arXiv subjects

Xiaoping Yang

Publications and source records attributed to Xiaoping Yang.

At least 37 records · Page 2Linked to original sources

arXiv2021

A Characteristic Function-based Algorithm for Geodesic Active Contours

Active contour models have been widely used in image segmentation, and the level set method (LSM) is the most popular approach for solving the models, via implicitly representing the contour by a level set function. However, the LSM suffers from high computational burden and numerical instability, requiring additional regularization terms or re-initialization techniques. In this paper, we use characteristic functions to implicitly represent the contours, propose a new representation to the geodesic active contours and derive an efficient algorithm termed as the iterative convolution-thresholding method (ICTM). Compared to the LSM, the ICTM is simpler and much more efficient. In addition, the ICTM enjoys most desired features of the level set-based methods. Extensive experiments, on 2D synthetic, 2D ultrasound, 3D CT, and 3D MR images for nodule, organ and lesion segmentation, demonstrate that the proposed method not only obtains comparable or even better segmentation results (compared to the LSM) but also achieves significant acceleration.

cs.CV↗

arXiv2020

Combining CNN and Hybrid Active Contours for Head and Neck Tumor Segmentation in CT and PET images

Automatic segmentation of head and neck tumors plays an important role in radiomics analysis. In this short paper, we propose an automatic segmentation method for head and neck tumors from PET and CT images based on the combination of convolutional neural networks (CNNs) and hybrid active contours. Specifically, we first introduce a multi-channel 3D U-Net to segment the tumor with the concatenated PET and CT images. Then, we estimate the segmentation uncertainty by model ensembles and define a segmentation quality score to select the cases with high uncertainties. Finally, we develop a hybrid active contour model to refine the high uncertainty cases. Our method ranked second place in the MICCAI 2020 HECKTOR challenge with average Dice Similarity Coefficient, precision, and recall of 0.752, 0.838, and 0.717, respectively.

eess.IV↗

arXiv2020

Towards Data-Efficient Learning: A Benchmark for COVID-19 CT Lung and Infection Segmentation

Purpose: Accurate segmentation of lung and infection in COVID-19 CT scans plays an important role in the quantitative management of patients. Most of the existing studies are based on large and private annotated datasets that are impractical to obtain from a single institution, especially when radiologists are busy fighting the coronavirus disease. Furthermore, it is hard to compare current COVID-19 CT segmentation methods as they are developed on different datasets, trained in different settings, and evaluated with different metrics. Methods: To promote the development of data-efficient deep learning methods, in this paper, we built three benchmarks for lung and infection segmentation based on 70 annotated COVID-19 cases, which contain current active research areas, e.g., few-shot learning, domain generalization, and knowledge transfer. For a fair comparison among different segmentation methods, we also provide standard training, validation and testing splits, evaluation metrics and, the corresponding code. Results: Based on the state-of-the-art network, we provide more than 40 pre-trained baseline models, which not only serve as out-of-the-box segmentation tools but also save computational time for researchers who are interested in COVID-19 lung and infection segmentation. We achieve average Dice Similarity Coefficient (DSC) scores of 97.3\%, 97.7\%, and 67.3\% and average Normalized Surface Dice (NSD) scores of 90.6\%, 91.4\%, and 70.0\% for left lung, right lung, and infection, respectively. Conclusions: To the best of our knowledge, this work presents the first data-efficient learning benchmark for medical image segmentation and the largest number of pre-trained models up to now. All these resources are publicly available, and our work lays the foundation for promoting the development of deep learning methods for efficient COVID-19 CT segmentation with limited data.

eess.IV↗

arXiv2020

Three-dimensional topological semimetal phase in layered TaNiTe5 probed by de Haas-van Alphen effect

Layered three-dimensional (3D) topological semimetals have attracted intensively attention due to the exotic phenomena and abundantly tunable properties. Here we report the experimental evidence for the 3D topological semimetal phase in layered material TaNiTe5 single crystals through quantum oscillations. Strong quantum oscillations have been observed with diamagnetism background in TaNiTe5. By analyzing the de Haas-van Alphen oscillations, multi-periodic oscillations were extracted, in content with magnetotransport measurements. Moreover, nontrivial "π" Berry phase with 3D Fermi surface is identified, indicating the topologically nontrivial feature in TaNiTe5. Additionally, we demonstrated the thin-layer of TaNiTe5 crystals is highly feasible by the mechanical exfoliation, which offers a platform to explore exotic properties in low dimensional topological semimetal and paves the way for potential applications in nanodevices.

cond-mat.str-el↗

arXiv2020

Multi-Site Infant Brain Segmentation Algorithms: The iSeg-2019 Challenge

To better understand early brain growth patterns in health and disorder, it is critical to accurately segment infant brain magnetic resonance (MR) images into white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). Deep learning-based methods have achieved state-of-the-art performance; however, one of major limitations is that the learning-based methods may suffer from the multi-site issue, that is, the models trained on a dataset from one site may not be applicable to the datasets acquired from other sites with different imaging protocols/scanners. To promote methodological development in the community, iSeg-2019 challenge (http://iseg2019.web.unc.edu) provides a set of 6-month infant subjects from multiple sites with different protocols/scanners for the participating methods. Training/validation subjects are from UNC (MAP) and testing subjects are from UNC/UMN (BCP), Stanford University, and Emory University. By the time of writing, there are 30 automatic segmentation methods participating in iSeg-2019. We review the 8 top-ranked teams by detailing their pipelines/implementations, presenting experimental results and evaluating performance in terms of the whole brain, regions of interest, and gyral landmark curves. We also discuss their limitations and possible future directions for the multi-site issue. We hope that the multi-site dataset in iSeg-2019 and this review article will attract more researchers on the multi-site issue.

eess.IV↗

arXiv2020

Epitaxial engineering of flat silver fluorides cuprate analogs

As-grown AgF2 has a remarkably similar electronic structure as insulating cuprates, but it is extremely electronegative, which makes it hard to handle and dope. Furthermore, buckling of layers reduces magnetic interactions and enhances unwanted self-trapping lattice effects. We argue that epitaxial engineering can solve all these problems. By using a high throughput approach and first principle computations, we find a set of candidate substrates which can sustain the chemical aggressiveness of AgF2 and at the same time have good lattice parameter matching for heteroepitaxy, enhancing AgF2 magnetic and transport properties and opening the possibility of field-effect carrier injection to achieve a new generation of high-Tc superconductors. Assuming a magnetic mechanism and extrapolating from cuprates we predict that the superconducting critical temperature of a single layer can reach 195 K.

cond-mat.str-el↗

arXiv2018

Critical points of solutions to a kind of linear elliptic equations in multiply connected domains

In this paper, we mainly study the critical points and critical zero points of solutions $u$ to a kind of linear elliptic equations with nonhomogeneous Dirichlet boundary conditions in a multiply connected domain $Ω$ in $\mathbb{R}^2$. Based on the fine analysis about the distributions of connected components of the super-level sets $\{x\in Ω: u(x)>t\}$ and sub-level sets $\{x\in Ω: u(x)<t\}$ for some $t$, we obtain the geometric structure of interior critical point sets of $u$. Precisely, let $Ω$ be a multiply connected domain with the interior boundary $γ_I$ and the external boundary $γ_E$, where $u|_{γ_I}=ψ_1(x),~u|_{γ_E}=ψ_2(x)$. When $ψ_1(x)$ and $ψ_2(x)$ have $N_1$ and $N_2$ local maximal points on $γ_I$ and $γ_E$ respectively, we deduce that $\sum_{i = 1}^k {m_i}\leq N_1+ N_2$, where $m_1,\cdots,m_k$ are the respective multiplicities of interior critical points $x_1,\cdots,x_k$ of $u$. In addition, when $\min_{γ_E}ψ_2(x)\geq \max_{γ_I}ψ_1(x)$ and $u$ has only $N_1$ and $N_2$ equal local maxima relative to $\overlineΩ$ on $γ_I$ and $γ_E$ respectively, we develop a new method to show that one of the following three results holds $\sum_{i = 1}^k {m_i}=N_1+N_2$ or $\sum_{i = 1}^k {m_i}+1=N_1+N_2$ or $\sum_{i = 1}^k {m_i}+2=N_1+N_2$. Moreover, we investigate the geometric structure of interior critical zero points of $u.$ We obtain that the sum of multiplicities of the interior critical zero points of $u$ is less than or equal to the half of the number of its isolated zero points on the boundaries.

math.AP↗

arXiv2018

Interior C^{1,1} regularity of solutions to degenerate Monge-Ampère type equations

In this paper, we study the interior C^{1,1} regularity of viscosity solutions for a degenerate Monge-Ampère type equation \det[D^{2}u-A(x, u, Du)]=B(x, u, Du) when B \geq 0 and B^{\frac{1}{n-1}}\in C^{1,1}(\barΩ\times\mathbb{R}\times \mathbb{R}^n). We prove that u\in C^{1,1}(Ω) under the A3 condition and A3w^+ condition respectively. In the former case, we construct a suitable auxiliary function to obtain uniform {\it a priori} estimates directly. In the latter case, the main argument is to establish the Pogorelov type estimates, which are interesting independently.

math.AP↗

arXiv2018

Measure Upper Bounds of Nodal Sets of Robin Eigenfunctions

In this paper, we obtain the upper bounds for the Hausdorff measures of nodal sets of eigenfunctions with the Robin boundary conditions, i.e., \begin{equation*} {\left\{\begin{array}{l} \triangle u+λu=0,\quad in\quad Ω,\\ u_ν+μu=0,\quad on\quad\partialΩ, \end{array} \right.} \end{equation*} where the domain $Ω\subseteq\mathbb{R}^n$, $u_ν$ means the derivative of $u$ along the outer normal direction of $\partialΩ$. We show that, if $Ω$ is bounded and analytic, and the corresponding eigenvalue $λ$ is large enough,then the measure upper bounds for the nodal sets of eigenfunctions are $C\sqrtλ$, where $C$ is a positive constant depending only on $n$ and $Ω$ but not on $μ$ We also show that, if $\partialΩ$ is $C^{\infty}$ smooth and $\partialΩ\setminusΓ$ is piecewise analytic, where $Γ\subseteq\partialΩ$ is a union of some $n-2$ dimensional submanifolds of $\partialΩ$, $μ>0$, and $λ$ is large enough, then the corresponding measure upper bounds for the nodal sets of $u$ are $C(\sqrtλ+μ^α+μ^{-cα})$ for some positive number $α$, where $c$ is a positive constant depending only on $n$, and $C$ is a positive constant depending on $n$, $Ω$, $Γ$ and $α$.

math.AP↗

arXiv2017

Pressure-induced Superconductivity in the Three-component Fermion Topological Semimetal Molybdenum Phosphide

Topological semimetal, a novel state of quantum matter hosting exotic emergent quantum phenomena dictated by the non-trivial band topology, has emerged as a new frontier in condensed-matter physics. Very recently, a coexistence of triply degenerate points of band crossing and Weyl points near the Fermi level was theoretically predicted and immediately experimentally verified in single crystalline molybdenum phosphide (MoP). Here we show in this material the high-pressure electronic transport and synchrotron X-ray diffraction (XRD) measurements, combined with density functional theory (DFT) calculations. We report the emergence of pressure-induced superconductivity in MoP with a critical temperature Tc of about 2 K at 27.6 GPa, rising to 3.7 K at the highest pressure of 95.0 GPa studied. No structural phase transitions is detected up to 60.6 GPa from the XRD. Meanwhile, the Weyl points and triply degenerate points topologically protected by the crystal symmetry are retained at high pressure as revealed by our DFT calculations. The coexistence of three-component fermion and superconductivity in heavily pressurized MoP offers an excellent platform to study the interplay between topological phase of matter and superconductivity.

cond-mat.supr-con↗

arXiv2017

Measure Upper Bounds for Nodal Sets of Eigenfunctions of the bi-Harmonic Operator

In this article, we consider eigenfunctions $u$ of the bi-harmonic operator, i.e., $\triangle^2u=λ^2u$ on $Ω$ with some homogeneous linear boundary conditions. We assume that $Ω\subseteq\mathbb{R}^n$ ($n\geq2$) is a $C^{\infty}$ bounded domain, $\partialΩ$ is piecewise analytic and $\partialΩ$ is analytic except a set $Γ\subseteq\partialΩ$ which is a finite union of some compact $(n-2)$ dimensional submanifolds of $\partialΩ$. The main result of this paper is that the measure upper bounds of the nodal sets of the eigenfunctions is controlled by $\sqrtλ$. We first define a frequency function and a doubling index related to these eigenfunctions. With the help of establishing the monotonicity formula, doubling conditions and various a priori estimates, we obtain that the $(n-1)$ dimensional Hausdorff measures of nodal sets of these eigenfunctions in a ball are controlled by the frequency function and $\sqrtλ$. In order to further control the frequency function with $\sqrtλ$, we first establish the relationship between the frequency function and the doubling index, and then separate the domain $Ω$ into two parts: a domain away from $Γ$ and a domain near $Γ$, and develop iteration arguments to deal with the two cases respectively.

math.AP↗

arXiv2015

Extremals in the Engel group with a sub-Lorentzian metric

Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first prove that timelike normal extremals are locally maximizing. Second, we obtain a parametrization of timelike, spacelike, lightlike normal extremal trajectories by Jacobi functions. Third, a discrete symmetry group and its fixed points which are Maxwell points of of timelike and spacelike normal extremals, are described. An estimate for the cut time (the time of loss of optimality) on extremal trajectories is derived on this basis.

math.DG↗

arXiv2015

Geodesics in the Engel group with a sub-Lorentzian metric

Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first study some properties of horizontal curves on E. Second, we prove that time-like normal geodesics are locally maximizers in the Engel group, and calculate the explicit expression of non-space-like geodesics.

math.OC↗

arXiv2014

Complex Monge-Ampère equations with oblique boundary value

The existence and regularity of the classical plurisubharmonic solution for complex Monge-Ampère equations subject to the semilinear oblique boundary condition which is C^1 perturbation of the Neumann boundary condition, are proved in the certain strictly pseudoconvex domain in C^n.

math.AP↗

arXiv2013

A mean value formula of sub-p-Laplace parabolic equations on the Heisenberg group

We derive two equivalent definitions of the viscosity solutions to the homogeneous sub-p- Laplace parabolic equations on the Heisenberg group, and characterize the viscosity solutions in terms of an asymptotic mean value formula. Moreover, we construct an example to show that these formulae do not hold in non-asymptotic sense.

math.AP↗

arXiv2012

On Regularity of Abnormal Subriemannian Geodesics

We prove the smoothness of abnormal minimizers of subriemannian manifolds of step 3 with a nilpotent basis. We prove that rank 2 Carnot groups of step 4 admit no strictly abnormal minimizers. For any subriemannian manifolds of step less than 7, we show all abnormal minimizers have no corner type singularities, which partly generalize the main result of Leonardi-Monti.

math.DG↗

arXiv2012

SubRiemannian geodesics for Carnot groups of step 3

In Carnot groups of step 3, all subriemannian geodesics are proved to be normal. The proof is based on a reduction argument and the Goh condition for minimality of singular curves. The Goh condition is deduced from a reformulation and a calculus of the end-point mapping which boils down to the graded structures of Carnot groups.

math.DG↗

arXiv2011

Electronic structure of nickelates: From two-dimensional heterostructures to three-dimensional bulk materials

Reduced dimensionality and strong electronic correlations, which are among the most important ingredients for cupratelike high-Tc superconductivity, characterize also the physics of nickelate-based heterostructures. Starting from the local-density approximation we arrive at a simple two-band model for quasi-two-dimensional 2D LaNiO3 /LaAlO3 heterostructures and extend it by introducing an appropriate hopping in the z direction to describe the dimensional crossover to three dimensions 3D. Using dynamical mean-field theory, we study the effects of electronic correlations with increasing interaction strength along the crossover from 2D to 3D. Qualitatively, the effects of electronic correlations are surprisingly similar, albeit quantitatively larger interaction strengths are required in three dimensions for getting a Mott-Hubbard insulating state. The exchange parameters of an effective Kugel-Khomskii-type spin-orbital model are also derived and reveal strong antiferromagnetic tendencies.

cond-mat.str-el↗