognition datasets (StanfordCars and CompCars) by finding a fine-grained 3D CAD model for each sub-category and manually annotating each object in images with 3D pose. We show that, with enough training data, a full perspective model with continuous parameters can be estimated using 2D appearance information alone. We achieve this via a framework based on Faster/Mask R-CNN. This goes beyond previous works on category-level pose estimation, which only estimate discrete/continuous viewpoint angles or recover rotation matrices often with the help of key points. Furthermore, with fine-grained 3D models available, we incorporate a dense 3D representation named as location field into the CNN-based pose estimation framework to further improve the performance. The new dataset is available at www.umiacs.umd.edu/~wym/3dpose.html

cs.CV↗

arXiv2018

Compact Generalized Non-local Network

The non-local module is designed for capturing long-range spatio-temporal dependencies in images and videos. Although having shown excellent performance, it lacks the mechanism to model the interactions between positions across channels, which are of vital importance in recognizing fine-grained objects and actions. To address this limitation, we generalize the non-local module and take the correlations between the positions of any two channels into account. This extension utilizes the compact representation for multiple kernel functions with Taylor expansion that makes the generalized non-local module in a fast and low-complexity computation flow. Moreover, we implement our generalized non-local method within channel groups to ease the optimization. Experimental results illustrate the clear-cut improvements and practical applicability of the generalized non-local module on both fine-grained object recognition and video classification. Code is available at: https://github.com/KaiyuYue/cgnl-network.pytorch.

cs.CV↗

arXiv2018

Fine-grained Video Categorization with Redundancy Reduction Attention

For fine-grained categorization tasks, videos could serve as a better source than static images as videos have a higher chance of containing discriminative patterns. Nevertheless, a video sequence could also contain a lot of redundant and irrelevant frames. How to locate critical information of interest is a challenging task. In this paper, we propose a new network structure, known as Redundancy Reduction Attention (RRA), which learns to focus on multiple discriminative patterns by sup- pressing redundant feature channels. Specifically, it firstly summarizes the video by weight-summing all feature vectors in the feature maps of selected frames with a spatio-temporal soft attention, and then predicts which channels to suppress or to enhance according to this summary with a learned non-linear transform. Suppression is achieved by modulating the feature maps and threshing out weak activations. The updated feature maps are then used in the next iteration. Finally, the video is classified based on multiple summaries. The proposed method achieves out- standing performances in multiple video classification datasets. Further- more, we have collected two large-scale video datasets, YouTube-Birds and YouTube-Cars, for future researches on fine-grained video categorization. The datasets are available at http://www.cs.umd.edu/~chenzhu/fgvc.

cs.CV↗

arXiv2018

Improving Annotation for 3D Pose Dataset of Fine-Grained Object Categories

Existing 3D pose datasets of object categories are limited to generic object types and lack of fine-grained information. In this work, we introduce a new large-scale dataset that consists of 409 fine-grained categories and 31,881 images with accurate 3D pose annotation. Specifically, we augment three existing fine-grained object recognition datasets (StanfordCars, CompCars and FGVC-Aircraft) by finding a specific 3D model for each sub-category from ShapeNet and manually annotating each 2D image by adjusting a full set of 7 continuous perspective parameters. Since the fine-grained shapes allow 3D models to better fit the images, we further improve the annotation quality by initializing from the human annotation and conducting local search of the pose parameters with the objective of maximizing the IoUs between the projected mask and the segmentation reference estimated from state-of-the-art deep Convolutional Neural Networks (CNNs). We provide full statistics of the annotations with qualitative and quantitative comparisons suggesting that our dataset can be a complementary source for studying 3D pose estimation. The dataset can be downloaded at http://users.umiacs.umd.edu/~wym/3dpose.html.

cs.CV↗

arXiv2018

On-chip multipurpose microwave frequency identification

We demonstrate a multipurpose microwave frequency identification solution that is implemented based on a photonic integrated chip and is able to identify different types of microwave signals, including single-frequency, multiple-frequency, chirped and frequency-hopping microwave signals. The key component is a thermally-tunable high-Q-factor silicon microring resonator which is used to implement the frequency-to-time mapping. The frequency measurement range is ultra-wide, from 1 to 30 GHz, with a high resolution of 375 MHz and a low measurement error of 237.3 MHz. This demonstration opens the door for future fully integrated solution for high speed, wideband and multipurpose signal identification with high resolution.

physics.app-ph↗

arXiv2018

Multi-Attention Multi-Class Constraint for Fine-grained Image Recognition

Attention-based learning for fine-grained image recognition remains a challenging task, where most of the existing methods treat each object part in isolation, while neglecting the correlations among them. In addition, the multi-stage or multi-scale mechanisms involved make the existing methods less efficient and hard to be trained end-to-end. In this paper, we propose a novel attention-based convolutional neural network (CNN) which regulates multiple object parts among different input images. Our method first learns multiple attention region features of each input image through the one-squeeze multi-excitation (OSME) module, and then apply the multi-attention multi-class constraint (MAMC) in a metric learning framework. For each anchor feature, the MAMC functions by pulling same-attention same-class features closer, while pushing different-attention or different-class features away. Our method can be easily trained end-to-end, and is highly efficient which requires only one training stage. Moreover, we introduce Dogs-in-the-Wild, a comprehensive dog species dataset that surpasses similar existing datasets by category coverage, data volume and annotation quality. This dataset will be released upon acceptance to facilitate the research of fine-grained image recognition. Extensive experiments are conducted to show the substantial improvements of our method on four benchmark datasets.

cs.CV↗

arXiv2018

On nonhomogeneous elliptic equations with the Hardy-Leray potentials

In this paper, we present some suitable distributional identities of the solutions for nonhomogeneous elliptic equations involving the Hardy-Leray potentials and study qualitative properties of the solutions to the corresponding nonhomogeneous problems by the distributional identities. We address some applications on the nonexistence of some nonhomogeneous problems with the Hardy-Leray potentials and the nonexistence principle eigenvalue with some indefinite potentials.

math.AP↗

arXiv2018

Fine-Grained Facial Expression Analysis Using Dimensional Emotion Model

Automated facial expression analysis has a variety of applications in human-computer interaction. Traditional methods mainly analyze prototypical facial expressions of no more than eight discrete emotions as a classification task. However, in practice, spontaneous facial expressions in naturalistic environment can represent not only a wide range of emotions, but also different intensities within an emotion family. In such situation, these methods are not reliable or adequate. In this paper, we propose to train deep convolutional neural networks (CNNs) to analyze facial expressions explainable in a dimensional emotion model. The proposed method accommodates not only a set of basic emotion expressions, but also a full range of other emotions and subtle emotion intensities that we both feel in ourselves and perceive in others in our daily life. Specifically, we first mapped facial expressions into dimensional measures so that we transformed facial expression analysis from a classification problem to a regression one. We then tested our CNN-based methods for facial expression regression and these methods demonstrated promising performance. Moreover, we improved our method by a bilinear pooling which encodes second-order statistics of features. We showed such bilinear-CNN models significantly outperformed their respective baselines.

cs.CV↗

arXiv2018

Radial symmetry of positive entire solutions of a fourth order elliptic equation with a singular nonlinearity

The necessary and sufficient conditions for a regular positive entire solution $u$ of the biharmonic equation: \begin{equation} \label{0.1} -Δ^2 u=u^{-p} \;\; \mbox{in $\R^N \; (N \geq 3)$}, \;\; p>1 \end{equation} to be a radially symmetric solution are obtained via the moving plane method (MPM) of a system of equations. It is well-known that for any $a>0$, \eqref{0.1} admits a unique minimal positive entire radial solution ${\underline u}_a (r)$ and a family of non-minimal positive entire radial solutions $u_a (r)$ such that $u_a (0)={\underline u}_a (0)=a$ and $u_a (r) \geq {\underline u}_a (r)$ for $r \in (0, \infty)$. Moreover, the asymptotic behaviors of ${\underline u}_a (r)$ and $u_a (r)$ at $r=\infty$ are also known. We will see in this paper that the asymptotic behaviors similar to those of ${\underline u}_a (r)$ and $u_a (r)$ at $r=\infty$ can determine the radial symmetry of a general regular positive entire solution $u$ of \eqref{0.1}. The precisely asymptotic behaviors of $u (x)$ and $-Δu (x)$ at $|x|=\infty$ need to be established such that the moving-plane procedure can be started. We provide the necessary and sufficient conditions not only for a regular positive entire solution $u$ of \eqref{0.1} to be the minimal entire radial solution, but also for $u$ to be a non-minimal entire radial solution.

math.AP↗

arXiv2018

Nanotesla-level, shield-less, field-compensation-free, wave-mixing-enhanced body-temperature atomic magnetometry for biomagnetism

We report an optical inelastic-wave-mixing-enhanced atomic magnetometry technique that results in nT-level magnetic field detection at temperatures compatible with the human body without magnetic shielding, zero-field compensation, or high-frequency modulated phase-locking spectroscopy. Using Gaussian magnetic pulses that mimic the transient magnetic field produced by an action potential on a frog's nerve, we demonstrate more than 300,000-fold (550-fold) enhancement of magneto-optical rotation signal power spectral-density (power amplitude) over the conventional single-beam $Λ-$scheme atomic magnetometry method. This new technique may bring possibilities for extremely sensitive magnetic field imaging of biological systems accessible via an optical fiber in clinical environments.

quant-ph↗

arXiv2018

Breaking the energy-symmetry blockade in magneto-optical rotation

The magneto-optical polarization rotation effect has prolific applications in various research areas spanning the scientific spectrum including space and interstellar research, nano-technology and material science, biomedical imaging, and sub-atomic particle research. In nonlinear magneto-optical rotation (NMOR), the intensity of a linearly-polarized probe field affects the rotation of its own polarization plane while propagating in a magnetized medium. However, typical NMOR signals of conventional single-beam $Λ-$scheme atomic magnetometers are peculiarly small, requiring sophisticated magnetic shielding under complex operational conditions. Here, we show the presence of an energy-symmetry blockade that undermines the NMOR effect in conventional single-beam $Λ-$scheme atomic magnetometers. We further demonstrate, both experimentally and theoretically, an inelastic wave-mixing technique that breaks this NMOR blockade, resulting in more than five orders of magnitude ($>$300,000-fold) NMOR optical signal power spectral density enhancement never before seen with conventional single-beam $Λ-$scheme atomic magnetometers. This new technique, demonstrated with substantially reduced light intensities, may lead to many applications, especially in the field of bio-magnetism and high-resolution low-field magnetic imaging.

physics.optics↗

arXiv2018

Semigroups and sequential importance sampling for multiway tables

When an interval of integers between the lower bound $l_i$ and the upper bound $u_i$ is the support of the marginal distribution $n_i|(n_{i-1}, ...,n_1)$, Chen et al, 2005 noticed that sampling from the interval at each step, for $n_i$ during a sequential importance sampling (SIS) procedure, always produces a table which satisfies the marginal constraints. However, in general, the interval may not be equal to the support of the marginal distribution. In this case, the SIS procedure may produce tables which do not satisfy the marginal constraints, leading to rejection Chen et al 2006. In this paper we consider the uniform distribution as the target distribution. First we show that if we fix the number of rows and columns of the design matrix of the model for contingency tables then there exists a polynomial time algorithm in terms of the input size to sample a table from the set of all tables satisfying all marginals defined by the given model via the SIS procedure without rejection. We then show experimentally that in general the SIS procedure may have large rejection rates even with small tables. Further we show that in general the classical SIS procedure in Chen et al, 2005 can have a large rejection rate whose limit is one. When estimating the number of tables in our simulation study, we used the univariate and bivariate logistic regression models since under this model the SIS procedure seems to have higher rate of rejections even with small tables.

math.CO↗

arXiv2017

Hyperspectral Image Classification with Markov Random Fields and a Convolutional Neural Network

This paper presents a new supervised classification algorithm for remotely sensed hyperspectral image (HSI) which integrates spectral and spatial information in a unified Bayesian framework. First, we formulate the HSI classification problem from a Bayesian perspective. Then, we adopt a convolutional neural network (CNN) to learn the posterior class distributions using a patch-wise training strategy to better use the spatial information. Next, spatial information is further considered by placing a spatial smoothness prior on the labels. Finally, we iteratively update the CNN parameters using stochastic gradient decent (SGD) and update the class labels of all pixel vectors using an alpha-expansion min-cut-based algorithm. Compared with other state-of-the-art methods, the proposed classification method achieves better performance on one synthetic dataset and two benchmark HSI datasets in a number of experimental settings.

cs.CV↗

arXiv2017

Dynamic Computational Time for Visual Attention

We propose a dynamic computational time model to accelerate the average processing time for recurrent visual attention (RAM). Rather than attention with a fixed number of steps for each input image, the model learns to decide when to stop on the fly. To achieve this, we add an additional continue/stop action per time step to RAM and use reinforcement learning to learn both the optimal attention policy and stopping policy. The modification is simple but could dramatically save the average computational time while keeping the same recognition performance as RAM. Experimental results on CUB-200-2011 and Stanford Cars dataset demonstrate the dynamic computational model can work effectively for fine-grained image recognition.The source code of this paper can be obtained from https://github.com/baidu-research/DT-RAM

cs.CV↗

arXiv2017

Deep Metric Learning with Angular Loss

The modern image search system requires semantic understanding of image, and a key yet under-addressed problem is to learn a good metric for measuring the similarity between images. While deep metric learning has yielded impressive performance gains by extracting high level abstractions from image data, a proper objective loss function becomes the central issue to boost the performance. In this paper, we propose a novel angular loss, which takes angle relationship into account, for learning better similarity metric. Whereas previous metric learning methods focus on optimizing the similarity (contrastive loss) or relative similarity (triplet loss) of image pairs, our proposed method aims at constraining the angle at the negative point of triplet triangles. Several favorable properties are observed when compared with conventional methods. First, scale invariance is introduced, improving the robustness of objective against feature variance. Second, a third-order geometric constraint is inherently imposed, capturing additional local structure of triplet triangles than contrastive loss or triplet loss. Third, better convergence has been demonstrated by experiments on three publicly available datasets.

cs.CV↗

arXiv2017

Exact Cancellation of Emittance Due to Coupled Transverse Dynamics in Solenoids and RF Couplers

Small, stray magnetic and RF fields in electron guns and injectors can perturb an electron beam and introduce correlations between the otherwise orthogonal transverse trajectories. These correlations couple the x and y dynamics which increases the transverse emittance. If the correlation becomes "diluted" or randomized in the beam transport then as the correlation disappears the 4D emittance increases. This paper discusses two important correlations common to most electron injectors. The first results from the coupling of a weak quadrupole field with beam rotation in a solenoid, and the second x-y coupling is generated by an asymmetric on-axis RF field due to a high-power RF coupler or cavity port. This paper shows that a small quadrupole field combined with solenoidal focusing can result in significant emittance growth due to coupled transverse dynamics. It also shows how adding a skewed quadrupole field can exactly cancel this correlation and its emittance. Similar emittance cancellation is demonstrated for asymmetric RF fields, with the degree of cancellation limited by the electron bunch length. Analytic expressions are derived and compared with simulations and experiments.

physics.acc-ph↗