高教深耕計畫

• 數學講座-侯一釗(數據中心)
  1080101~1081231
  

國科會計畫統計

• 深度學習的數學影像處理
  1160801~1170731
  

• 深度學習的數學影像處理
  1150801~1160731
  

• 深度學習的數學影像處理
  1140801~1150731
  

• 強度非均勻圖像分割的數值分析與計算
  1130801~1150131
  

• 強度非均勻圖像分割的數值分析與計算
  1120801~1130731
  

• 強度非均勻圖像分割的數值分析與計算
  1110801~1120731
  

• 影像處理的自適應變分模型與數值計算
  1100801~1120731
  [影像處理,變分模型,自適應方法,影像對比強化,影像融合,影像超解析度重建 , image processing,variational model,adaptive method,image contrast enhancement,image fusion,image super-resolution reconstruction.]

• 自然科學及永續研究圖書服務計畫-數學領域(子計畫二)(1/5)
  1100101~1111231
  [圖書服務計畫 , library service project]

• 影像處理的自適應變分模型與數值計算
  1090801~1100731
  [影像處理,變分模型,自適應方法,影像對比強化,影像融合,影像超解析度重建 , image processing,variational model,adaptive method,image contrast enhancement,image fusion,image super-resolution reconstruction.]

• 數學圖書期刊服務計畫-桃園中壢地區
  1081201~1091231
  

• 影像處理的自適應變分模型與數值計算
  1080801~1090731
  [影像處理,變分模型,自適應方法,影像對比強化,影像融合,影像超解析度重建 , image processing,variational model,adaptive method,image contrast enhancement,image fusion,image super-resolution reconstruction.]

• 數學學門 (應數組) 研究發展及推動計畫
  1080101~1081231
  [數學學門業務推展,數學學門重點研究領域,計畫審查 , Mathematical research and promotion, frontier research in mathematics, grant review]

• 模擬流構耦合動力行為的高效率數值方法之研究
  1070801~1080731
  [不可壓縮那維爾-史托克方程,流構耦合,沉浸邊界法,懲罰法,人工壓縮法,直 接施力法,投影法, , incompressible Navier-Stokes equations, fluid-structure interaction, immersed boundary method, penalty method, artificial compressibility method, direct-forcing method, projection scheme,]

• 數學學門(應數組)研究發展及推動計畫
  1070101~1071231
  [數學學門業務推展,數學學門重點研究領域,計畫審查 , Mathematical research and promotion,frontier research in mathematics,grant review]

• 模擬流構耦合動力行為的高效率數值方法之研究
  1060801~1070731
  [不可壓縮那維爾-史托克方程,流構耦合,沉浸邊界法,懲罰法,人工壓縮法,直 接施力法,投影法, , incompressible Navier-Stokes equations, fluid-structure interaction, immersed boundary method, penalty method, artificial compressibility method, direct-forcing method, projection scheme,]

• 數學學門(應數組)研究發展及推動計畫
  1060101~1061231
  [數學學門業務推展,數學學門重點研究領域,計畫審查 , Mathematical research and promotion,frontier research in mathematics,grant review]

產學合作計畫統計

• 開發用於針孔相機模型校準和低秩紋理缺陷檢測的計算最佳化方法
  1110801~1120731
  [相機校準,計算最佳化,非線性最小平方,缺陷檢測,低秩紋理,轉換不變,穩健主成份分析 , camera calibration,computational optimization,nonlinear least-squares,defect detection,low-rank texture,transform invariant,robust PCA]

期刊著作

• Fractional Laplacian-Enhanced Local-Global Intensity Fitting Energy for Noisy and Inhomogeneous Image Segmentation
  Journal of Scientific Computing, 104, 2, 2025-08-01
  [ Fractional Laplacian,Intensity inhomogeneity,Iterative convolution-thresholding method,Variational image Segmentation ]

• Additive-Bias-Correction Variational Model for Noisy and Intensity-Inhomogeneous Image Segmentation*
  SIAM Journal on Imaging Sciences, 18, 2, 1235-1259, 2025-01-01
  [ additive bias correction,intensity inhomogeneity,iterative convolution-thresholding method,noise removal,unconditional energy stability,variational image segmentation ]

• Efficient variational segmentation with local intensity fitting for noisy and inhomogeneous images
  Multimedia Systems, 30, 5, 2024-10-01
  [ 65K10,68U10,Intensity inhomogeneity,Iterative convolution-thresholding method,Local intensity fitting energy,Noise,Variational image segmentation ]

• An entropy-weighted local intensity clustering-based model for segmenting intensity inhomogeneous images
  Multimedia Systems, 30, 1, 2024-02-01
  [ Bias correction,Chan-Vese model,Image segmentation,Intensity clustering,Intensity inhomogeneity,Iterative convolution-thresholding scheme,Local entropy,Mumford-Shah model ]

• A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems
  Advances in Applied Mathematics and Mechanics, 15, 1, 1-29, 2023-01-01
  [ direct-forcing method,Fluid-solid interaction,heat transfer,immersed boundary method,projection scheme ]

• A simple and effective multi-focus image fusion method based on local standard deviations enhanced by the guided filter
  Displays, 72, 2022-04-01
  [ Guided filter,Local standard deviation,Local variance,Multi-focus image fusion ]

• Adaptive variational model for contrast enhancement of low-light images
  SIAM Journal on Imaging Sciences, 13, 1, 1-28, 2020-01-01
  [ Adaptive variational model,Contrast enhancement,Image enhancement,Low-light images,Nonuniform illumination ]

• A direct-forcing immersed boundary projection method for simulating the dynamics of freely falling solid bodies in an incompressible viscous fluid∗
  Annals of Mathematical Sciences and Applications, 5, 1, 75-100, 2020-01-01
  [ direct-forcing method,fluid-solid interaction,free falling body,immersed boundary method,Incompressible Navier-Stokes equations,projection scheme,sedimentation ]

• Advection-enhanced gradient vector flow for active-contour image segmentation
  Communications in Computational Physics, 26, 1, 206-232, 2019-01-01

• A simple direct-forcing immersed boundary projection method with prediction-correction for fluid-solid interaction problems
  Computers and Fluids, 176, 135-152, 2018-11-15
  [ Direct-forcing method , Fluid-solid interaction , Immersed boundary method , Incompressible Navier–Stokes equations , Prediction-correction , Projection scheme ]

• A regularization model with adaptive diffusivity for variational image denoising
  Signal Processing, 149, 214-228, 2018-08-01
  [ Adaptivity , Image denoising , Regularization , Split Bregman iteration , Total variation ]

• A mixed H1-conforming finite element method for solving Maxwell's equations with non-H1 solution
  SIAM Journal of Scientific Computing, 40, 1, A224-A250, 2018-01-01
  [ Babuška-Brezzi inf-sup condition , C elements 1 , Coercivity , Error estimates , H -conforming finite element method 1 , Maxwell's equations , Non-H very weak solution 1 ]

• A robust finite difference scheme for strongly coupled systems of singularly perturbed convection-diffusion equations
  Numerical Methods for Partial Differential Equations, 34, 1, 121-144, 2018-01-01
  [ boundary and interior layers , Il'in-Allen-Southwell scheme , magnetohydrodynamic duct flow , singularly perturbed convection-diffusion equation , strongly coupled system , uniform convergence ]

• A new discrete cucker-smale flocking model under hierarchical leadership
  Discrete and Continuous Dynamical Systems - Series B, 21, 8, 2587-2599, 2016-10-01
  [ Cucker-Smale model , Discrete-Time system. , Emergence behavior , Flocking , Hierarchical lead-ership ]

• A new stabilized linear finite element method for solving reaction-convection-diffusion equations
  Computer Methods in Applied Mechanics and Engineering, 307, 362-382, 2016-08-01
  [ Boundary layer , Interior layer , Reaction-convection-diffusion equation , Stabilization parameter , Stabilized finite element method ]

• A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations
  Communications in Computational Physics, 19, 5, 1287-1301, 2016-05-01
  [ boundary layer,formally second-order scheme,Il'in-Allen-Southwell scheme,interior layer,System of singularly perturbed equations,system of viscous Burgers' equations ]

• Effects of network structure on the synchronizability of nonlinearly coupled Hindmarsh-Rose neurons
  Physics Letters, Section A: General, Atomic and Solid State Physics, 379, 40-41, 2541-2548, 2015-10-23
  [ Coupled dynamical network,Hindmarsh-Rose neuron,Modular network,Scale-free network,Small-world network,Synchronization ]

• An Unconditionally Energy Stable Penalty Immersed Boundary Method for Simulating the Dynamics of an Inextensible Interface Interacting with a Solid Particle
  Journal of Scientific Computing, 64, 2, 289-316, 2015-08-29
  [ Immersed boundary method , Inextensible interface , Penalty method , Solid particle , Stability , Stokes flow ]

• Eventual dissipativeness and synchronization of nonlinearly coupled dynamical network of Hindmarsh-Rose neurons
  Applied Mathematical Modelling, 39, 21, 6631-6644, 2015-01-01
  [ Coupled dynamical network , Eventual dissipativeness , Global synchronization , Hindmarsh-Rose neuron , Lyapunov function , Modular network ]

• Computation of Maxwell singular solution by nodal-continuous elements
  Journal of Computational Physics, 268, 63-83, 2014-07-01
  [ Eigenvalue problem , Interface problem , Maxwell's equations , Nodal-continuous element ]

• Analysis of the small viscosity and large reaction coefficient in the computation of the generalized Stokes problem by a novel stabilized finite element method
  Computer Methods in Applied Mechanics and Engineering, 271, 23-47, 2014-04-01
  [ Generalized Stokes problem , Large reaction coefficient , Small viscosity , Stabilization parameter , Stabilized finite element method ]

• Error and attack tolerance of synchronization in Hindmarsh-Rose neural networks with community structure
  Physics Letters, Section A: General, Atomic and Solid State Physics, 378, 18-19, 1239-1248, 2014-03-28
  [ Centrality,Community structure,Complex network,Failure tolerance,Hindmarsh-Rose neuron,Synchronization ]

• An SPD stabilized finite element method for the Stokes equations
  IMA Journal of Numerical Analysis, 35, 4, 1812-1841, 2014-02-24
  [ H norm -1 , linear finite element solution of the Poisson Dirichlet problem , stabilized finite element method , Stokes equations , symmetric positivedefiniteness ]

• A high-accuracy finite difference scheme for solving reaction-convection-diffusion problemswith a small diffusivity
  Advances in Applied Mathematics and Mechanics, 6, 5, 637-662, 2014-01-01
  [ Boundary layer , Finite difference scheme , Incompressible Navier-Stokes equations , Interior layer , Reaction-convection-diffusion equation ]

• Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks
  Communications in Nonlinear Science and Numerical Simulation, 19, 4, 1042-1054, 2014-01-01
  [ Community structure,Complex network,Epidemic model,Global stability,Lyapunov function ]

• Effect of permeability-porosity functions on simulated morphological evolution of a chemical dissolution front
  Hydrological Processes, 28, 1, 16-24, 2014-01-01
  [ Chemical reaction front , Fair-Hatch model , Kozeny-Carman model , Permeability-porosity relationship , Verma-Pruess model ]

• Analysis of a new stabilized finite element method for the reaction-convection-diffusion equations with a large reaction coefficient
  Computer Methods in Applied Mechanics and Engineering, 247-248, 15-36, 2012-11-01
  [ Boundary layer , Finite element method , Interior layer , Reaction-convection-diffusion equation , Stabilization method ]

• Analysis of the permanence of an SIR epidemic model with logistic process and distributed time delay
  Communications in Nonlinear Science and Numerical Simulation, 17, 9, 3696-3707, 2012-09-01
  [ Asymptotic stability , Permanence , SIR epidemic model , Time delay ]

• Permanence of an SIR epidemic model with density dependent birth rate and distributed time delay
  Applied Mathematics and Computation, 218, 5, 1682-1693, 2011-11-01
  [ Asymptotic stability , Permanence , SIR epidemic model , Time delay ]

• A tailored finite point method for solving steady MHD duct flow problems with boundary layers
  Communications in Computational Physics, 10, 1, 161-182, 2011-01-01
  [ Boundary layers,Convection-dominated problems,Finite difference methods,Hartmann numbers,Magnetohydrodynamic equations,Tailored finite point methods ]

• A graph approach to synchronization in complex networks of asymmetrically nonlinear coupled dynamical systems
  Journal of the London Mathematical Society, 83, 3, 711-732, 2011-01-01

• Two new upwind difference schemes for a coupled system of convection-diffusion equations arising from the steady MHD duct flow problems
  Journal of Computational Physics, 229, 24, 9216-9234, 2010-12-10
  [ Boundary layers , Convection-diffusion equations , Duct flows , Hartmann numbers , Magnetohydrodynamic equations , Upwind difference schemes ]

• A novel least-squares finite e lement method enriched with residual-free bubbles for solving convection-dominated problems
  SIAM Journal of Scientific Computing, 32, 4, 2047-2073, 2010-08-23
  [ Boundary and interior layers , Convection-dominated problems , Least-squares finite element methods , Residual-free bubbles , Stabilized methods ]

• Stability and bifurcation of a two-neuron network with distributed time delays
  Nonlinear Analysis: Real World Applications, 11, 3, 1472-1490, 2010-06-01
  [ Characteristic equation , Distributed time delay , Hopf bifurcation , Neural network , Normal form , Pitchfork bifurcation ]

• Existence of periodic solutions for a system of delay differential equations
  Nonlinear Analysis, Theory, Methods and Applications, 71, 12, 6222-6231, 2009-12-15
  [ Delay differential equation , Global exponential stability , Lyapunov functional , Periodic solution , Poincaré-Bendixson theorem ]

• A bubble-stabilized least-squares finite element method for steady MHD duct flow problems at high Hartmann numbers
  Journal of Computational Physics, 228, 22, 8301-8320, 2009-12-01
  [ Convection-dominated problems , Finite element methods , Hartmann numbers , Least-squares , Magnetohydrodynamic equations , Residual-free bubbles ]

• On efficient least-squares finite element methods for convection-dominated problems
  Computer Methods in Applied Mechanics and Engineering, 199, 1-4, 183-196, 2009-12-01
  [ Boundary and interior layers , Convection-dominated problems , Finite element methods , Least-squares , Stabilized methods , Streamline diffusion ]

• Existence and attractivity of periodic solutions to non-autonomous Cohen-Grossberg neural networks with time delays
  Chaos, Solitons and Fractals, 41, 3, 1235-1244, 2009-08-15

• On two iterative least-squares finite element schemes for the incompressible navier-stokes problem
  Numerical Functional Analysis and Optimization, 30, 5-6, 436-461, 2009-05-01
  [ Driven cavity flows , Finite element methods , Iterative methods , Least squares , Navier-Stokes equations , Oseen equations ]

• Synchronization in delayed Cohen-Grossberg neural networks with bounded external inputs
  IMA Journal of Applied Mathematics, 74, 2, 178-200, 2009-04-08
  [ Cohen-Grossberg neural networks , Discrete time delays , Distributed time delays , Exponential synchronization , Lyapunov functionals ]

• Global attractivity in delayed Cohen-Grossberg neural network models
  Chaos, Solitons and Fractals, 39, 4, 1975-1987, 2009-02-28

• Synchronization in linearly coupled dynamical networks with distributed time delays
  International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 18, 7, 2039-2047, 2008-01-01
  [ Coupled Chua's circuits , Coupled Hindmarsh-Rose neurons , Distributed time delays , Exponential synchronization , Linearly coupled dynamical networks ]

• Diversity of traveling wave solutions in delayed cellular neural networks
  International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 18, 12, 3515-3550, 2008-01-01
  [ Comparison principle , Delayed cellular neural networks , Lattice dynamical systems , Method of step , Monotone iteration scheme , Traveling waves ]

• Analysis of the [L2,L2,L2] least-squares finite element method for incompressible oseen-type problems
  International Journal of Numerical Analysis and Modeling, 4, 3-4, 402-424, 2007-12-01
  [ Finite element methods , Least squares , Navier-Stokes equations , Oseen-type equations ]

• A further analysis on harmless delays in Cohen-Grossberg neural networks
  Chaos, Solitons and Fractals, 34, 2, 646-653, 2007-10-01

• Analysis of a splitting method for incompressible inviscid rotational flow problems
  Journal of Computational and Applied Mathematics, 200, 1, 364-376, 2007-03-01
  [ Finite element methods , Incompressible inviscid rotational flows , Least squares , Velocity-vorticity-pressure formulation ]

• Analysis of the L2 least-squares finite element method for a velocity-vorticity problem arising in incompressible inviscid rotational flows
  Applied Mathematics and Computation, 185, 1, 604-613, 2007-02-01
  [ Finite element methods , Incompressible inviscid rotational flows , Least squares ]

• Exponential synchronization in drive-response systems of hopfield-type neural networks with time delays
  International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 17, 11, 4167-4176, 2007-01-01
  [ Discrete time delays , Distributed time delays , Drive-response systems , Exponential synchronization , Lyapunov functional , Neural networks ]

• On periodic solutions of a two-neuron network system with sigmoidal activation functions
  International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 16, 5, 1405-1417, 2006-01-01
  [ Contraction mapping theorem , Dulac's criterion , Liapunov functions , Neural networks , Periodic solutions , Poincaré-Bendixson theorem ]

• On the velocity-vorticity-pressure least-squares finite element method for the stationary incompressible Oseen problem
  Journal of Computational and Applied Mathematics, 182, 1, 211-232, 2005-10-01
  [ Driven cavity flows , Least-squares finite element methods , Navier-stokes equations , Oseen equations , Velocity-vorticity-pressure formulation ]

• On a conjecture in D-optimal designs with n ≡ 0 mod 4
  Linear Algebra and Its Applications, 400, 1-3, 279-290, 2005-05-01
  [ D-optimal designs , Fisher's inequality , Hadamard's inequality ]

• Structure of a class of traveling waves in delayed cellular neural networks
  Discrete and Continuous Dynamical Systems, 13, 2, 339-359, 2005-01-01
  [ Delayed cellular neural network , Lattice dynamical system , Method of step , Traveling wave ]

• Existence of monotonic traveling waves in lattice dynamical systems
  International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 15, 8, 2375-2394, 2005-01-01
  [ Cellular neural networks , Lattice dynamical systems , Monotone iteration methods , Standing waves , Traveling waves ]

• Analysis of [H-1, L2, L2] first-order system least squares for the incompressible Oseen type equations
  Applied Numerical Mathematics, 52, 1, 77-88, 2005-01-01
  [ Finite element methods , First-order system least squares , Navier-Stokes equations , Oseen type equations , Velocity-vorticity-Bernoulli pressure formulation , Velocity-vorticity-pressure formulation ]

• Wave propagation in RTD-based cellular neural networks
  Journal of Differential Equations, 204, 2, 339-379, 2004-09-20
  [ Discrete Fisher equation , Discrete Nagumo equation , Lattice dynamical systems , Monotone iteration methods , RTD-based cellular neural networks , Standing waves , Traveling waves ]

• On camel-like traveling wave solutions in cellular neural networks
  Journal of Differential Equations, 196, 2, 481-514, 2004-01-20
  [ Camel-like traveling waves , Cellular neural networks , Lattice dynamical systems , Oscillating traveling waves ]

• Error analysis of the L2 least-Squares finite element method for incompressible inviscid rotational flows
  Numerical Methods for Partial Differential Equations, 20, 6, 831-842, 2004-01-01
  [ Euler equations,Incompressible inviscid rotational flows,Least-squares finite element methods,Standing vortex problems,Velocity-vorticity-pressure formulation ]

• On the subdomain-Galerkin/least squares method for 2- and 3-D mixed elliptic problems with reaction terms
  Numerical Methods for Partial Differential Equations, 18, 6, 738-751, 2002-11-01
  [ Error estimates , Finite volume methods , Least-squares methods , Mixed elliptic problems , Raviart-Thomas spaces ]

• Analysis of piecewise linear approximations to the generalized stokes problem in the velocity-stress-pressure formulation
  Journal of Computational and Applied Mathematics, 147, 1, 53-73, 2002-10-01
  [ Elasticity equations , Finite volume methods , Generalized stokes equations , Least squares , Velocity-stress-pressure formulation ]

• Analysis of the L2 least-squares finite element method for the velocity-vorticity-pressure Stokes equations with velocity boundary conditions
  Applied Mathematics and Computation, 130, 1, 121-144, 2002-07-25
  [ A priori error estimates , Condition numbers , Convergence , Least-squares finite element methods , Stability , Velocity-vorticity-pressure Stokes equations ]

• Analysis of least-squares approximations to second-order elliptic problems. I. Finite element method
  Numerical Functional Analysis and Optimization, 23, 3-4, 419-432, 2002-05-01
  [ A posteriori error estimates , A priori error estimates , Elliptic problems , Finite element methods , Least squares ]

• Analysis of least-squares approximations to second-order elliptic problems. II. Finite volume method
  Numerical Functional Analysis and Optimization, 23, 3-4, 433-451, 2002-05-01
  [ A posteriori error estimates , A priori error estimates , Elliptic problems , Finite volume methods , Least squares ]

• Least-squares finite element approximations to the Timoshenko beam problem
  Applied Mathematics and Computation, 115, 1, 63-75, 2000-10-06

• Analysis of a least squares finite element method for the circular arch problem
  Applied Mathematics and Computation, 114, 2-3, 263-278, 2000-09-11
  [ A posteriori error estimator , Circular arch problem , Finite element method , Least squares , Locking phenomenon ]

• Analysis of a two-stage least-squares finite element method for the planar elasticity problem
  Mathematical Methods in the Applied Sciences, 22, 9, 713-732, 1999-06-01

• Analysis of least squares finite element methods for a parameter-dependent first-order system
  Numerical Functional Analysis and Optimization, 19, 1-2, 191-213, 1998-01-01
  [ Convergence , Elasticity equations , Error estimates , Finite elements , Least squares , Poisson's ratios , Stokes equations ]

• Error analysis of a weighted least-squares finite element method for 2-D incompressible flows in velocity-stress-pressure formulation
  Mathematical Methods in the Applied Sciences, 21, 18, 1637-1654, 1998-01-01
  [ Finite element method , Generalized Stokes equations , Incompressible flow , Least-squares ]

• A Two-Stage Least-Squares Finite Element Method for the Stress-Pressure-Displacement Elasticity Equations
  Numerical Methods for Partial Differential Equations, 14, 3, 297-315, 1998-01-01
  [ Elasticity equations , Error estimates , Finite elements , Least-squares ]

• A unified analysis of a weighted least squares method for first-order systems
  Applied Mathematics and Computation, 92, 1, 9-27, 1998-01-01
  [ Adn elliptic systems , Boundary value problems , Convergence , Error estimates , First-order systems , Friedrichs' systems , Least squares methods ]

• On the convergence and stability of the standard least squares finite element method for first-order elliptic systems
  Applied Mathematics and Computation, 93, 1, 51-62, 1998-01-01
  [ Convergence , Finite elements , Least squares , Stability ]

• Least-squares finite element methods for the elasticity problem
  Journal of Computational and Applied Mathematics, 87, 1, 39-60, 1997-12-18
  [ Convergence , Elasticity , Elliptic systems , Error estimates , Finite elements , Least squares , Poisson ratios ]

• A least-squares finite element method for incompressible flow in stress-velocity-pressure version
  Computer Methods in Applied Mechanics and Engineering, 128, 1-2, 1-9, 1995-12-01