arXiv subjects
Publications and source records attributed to Xiang Xu.
In this paper we study the global well-posedness of the Allen-Cahn Ohta-Nakazawa model with two fixed nonlinear volume constraints. Utilizing the gradient flow structure of its free energy, we prove the existence and uniqueness of the solution by following De Giorgi's minimizing movement scheme in a novel way.
We study some maximum principle preserving and energy stable schemes for the Allen-Cahn-Ohta-Kawasaki model with fixed volume constraint. With the inclusion of a nonlinear term in the Ohta-Kawasaki free energy functional, we show that the Allen-Cahn-Ohta-Kawasaki dynamics is maximum principle preserving. We further design some first order energy stable numerical schemes which inherit the maximum principle preservation in both semi-discrete and fully-discrete levels. Furthermore, we apply the maximum principle preserving schemes to a general framework for binary systems with long-range interactions. We also present some numerical results to support our theoretical findings.
From late December, 2019, the novel Corona-Virus began to spread in the mainland of China. For predicting the trend of the Corona Virus spread, several time delay dynamic systems (TDD) are proposed. In this paper, we establish a novel fractional time delay dynamic system (FTDD) to describe the local outbreak of COVID-19. The fractional derivative is introduced to account for the sub-diffusion process of the confirmed and cured peoples growth. Based on the public health data by the government, we propose a stable reconstruction algorithm of the coefficients. The reconstructed coefficients are used to predict the trend of the Corona-Virus. The numerical results are in good agreement with the public data.
Misalignment angle will result in a considerable error for the integration of Doppler Velocity Log (DVL) and of Strapdown Inertial Navigation System (SINS). In this paper, a robust initial alignment method for SINS/DVL is proposed to solve a practical applicable issue, which is that the outputs of DVL are often corrupted by the outliers. Firstly, the alignment principle for SINS/DVL is summarized. Secondly, based on the principle of this alignment method, the apparent velocity model is investigated, and the parameters expression of the apparent velocity model are derived detailed. Using the apparent velocity model, the unknown parameters of the apparent velocity model are estimated by the developed Robust Kalman Filter (RKF), then the reconstructed observation vector, where the outliers are detected and isolated, is reconstructed by the estimated parameters. Based on the reconstructed observation vectors, the initial attitude is determined. Finally, the simulation and field tests are carried out to verify the performance of the proposed method. The test results are shown that the proposed method can detect and isolate the outliers effectively and get better performance than the previous work.
For many computer vision applications such as image captioning, visual question answering, and person search, learning discriminative feature representations at both image and text level is an essential yet challenging problem. Its challenges originate from the large word variance in the text domain as well as the difficulty of accurately measuring the distance between the features of the two modalities. Most prior work focuses on the latter challenge, by introducing loss functions that help the network learn better feature representations but fail to account for the complexity of the textual input. With that in mind, we introduce TIMAM: a Text-Image Modality Adversarial Matching approach that learns modality-invariant feature representations using adversarial and cross-modal matching objectives. In addition, we demonstrate that BERT, a publicly-available language model that extracts word embeddings, can successfully be applied in the text-to-image matching domain. The proposed approach achieves state-of-the-art cross-modal matching performance on four widely-used publicly-available datasets resulting in absolute improvements ranging from 2% to 5% in terms of rank-1 accuracy.
This paper revisits the classical problem "Can we hear the density of a string?", which can be formulated as an inverse spectral problem for a Sturm-Liouville operator. Based on inverting a sequence of trace formulas, we propose a new numerical scheme to reconstruct the density. Numerical experiments are presented to verify the validity and effectiveness of the numerical scheme.
Deep neural networks often require copious amount of labeled-data to train their scads of parameters. Training larger and deeper networks is hard without appropriate regularization, particularly while using a small dataset. Laterally, collecting well-annotated data is expensive, time-consuming and often infeasible. A popular way to regularize these networks is to simply train the network with more data from an alternate representative dataset. This can lead to adverse effects if the statistics of the representative dataset are dissimilar to our target. This predicament is due to the problem of domain shift. Data from a shifted domain might not produce bespoke features when a feature extractor from the representative domain is used. In this paper, we propose a new technique ($d$-SNE) of domain adaptation that cleverly uses stochastic neighborhood embedding techniques and a novel modified-Hausdorff distance. The proposed technique is learnable end-to-end and is therefore, ideally suited to train neural networks. Extensive experiments demonstrate that $d$-SNE outperforms the current states-of-the-art and is robust to the variances in different datasets, even in the one-shot and semi-supervised learning settings. $d$-SNE also demonstrates the ability to generalize to multiple domains concurrently.
Biometrics-related research has been accelerated significantly by deep learning technology. However, there are limited open-source resources to help researchers evaluate their deep learning-based biometrics algorithms efficiently, especially for the face recognition tasks. In this work, we design and implement a light-weight, maintainable, scalable, generalizable, and extendable face recognition evaluation toolbox named FaRE that supports both online and offline evaluation to provide feedback to algorithm development and accelerate biometrics-related research. FaRE consists of a set of evaluation metric functions and provides various APIs for commonly-used face recognition datasets including LFW, CFP, UHDB31, and IJB-series datasets, which can be easily extended to include other customized datasets. The package and the pre-trained baseline models will be released for public academic research use after obtaining university approval.
In recent years, face detection has experienced significant performance improvement with the boost of deep convolutional neural networks. In this report, we reimplement the state-of-the-art detector SRN and apply some tricks proposed in the recent literatures to obtain an extremely strong face detector, named VIM-FD. In specific, we exploit more powerful backbone network like DenseNet-121, revisit the data augmentation based on data-anchor-sampling proposed in PyramidBox, and use the max-in-out label and anchor matching strategy in SFD. In addition, we also introduce the attention mechanism to provide additional supervision. Over the most popular and challenging face detection benchmark, i.e., WIDER FACE, the proposed VIM-FD achieves state-of-the-art performance.
In this paper, we propose a first order energy stable linear semi-implicit method for solving the Allen-Cahn-Ohta-Kawasaki equation. By introducing a new nonlinear term in the Ohta-Kawasaki free energy functional, all the system forces in the dynamics are localized near the interfaces which results in the desire hyperbolic tangent profile. In our numerical method, the time discretization is done by some stabilization technique in which some extra nonlocal but linear term is introduced and treated explicitly together with other linear terms, while other nonlinear and nonlocal terms are treated implicitly. The spatial discretization is performed by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are proved for this method in both semi-discretization and full discretization levels. Numerical experiments indicate the force localization and desire hyperbolic tangent profile due to the new nonlinear term. We test the first order temporal convergence rate of the proposed scheme. We also present hexagonal bubble assembly as one type of equilibrium for the Ohta-Kawasaki model. Additionally, the two-third law between the number of bubbles and the strength of long-range interaction is verified which agrees with the theoretical studies.
In this paper, we consider the Beris-Edwards system for incompressible nematic liquid crystal flows. The system under investigation consists of the Navier-Stokes equations for the fluid velocity $\mathbf{u}$ coupled with an evolution equation for the order parameter $Q$-tensor. One important feature of the system is that its elastic free energy takes a general form and in particular, it contains a cubic term that possibly makes it unbounded from below. In the two dimensional periodic setting, we prove that if the initial $L^\infty$-norm of the $Q$-tensor is properly small, then the system admits a unique global weak solution. The proof is based on the construction of a specific approximating system that preserves the $L^\infty$-norm of the $Q$-tensor along the time evolution.
We study the co-rotational Beris-Edwards system modeling nematic liquid crystals and revisit the eigenvalue preservation property discussed in \cite{XZ16}. We give an alternative but direct proof to the eigenvalue preservation of the initial data for the $Q$-tensor. It is noted that our proof is not only valid in the whole space case, but in the bounded domain case as well.
We propose to use the concept of the Hamming bound to derive the optimal criteria for learning hash codes with a deep network. In particular, when the number of binary hash codes (typically the number of image categories) and code length are known, it is possible to derive an upper bound on the minimum Hamming distance between the hash codes. This upper bound can then be used to define the loss function for learning hash codes. By encouraging the margin (minimum Hamming distance) between the hash codes of different image categories to match the upper bound, we are able to learn theoretically optimal hash codes. Our experiments show that our method significantly outperforms competing deep learning-based approaches and obtains top performance on benchmark datasets.
For many computer vision applications, such as image description and human identification, recognizing the visual attributes of humans is an essential yet challenging problem. Its challenges originate from its multi-label nature, the large underlying class imbalance and the lack of spatial annotations. Existing methods follow either a computer vision approach while failing to account for class imbalance, or explore machine learning solutions, which disregard the spatial and semantic relations that exist in the images. With that in mind, we propose an effective method that extracts and aggregates visual attention masks at different scales. We introduce a loss function to handle class imbalance both at class and at an instance level and further demonstrate that penalizing attention masks with high prediction variance accounts for the weak supervision of the attention mechanism. By identifying and addressing these challenges, we achieve state-of-the-art results with a simple attention mechanism in both PETA and WIDER-Attribute datasets without additional context or side information.
The video-based person re-identification is to recognize a person under different cameras, which is a crucial task applied in visual surveillance system. Most previous methods mainly focused on the feature of full body in the frame. In this paper we propose a novel Spatial and Temporal Features Mixture Model (STFMM) based on convolutional neural network (CNN) and recurrent neural network (RNN), in which the human body is split into $N$ parts in horizontal direction so that we can obtain more specific features. The proposed method skillfully integrates features of each part to achieve more expressive representation of each person. We first split the video sequence into $N$ part sequences which include the information of head, waist, legs and so on. Then the features are extracted by STFMM whose $2N$ inputs are obtained from the developed Siamese network, and these features are combined into a discriminative representation for one person. Experiments are conducted on the iLIDS-VID and PRID-2011 datasets. The results demonstrate that our approach outperforms existing methods for video-based person re-identification. It achieves a rank-1 CMC accuracy of 74\% on the iLIDS-VID dataset, exceeding the the most recently developed method ASTPN by 12\%. For the cross-data testing, our method achieves a rank-1 CMC accuracy of 48\% exceeding the ASTPN method by 18\%, which shows that our model has significant stability.
We present a robust method for estimating the facial pose and shape information from a densely annotated facial image. The method relies on Convolutional Point-set Representation (CPR), a carefully designed matrix representation to summarize different layers of information encoded in the set of detected points in the annotated image. The CPR disentangles the dependencies of shape and different pose parameters and enables updating different parameters in a sequential manner via convolutional neural networks and recurrent layers. When updating the pose parameters, we sample reprojection errors along with a predicted direction and update the parameters based on the pattern of reprojection errors. This technique boosts the model's capability in searching a local minimum under challenging scenarios. We also demonstrate that annotation from different sources can be merged under the framework of CPR and contributes to outperforming the current state-of-the-art solutions for 3D face alignment. Experiments indicate the proposed CPRFA (CPR-based Face Alignment) significantly improves 3D alignment accuracy when the densely annotated image contains noise and missing values, which is common under "in-the-wild" acquisition scenarios.
Faster RCNN has achieved great success for generic object detection including PASCAL object detection and MS COCO object detection. In this report, we propose a detailed designed Faster RCNN method named FDNet1.0 for face detection. Several techniques were employed including multi-scale training, multi-scale testing, light-designed RCNN, some tricks for inference and a vote-based ensemble method. Our method achieves two 1th places and one 2nd place in three tasks over WIDER FACE validation dataset (easy set, medium set, hard set).
Most of the face recognition works focus on specific modules or demonstrate a research idea. This paper presents a pose-invariant 3D-aided 2D face recognition system (UR2D) that is robust to pose variations as large as 90? by leveraging deep learning technology. The architecture and the interface of UR2D are described, and each module is introduced in detail. Extensive experiments are conducted on the UHDB31 and IJB-A, demonstrating that UR2D outperforms existing 2D face recognition systems such as VGG-Face, FaceNet, and a commercial off-the-shelf software (COTS) by at least 9% on the UHDB31 dataset and 3% on the IJB-A dataset on average in face identification tasks. UR2D also achieves state-of-the-art performance of 85% on the IJB-A dataset by comparing the Rank-1 accuracy score from template matching. It fills a gap by providing a 3D-aided 2D face recognition system that has compatible results with 2D face recognition systems using deep learning techniques.