arXiv subjects

Fei Yang

Publications and source records attributed to Fei Yang.

At least 109 records · Page 6Linked to original sources

arXiv2021

On the formulas of meromorphic functions with periodic Herman rings

We construct some explicit formulas of rational maps and transcendental meromorphic functions having Herman rings of period strictly larger than one. This gives an answer to a question raised by Shishikura in the 1980s. Moreover, the formulas of some rational maps with nested Herman rings are also found. To obtain the formulas of transcendental meromorphic functions having periodic Herman rings, a crucial step is to find an explicit family of transcendental entire functions having bounded Siegel disks of all possible periods and rotation numbers. This is based on proving the existence of a Mandelbrot-like set of period one in the corresponding parameter space.

math.DS↗

arXiv2021

Continuous Conditional Random Field Convolution for Point Cloud Segmentation

Point cloud segmentation is the foundation of 3D environmental perception for modern intelligent systems. To solve this problem and image segmentation, conditional random fields (CRFs) are usually formulated as discrete models in label space to encourage label consistency, which is actually a kind of postprocessing. In this paper, we reconsider the CRF in feature space for point cloud segmentation because it can capture the structure of features well to improve the representation ability of features rather than simply smoothing. Therefore, we first model the point cloud features with a continuous quadratic energy model and formulate its solution process as a message-passing graph convolution, by which it can be easily integrated into a deep network. We theoretically demonstrate that the message passing in the graph convolution is equivalent to the mean-field approximation of a continuous CRF model. Furthermore, we build an encoder-decoder network based on the proposed continuous CRF graph convolution (CRFConv), in which the CRFConv embedded in the decoding layers can restore the details of high-level features that were lost in the encoding stage to enhance the location ability of the network, thereby benefiting segmentation. Analogous to the CRFConv, we show that the classical discrete CRF can also work collaboratively with the proposed network via another graph convolution to further improve the segmentation results. Experiments on various point cloud benchmarks demonstrate the effectiveness and robustness of the proposed method. Compared with the state-of-the-art methods, the proposed method can also achieve competitive segmentation performance.

cs.CV↗

arXiv2021

3D Shapes Local Geometry Codes Learning with SDF

A signed distance function (SDF) as the 3D shape description is one of the most effective approaches to represent 3D geometry for rendering and reconstruction. Our work is inspired by the state-of-the-art method DeepSDF that learns and analyzes the 3D shape as the iso-surface of its shell and this method has shown promising results especially in the 3D shape reconstruction and compression domain. In this paper, we consider the degeneration problem of reconstruction coming from the capacity decrease of the DeepSDF model, which approximates the SDF with a neural network and a single latent code. We propose Local Geometry Code Learning (LGCL), a model that improves the original DeepSDF results by learning from a local shape geometry of the full 3D shape. We add an extra graph neural network to split the single transmittable latent code into a set of local latent codes distributed on the 3D shape. Mentioned latent codes are used to approximate the SDF in their local regions, which will alleviate the complexity of the approximation compared to the original DeepSDF. Furthermore, we introduce a new geometric loss function to facilitate the training of these local latent codes. Note that other local shape adjusting methods use the 3D voxel representation, which in turn is a problem highly difficult to solve or even is insolvable. In contrast, our architecture is based on graph processing implicitly and performs the learning regression process directly in the latent code space, thus make the proposed architecture more flexible and also simple for realization. Our experiments on 3D shape reconstruction demonstrate that our LGCL method can keep more details with a significantly smaller size of the SDF decoder and outperforms considerably the original DeepSDF method under the most important quantitative metrics.

cs.CV↗

arXiv2021

Learn to Predict Vertical Track Irregularity with Extremely Imbalanced Data

Railway systems require regular manual maintenance, a large part of which is dedicated to inspecting track deformation. Such deformation might severely impact trains' runtime security, whereas such inspections remain costly for both finance and human resources. Therefore, a more precise and efficient approach to detect railway track deformation is in urgent need. In this paper, we showcase an application framework for predicting vertical track irregularity, based on a real-world, large-scale dataset produced by several operating railways in China. We have conducted extensive experiments on various machine learning & ensemble learning algorithms in an effort to maximize the model's capability in capturing any irregularity. We also proposed a novel approach for handling imbalanced data in multivariate time series prediction tasks with adaptive data sampling and penalized loss. Such an approach has proven to reduce models' sensitivity to the imbalanced target domain, thus improving its performance in predicting rare extreme values.

cs.LG↗

arXiv2021

DANICE: Domain adaptation without forgetting in neural image compression

Neural image compression (NIC) is a new coding paradigm where coding capabilities are captured by deep models learned from data. This data-driven nature enables new potential functionalities. In this paper, we study the adaptability of codecs to custom domains of interest. We show that NIC codecs are transferable and that they can be adapted with relatively few target domain images. However, naive adaptation interferes with the solution optimized for the original source domain, resulting in forgetting the original coding capabilities in that domain, and may even break the compatibility with previously encoded bitstreams. Addressing these problems, we propose Codec Adaptation without Forgetting (CAwF), a framework that can avoid these problems by adding a small amount of custom parameters, where the source codec remains embedded and unchanged during the adaptation process. Experiments demonstrate its effectiveness and provide useful insights on the characteristics of catastrophic interference in NIC.

cs.CV↗

arXiv2021

Representation, Analysis of Bayesian Refinement Approximation Network: A Survey

After an artificial model background subtraction, the pixels have been labelled as foreground and background. Previous approaches to secondary processing the output for denoising usually use traditional methods such as the Bayesian refinement method. In this paper, we focus on using a modified U-Net model to approximate the result of the Bayesian refinement method and improve the result. In our modified U-Net model, the result of background subtraction from other models will be combined with the source image as input for learning the statistical distribution. Thus, the losing information caused by the background subtraction model can be restored from the source image. Moreover, since the part of the input image is already the output of the other background subtraction model, the feature extraction should be convenient, it only needs to change the labels of the noise pixels. Compare with traditional methods, using deep learning methods superiority in keeping details.

cs.CV↗

arXiv2021

The $π$-Calculus is Behaviourally Complete and Orbit-Finitely Executable

Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour (finitely) executable if, and only if, it is equivalent to the behaviour of a (finite) reactive Turing machine. In this paper, we study the relationship between executable behaviour and behaviour that can be specified in the $π$-calculus. We establish that every finitely executable behaviour can be specified in the $π$-calculus up to divergence-preserving branching bisimilarity. The converse, however, is not true due to (intended) limitations of the model of reactive Turing machines. That is, the $π$-calculus allows the specification of behaviour that is not finitely executable up to divergence-preserving branching bisimilarity. We shall prove, however, that if the finiteness requirement on reactive Turing machines and the associated notion of executability is relaxed to orbit-finiteness, then the $π$-calculus is executable up to (divergence-insensitive) branching bisimilarity.

cs.LO↗

arXiv2021

Quasisymmetric uniformization and Hausdorff dimensions of Cantor circle Julia sets

For Cantor circle Julia sets of hyperbolic rational maps, we prove that they are quasisymmetrically equivalent to standard Cantor circles (i.e., connected components are round circles). This gives a quasisymmetric uniformization of all Cantor circle Julia sets of hyperbolic rational maps. By analyzing the combinatorial information of the rational maps whose Julia sets are Cantor circles, we give a computational formula of the number of the Cantor circle hyperbolic components in the moduli space of rational maps for any fixed degree. We calculate the Hausdorff dimensions of the Julia sets which are Cantor circles, and prove that for any Cantor circle hyperbolic component $\mathcal{H}$ in the space of rational maps, the infimum of the Hausdorff dimensions of the Julia sets of the maps in $\mathcal{H}$ is equal to the conformal dimension of the Julia set of any representative $f_0\in\mathcal{H}$, and that the supremum of the Hausdorff dimensions is equal to $2$.

math.DS↗

arXiv2020

Quasisymmetric geometry of the Julia sets of McMullen maps

We study the quasisymmetric geometry of the Julia sets of McMullen maps $f_λ(z)=z^m+λ/z^\ell$, where $\ell$, $m\geq 2$ are integers satisfying $1/\ell+1/m<1$ and $λ\in\mathbb{C}\setminus\{0\}$. If the free critical points of $f_λ$ are escaped to the infinity, we prove that the Julia set $J_λ$ of $f_λ$ is quasisymmetrically equivalent to either a standard Cantor set, a standard Cantor set of circles or a round Sierpiński carpet (which is also standard in some sense). If the free critical points are not escaped, we give a sufficient condition on $λ$ such that $J_λ$ is a Sierpiński carpet and prove that most of them are quasisymmetrically equivalent to some round carpets. In particular, there exist infinitely renormalizable rational maps whose Julia sets are quasisymmetrically equivalent to round carpets.

math.DS↗

arXiv2020

Gaussian Constrained Attention Network for Scene Text Recognition

Scene text recognition has been a hot topic in computer vision. Recent methods adopt the attention mechanism for sequence prediction which achieve convincing results. However, we argue that the existing attention mechanism faces the problem of attention diffusion, in which the model may not focus on a certain character area. In this paper, we propose Gaussian Constrained Attention Network to deal with this problem. It is a 2D attention-based method integrated with a novel Gaussian Constrained Refinement Module, which predicts an additional Gaussian mask to refine the attention weights. Different from adopting an additional supervision on the attention weights simply, our proposed method introduces an explicit refinement. In this way, the attention weights will be more concentrated and the attention-based recognition network achieves better performance. The proposed Gaussian Constrained Refinement Module is flexible and can be applied to existing attention-based methods directly. The experiments on several benchmark datasets demonstrate the effectiveness of our proposed method. Our code has been available at https://github.com/Pay20Y/GCAN.

cs.CV↗

arXiv2020

Two-Level Residual Distillation based Triple Network for Incremental Object Detection

Modern object detection methods based on convolutional neural network suffer from severe catastrophic forgetting in learning new classes without original data. Due to time consumption, storage burden and privacy of old data, it is inadvisable to train the model from scratch with both old and new data when new object classes emerge after the model trained. In this paper, we propose a novel incremental object detector based on Faster R-CNN to continuously learn from new object classes without using old data. It is a triple network where an old model and a residual model as assistants for helping the incremental model learning on new classes without forgetting the previous learned knowledge. To better maintain the discrimination of features between old and new classes, the residual model is jointly trained on new classes in the incremental learning procedure. In addition, a corresponding distillation scheme is designed to guide the training process, which consists of a two-level residual distillation loss and a joint classification distillation loss. Extensive experiments on VOC2007 and COCO are conducted, and the results demonstrate that the proposed method can effectively learn to incrementally detect objects of new classes, and the problem of catastrophic forgetting is mitigated in this context.

cs.CV↗

arXiv2020

Variable Rate Deep Image Compression with Modulated Autoencoder

Variable rate is a requirement for flexible and adaptable image and video compression. However, deep image compression methods are optimized for a single fixed rate-distortion tradeoff. While this can be addressed by training multiple models for different tradeoffs, the memory requirements increase proportionally to the number of models. Scaling the bottleneck representation of a shared autoencoder can provide variable rate compression with a single shared autoencoder. However, the R-D performance using this simple mechanism degrades in low bitrates, and also shrinks the effective range of bit rates. Addressing these limitations, we formulate the problem of variable rate-distortion optimization for deep image compression, and propose modulated autoencoders (MAEs), where the representations of a shared autoencoder are adapted to the specific rate-distortion tradeoff via a modulation network. Jointly training this modulated autoencoder and modulation network provides an effective way to navigate the R-D operational curve. Our experiments show that the proposed method can achieve almost the same R-D performance of independent models with significantly fewer parameters.

eess.IV↗

arXiv2020

Self-Training for Domain Adaptive Scene Text Detection

Though deep learning based scene text detection has achieved great progress, well-trained detectors suffer from severe performance degradation for different domains. In general, a tremendous amount of data is indispensable to train the detector in the target domain. However, data collection and annotation are expensive and time-consuming. To address this problem, we propose a self-training framework to automatically mine hard examples with pseudo-labels from unannotated videos or images. To reduce the noise of hard examples, a novel text mining module is implemented based on the fusion of detection and tracking results. Then, an image-to-video generation method is designed for the tasks that videos are unavailable and only images can be used. Experimental results on standard benchmarks, including ICDAR2015, MSRA-TD500, ICDAR2017 MLT, demonstrate the effectiveness of our self-training method. The simple Mask R-CNN adapted with self-training and fine-tuned on real data can achieve comparable or even superior results with the state-of-the-art methods.

cs.CV↗

arXiv2020

Julia sets as buried Julia components

Let $f$ be a rational map with degree $d\geq 2$ whose Julia set is connected but not equal to the whole Riemann sphere. It is proved that there exists a rational map $g$ such that $g$ contains a buried Julia component on which the dynamics is quasiconformally conjugate to that of $f$ on the Julia set if and only if $f$ does not have parabolic basins and Siegel disks. If such $g$ exists, then the degree can be chosen such that $\text{deg}(g)\leq 7d-2$. In particular, if $f$ is a polynomial, then $g$ can be chosen such that $\text{deg}(g)\leq 4d+4$. Moreover, some quartic and cubic rational maps whose Julia sets contain buried Jordan curves are also constructed.

math.DS↗

arXiv2019

Fiber-optic joint time and frequency transfer with the same wavelength

Optical fiber links have demonstrated their ability to transfer the ultra-stable clock signals. In this paper we propose and demonstrate a new scheme to transfer both time and radio frequency with the same wavelength based on coherent demodulation technique. Time signal is encoded as a binary phase-shift keying (BPSK) to the optical carrier using electro optic modulator (EOM) by phase modulation and makes sure the frequency signal free from interference with single pulse. The phase changes caused by the fluctuations of the transfer links are actively cancelled at local site by optical delay lines. Radio frequency with 1GHz and time signal with one pulse per second (1PPS) transmitted over a 110km fiber spools are obtained. The experimental results demonstrate that frequency instabilities of 1.7E-14 at 1s and 5.9E-17 at 104s. Moreover, time interval transfer of 1PPS signal reaches sub-ps stability after 1000s. This scheme offers advantages with respect to reduce the channel in fiber network, and can keep time and frequency signal independent of each other.

eess.SP↗

arXiv2019

Efficient Segmentation: Learning Downsampling Near Semantic Boundaries

Many automated processes such as auto-piloting rely on a good semantic segmentation as a critical component. To speed up performance, it is common to downsample the input frame. However, this comes at the cost of missed small objects and reduced accuracy at semantic boundaries. To address this problem, we propose a new content-adaptive downsampling technique that learns to favor sampling locations near semantic boundaries of target classes. Cost-performance analysis shows that our method consistently outperforms the uniform sampling improving balance between accuracy and computational efficiency. Our adaptive sampling gives segmentation with better quality of boundaries and more reliable support for smaller-size objects.

cs.CV↗

arXiv2019

Sparse data interpolation using the geodesic distance affinity space

In this paper, we adapt the geodesic distance-based recursive filter to the sparse data interpolation problem. The proposed technique is general and can be easily applied to any kind of sparse data. We demonstrate the superiority over other interpolation techniques in three experiments for qualitative and quantitative evaluation. In addition, we compare our method with the popular interpolation algorithm presented in the EpicFlow optical flow paper that is intuitively motivated by a similar geodesic distance principle. The comparison shows that our algorithm is more accurate and considerably faster than the EpicFlow interpolation technique.

cs.CV↗

arXiv2019

On the classification of four-dimensional gradient Ricci solitons

In this paper, we prove some classification results for four-dimensional gradient Ricci solitons. For a four-dimensional gradient shrinking Ricci soliton with $div^4Rm^\pm=0$, we show that it is either Einstein or a finite quotient of $\mathbb{R}^4$, $\mathbb{S}^2\times\mathbb{R}^2$ or $\mathbb{S}^3\times\mathbb{R}$. The same result can be obtained under the condition of $div^4W^\pm=0$. We also present some classification results of four-dimensional complete non-compact gradient expanding Ricci soliton with non-negative Ricci curvature and gradient steady Ricci solitons under certain curvature conditions.

math.DG↗