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IMAGE SEGMENTATION BY PIECEWISE CONSTANT MUMFORD-SHAH MODEL WITHOUT ESTIMATING THE CONSTANTS

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Journal of Computational Mathematics 2006年第3期24卷 435-443页

作者： xue-cheng tai Chang-hui Yao CIPR Department of Mathematics University of Bergen Norway Department of Mathematics University of Bergen Norway

In this work, we try to use the so-called Piecewise Constant Level Set Method （PCLSM） for the Mumford-Shah segmentation model. For image segmentation, the Mumford-Shah model needs to find the regions and the constant values inside the regions for the segmen- tation. In order to use PCLSM for this purpose, we need to solve a minimization problem using the level set function and the constant values as minimization variables. In this work, we test on a model such that we only need to minimize with respect to the level set function, i.e., we do not need to minimize with respect to the constant values. Gradient descent method and Newton method are used to solve the Euler-Lagrange equation for the minimization problem. Numerical experiments are given to show the efficiency and advantages of the new model and algorithms.

关键词： PCLSM Image Segmentation Mumford-Shah model.

Augmented Lagrangian Methods for p-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing

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Numerical Mathematics(Theory,Methods and Applications) 2013年第1期6卷 1-20页

作者： Huibin Chang xue-cheng tai School of Mathematical Sciences Tianjin Normal UniversityTianjin 300387 Department of Mathematics East China Normal UniversityShanghai 200241China Department of Mathematics University of BergenJohaness Brunsgate 12Bergen 5007Norway

In this paper,we propose a generalized penalization technique and a convex constraint minimization approach for the p-harmonic flow problem following the ideas in[Kang&March,IEEE *** Process.,16(2007),2251–2261].We use fast algorithms to solve the subproblems,such as the dual projection methods,primal-dual methods and augmented Lagrangian *** a special penalization term,some special algorithms are *** experiments are given to demonstrate the performance of the proposed *** successfully show that our algorithms are effective and efficient due to two reasons:the solver for subproblem is fast in essence and there is no need to solve the subproblem accurately(even 2 inner iterations of the subproblem are enough).It is also observed that better PSNR values are produced using the new algorithms.

关键词： p-harmonic flows denoising generalized penalization terms saddle-point problem image processing augmented Lagrangian methods

Model the Solvent-Excluded Surface of 3D Protein Molecular Structures Using Geometric PDE-Based Level-Set Method

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Communications in Computational Physics 2009年第9期6卷 777-792页

作者： Qing Pan xue-cheng tai College of Mathematics and Computer Science Hunan Normal UniversityChangsha410081China Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore Department of Mathematics University of BergenNorway

This paper presents an approach to model the solvent-excluded surface(SES)of 3D protein molecular structures using the geometric PDE-based level-set *** level-set method embeds the shape of 3D molecular objects as an isosurface or level set corresponding to some isovalue of a scattered dense scalar field,which is saved as a discretely-sampled,rectilinear grid,i.e.,a volumetric *** level-set model is described as a class of tri-cubic tensor product B-spline implicit surface with control point values that are the signed distance *** geometric PDE is evolved in the discrete *** geometric PDE we use is the mean curvature specified flow,which coincides with the definition of the SES and is geometrically *** technique of speeding up is achieved by use of the narrow band strategy incorporated with a good initial approximate construction for the *** get a very desirable approximate surface for the SES.

关键词： Solvent-excluded surface implicit surface mean curvature specified flow level-set method

Segmentation by Elastica Energy with L^(1) and L^(2) Curvatures: a Performance Comparison

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Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 285-311页

作者： Xuan He Wei Zhu xue-cheng tai Department of Mathematics University of AlabamaBox 870350TuscaloosaAL 35487USA Department of Mathematics Hong Kong Baptist UniversityKowloonTong KowloonHong Kong

In this paper,we propose an algorithm based on augmented Lagrangian method and give a performance comparison for two segmentation models that use the L^(1)-and L^(2)-Euler’s elastica energy respectively as the regularization for image *** capture contour curvature more reliably,we develop novel augmented Lagrangian functionals that ensure the segmentation level set function to be signed dis-tance functions,which avoids the reinitialization of segmentation function during the iterative *** the proposed algorithm and with the same initial contours,we compare the performance of these two high-order segmentation models and numerically verify the different properties of the two models.

关键词： Augmented Lagrangian method Euler’s elastica image segmentation

Connections between Operator-Splitting Methods and Deep Neural Networks with Applications in Image Segmentation

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Annals of Applied Mathematics 2023年第4期39卷 406-428页

作者： Hao Liu xue-cheng tai Raymond Chan Department of Mathematics Hong Kong Baptist UniversityKowloon TongHong Kong Norwegian Research Centre(NORCE) Nyg˚ardsgaten 1125008 BergenNorway Department of Mathematics City University of Hong Kong and Hong Kong Center for Cerebro-Cardiovascular Health EngineeringHong Kong

Deep neural network is a powerful tool for many *** why it is so successful and providing a mathematical explanation is an important problem and has been one popular research direction in past *** the literature of mathematical analysis of deep neural networks,a lot of works is dedicated to establishing representation *** to make connections between deep neural networks and mathematical algorithms is still under *** this paper,we give an algorithmic explanation for deep neural networks,especially in their connections with operator *** show that with certain splitting strategies,operator-splitting methods have the same structure as *** this connection and the Potts model for image segmentation,two networks inspired by operator-splitting methods are *** two networks are essentially two operator-splitting algorithms solving the Potts *** experiments are presented to demonstrate the effectiveness of the proposed networks.

关键词： Potts model operator splitting deep neural network image segmentation

Efficient Convex Optimization Approaches to Variational Image Fusion

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Numerical Mathematics(Theory,Methods and Applications) 2014年第2期7卷 234-250页

作者： Jing Yuan Brandon Miles Greg Garvin xue-cheng tai Aaron Fenster Medical Imaging Lab Robarts Research InstituteUniversity of Western OntarioLondon ONCanada N6A 5B7 Department of Medical Imaging St Jospeh’s HealthCareLondon ONCanada Department of Mathematics University of BergenBergenNorway

Image fusion is an imaging technique to visualize information from multiple imaging sources in one single image,which is widely used in remote sensing,medical imaging *** this work,we study two variational approaches to image fusion which are closely related to the standard TV-L_(2) and TV-L_(1) image approximation *** investigate their convex optimization formulations,under the perspective of primal and dual,and propose their associated new image decomposition *** addition,we consider the TV-L_(1) based image fusion approach and study the specified problem of fusing two discrete-constrained images f_(1)(x)∈L_(1) and f_(2)(x)∈L_(2),where L_(1) and L_(2) are the sets of linearly-ordered discrete *** prove that the TV-L_(1) based image fusion actually gives rise to the exact convex relaxation to the corresponding nonconvex image fusion constrained by the discretevalued set u(x)∈L_(1)∪L_(2).This extends the results for the global optimization of the discrete-constrained TV-L_(1) image approximation[8,36]to the case of image *** a big numerical advantage of the two proposed dual models,we show both of them directly lead to new fast and reliable algorithms,based on modern convex optimization *** with medical images,remote sensing images and multi-focus images visibly show the qualitative differences between the two studied variational models of image *** also apply the new variational approaches to fusing 3D medical images.

关键词： Convex optimization primal-dual programming combinatorial optimization totalvariation regularization image fusion

Stroke-Based Surface Reconstruction

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Numerical Mathematics(Theory,Methods and Applications) 2013年第1期6卷 297-324页

作者： Jooyoung Hahn Jie Qiu Eiji Sugisaki Lei Jia xue-cheng tai Hock Soon Seah Institute of Mathematics and Scientific Computing University of GrazAustria School of Computer Engineering Nanyang Technological UniversitySingapore N-Design Inc. Japan Mathematics Institute University of BergenNorway

In this paper,we present a surface reconstruction via 2D strokes and a vector field on the strokes based on a two-step *** the first step,from sparse strokes drawn by artists and a given vector field on the strokes,we propose a nonlinear vector interpolation combining total variation(TV)and H1 regularization with a curl-free constraint for obtaining a dense vector *** the second step,a height map is obtained by integrating the dense vector field in the first *** discontinuities in surface and discontinuities of surface gradients can be well reconstructed without any surface *** also provide a fast and efficient algorithm for solving the proposed *** vectors on the strokes are interpreted as a projection of surface gradients onto the plane,different types of strokes are easily devised to generate geometrically crucial structures such as ridge,valley,jump,bump,and dip on the *** stroke types help users to create a surface which they intuitively imagine from 2D *** compare our results with conventional methods via many examples.

关键词： Surface reconstruction from a sparse vector field augmented Lagrangian method twostep method curl-free constraint total variation regularization preservation of discontinuities in surface normal vectors

A Level Set Representation Method for N-Dimensional Convex Shape and Applications

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Communications in Mathematical Research 2021年第2期37卷 180-208页

作者： Lingfeng Li Shousheng Luo xue-cheng tai Jiang Yang Department of Mathematics of Hong Kong Baptist University Hong KongSARChina Department of Mathematics of Southern University of Science and Technology ShenzhenChina School of Mathematics and Statistics Henan Engineering Research Center for Artificial Intelligence Theory and AlgorithmsHenan UniversityKaifengChina

In this work,we present a new method for convex shape representation,which is regardless of the dimension of the concerned objects,using level-set *** the best of our knowledge,the proposed prior is the first one which can work for high dimensional *** prior is very useful for object completion in computer *** is a very challenging task to represent high dimensional convex *** this paper,we first prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance ***,the second order condition of convex functions is used to characterize the shape convexity *** apply this new method to two applications:object segmentation with convexity prior and convex hull problem(especially with outliers).For both applications,the involved problems can be written as a general optimization problem with three *** algorithm based on the alternating direction method of multipliers is presented for the optimization *** experiments are conducted to verify the effectiveness of the proposed representation method and algorithm.

关键词： Convex shape prior level-set method image segmentation convex hull ADMM

ZNF554 Inhibits Endometrial Cancer Progression via Regulating RBM5 and Inactivating WNT/β-Catenin Signaling Pathway

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Current Medical Science 2024年第2期44卷 406-418页

作者： cheng-cheng ZHU Heng-liang SUN Teng-fei LONG Yuan-yuan LYU Jiang-li LIU Guan-tai NI Anhui Medical University Hefei 230032China Department of Obstetrics and Gynecology The First Affiliated Hospital of Wannan Medical CollegeWuhu 241001China

Objective:Uterine corpus endometrial carcinoma(UCEC),a kind of gynecologic malignancy,poses a significant risk to women’s *** precise mechanism underlying the development of UCEC remains *** finger protein 554(ZNF554),a member of the Krüppel-associated box domain zinc finger protein superfamily,was reported to be dysregulated in various illnesses,including malignant *** study aimed to examine the involvement of ZNF554 in the development of ***:The expression of ZNF554 in UCEC tissues and cell lines were examined by qRT-PCR and Western blot *** with stably overexpressed or knocked-down ZNF554 were established through lentivirus ***-8,wound healing,and Transwell invasion assays were employed to assess cell proliferation,migration,and *** iodide(PI)staining combined with fluorescence-activated cell sorting(FACS)flow cytometer was utilized to detect cell cycle ***-PCR and Western blotting were conducted to examine relative mRNA and protein *** immunoprecipitation assay and luciferase reporter assay were used to explore the regulatory role of ZNF554 in RNA binding motif 5(RBM5).Results:The expression of ZNF554 was found to be reduced in both UCEC samples and cell *** expression of ZNF554 was associated with higher tumor stage,decreased overall survival,and reduced disease-free survival in ***554 overexpression suppressed cell proliferation,migration,and invasion,while also inducing cell cycle *** contrast,a decrease in ZNF554 expression resulted in the opposite ***,ZNF554 transcriptionally regulated RBM5,leading to the deactivation of the Wingless(WNT)/β-catenin signaling ***,the findings from rescue studies demonstrated that the inhibition of RBM5 negated the impact of ZNF554 overexpression onβ-catenin and p-glycogen synthase kinase-3β(p-GSK-3β).Similarly,the deliberate activation of RBM5 reduced the increase inβ-catenin and

关键词： zinc finger protein 554 endometrial carcinoma RNA binding motif 5 Wingless/β-catenin signaling pathway