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Book Publications

  1. Tai, Xue-Cheng; Lie, Knut-Andreas; Chan, Tony F.; Osher, Stanley (eds): Image Processing based on Partial differential equations , "Mathematics and Visualization ", Heidelberg: Springer Verlag 2006. ISBN 978-3-540-33266-4. 440 pages.
  2. Tai, Xue-Cheng, Knot Morkken, Marius Lysaker and Lie, Knut-Andreas (eds), "Scale Space and Variational Methods in Computer Vision", second international conference, SSVM 2009, proceedings. Lecture notes in computer science LNCS 5567, Springer, 2009. ISSN 0302-9743, Refereed journal publications

Journal Publications

  1. C. Wu, J. Deng, F. Chen and X.-C. Tai, Scale-space analysis of discrete filtering over arbitrary triangulated surfaces, To appear in: "SIAM Journal on Imaging Sciences".
  2. E. Hodneland, N. Bukoreshtliev, T. Eichler, X.-C. Tai, S. Gurke, A. Lundervold, A unified framework for automated 3D whole cell segmentation of living cells and a comprehensive segmentation evaluation. Accepted by IEEE Transactions on Medical Imaging.
  3. Qing Pan and X.-C. Tai, Model the Solvent-excluded Surface of 3D Protein Molecular Structures Using Geometric PDE-based Level-set Method. Communications in Computational Physics (CiCP), vol. 6, no. 4, pp. 777-792, 2009.
  4. A. DeCezaro, A. Leitao and X.-C. Tai, On multiple level-set regularization methods for inverse problems. Inverse Problems. vol. 25, pp. 1-22, 2009. Proceedings (Referee Reviewed), 25(035004), doi: 10.1088/0266-5611/25/3/035004, 2009.
  5. E. Hodneland, X.-C. Tai, and H. Gerdes, Four-color theorem and level-set methods for watershed segmentation. International Journal of Computer Vision, vol. 82, pp. 264-283, 2009.
  6. Q. Hu, X.-C. Tai and R. Winther, A saddle point approach to the computation of harmonic maps. SIAM J. Numer. Anal., vol. 47, no. 2, pp. 1500-1523, 2009.
  7. Ran Gao, Jinping Song and Xue-Cheng Tai, Image Zooming Algorithm Based on Partial Differential Equations. International J. Numer. Anal. Modeling vol 6, no. 2, pp. 284 -- 292, 2009.
  8. T. K. Nilssen1, K. H. Karlsen, T. Mannseth and X.-C. Tai, Identification of diffusion parameters in a nonlinear convection-diffusion equation using the augmented Lagrangian method. Computational Geosciences, pp. 1 -- 13, 2008, doi: 10.1007/s10596-008-9120-z.
  9. Lars Nielsen, Hongwei Li, Xue-Cheng Tai, Sigurd Ivar Aanonsen and Magne Espedal, Reservoir description using a binary level set model. Computing and Visualization in Science , online published 2008. DOI 10.1007/s00791-008-0121-1.
  10. Huazhu Chen, Jinping Song and Xue-Cheng Tai, A Dual Algorithm for Minimization of the LLT Model. Advances in Computational Mathematics, pp 1 --16, 2008. DOI 10.1007/s10444-008-9097-0.
  11. Hongwei Li, Xue-Cheng Tai and Sigurd Ivar Aanonsen, Reservoir Description By Using a Piecewise Constant Level Set Method, J. of Comput. Math., Vol. 26, Issue 3, Pages: 365-377, Published: MAY 2008. Blue Point Download pdf file.
  12. Ke Chen and Xue-Cheng Tai, A nonlinear multigrid method for total variation minimization from image restoration, Journal of Scientific Computing, vol. 33 (2): 115-138 NOV 2007. Blue Point Download pdf file.
  13. Tony F. Chan, Hongwei Li, Marius Lysaker, and Xue-Cheng Tai, Level Set Method for Positron Emission Tomography. International Journal of Biomedical Imaging, 2007 : 1-15, 2007. Blue Point Download pdf file.
  14. Xue-Cheng Tai, Stanlery Osher and Randi Holm, Image inpainting using a TV-Stokes equation , p. 3-22, 2007; in "Image Processing based on partial differential equations" Tai, Lie, Chan and Osher eds; Springer. Heidelberg, 2006. Blue Point Download pdf file.
  15. Xue-Cheng Tai and Hongwei Li, A Piecewise Constant Level Set Method for Elliptic Inverse Problems, APPLIED NUMERICAL MATHEMATICS, Volume: 57, Issue: 5-7 Pages: 686-696, Published: MAY-JUL 2007. Blue Point Download pdf file.
  16. Xue-Cheng Tai, Oddvar Christiansen, Ping Lin and Inge Skjaelaaen, Image segmentation using some piecewise constant level set methods with MBO type of project. International Journal of Computer Vision, 73 (1): 61-76 JUN 2007. Blue Point Download pdf file.
  17. Lars Kristian Nielsen, Xue-Cheng Tai, Sigurd Ivar Aanonsen and Magne Espedal, A Binary Level Set Model for Elliptic Inverse Problems with Discontinuous Coefficients . International J. Numer. Anal. Modelling , vol. 4, no.1, pp. 75-100, 2007. ( Also as UCLA CAM-report cam05-51.) Blue Point Download pdf file.
  18. Hongwei Li and Xue-Cheng Tai, Piecewise constant level set methods for multiphase motion. International J. Numer. Anal. Modeling, vol. 4, no. 2. pp. 293, 2007. Blue Point Download pdf file.
  19. Xue-Cheng Tai and Ragnar Winther, A discrete De Rham complex with enhanced smoothness, CALCOLO 43 (4): 287-306 2006. Blue Point Download pdf file.
  20. Hodneland E, Lundervold A, Gurke S, Tai X-C, Rustom A, Gerdes H. H, Automated detection of tunneling nanotubes in 3D images, Cytometry, Part A 69A (9): 961-972 SEP 2006. Blue Point Download pdf file.
  21. Lars Kristian Nielsen, Xue-Cheng Tai, Sigurd Ivar Aanonsen and Magne Espedal, Noise Removal of Seismic Data Using a Fourth-Order Parabolic PDE, International Journal of Tomography & Statistics (IJTS), vol. 4, no. 6, pp. 63, 2006.
  22. D. Krishnan, P. Lin and X.C. Tai, An Efficient Operator-Splitting Method for Noise Removal in Images, Commun. Comput. Phys., 1 (2006), pp. 847-858. Published Online: June 5, 2006. Blue Point Abstract ( Also as UCLA CAM-report cam05-60.) Blue Point Download pdf file.
  23. Xue-cheng Tai and Changhui Yao, Image segmentation by piecewise constant Mumford-Shah model without estimating the constants. Journal of Computational Math. , 24 (2006), no. 3, 435--443. Blue Point Download pdf file.
  24. Johan Lie, Marius Lysaker and Xue-Cheng Tai, A variant of the level set method and applications to image segmentation. Math. Comp. 75 (2006), no. 255, 1155--1174 (electronic).. Also as September 2003. UCLA, Applied Mathematics, CAM-report-03-50. Blue Point Download pdf file.
  25. Johan Lie, Marius Lysaker and Xue-Cheng Tai, A Binary Level Set Model and Some Applications to Mumford-Shah Image Segmentation. IEEE Transection on image processing, vo. 15, no. 5, pp. 1171-1181, 2006. Blue Point Download pdf file.
  26. M. Lysaker and X.-C. Tai, Iterative image restoration combining total variation minimization and a second order functional. International Journal of Computer Vision , vol. 66, no. 1, pp. 5-18, 2006.
  27. Lie, Johan, Lysaker, Marius and Tai, Xue-Cheng A piecewise constant level set framework. International J. Numer. Anal. Modelling, 2 (2005), no. 4, 422--438. Blue Point Download pdf file.
  28. Eric T. Chung, Tony F. Chan and Xue-Cheng Tai, Electrical Impedance Tomography Using Level Set Representation and Total Variational Regularization. Journal of Computational Physics, vol 205, pp.357-372, 2005. (also as UCLA, Applied Mathematics, CAM-report-03-64). Blue Point Download pdf file
  29. T. K. Nilssen and X.-C. Tai, Parameter estimation with the augmented Lagrangian method for a parabolic equation, Journal of Optimization Theory and Applications, vol. 124, no. 2, pp. 435-453, 2005. (see also report-153, Department of Mathematics, University of Bergen, 2001). Blue Point See abstract. Blue Point Download pdf file.
  30. K. Majava and X.-C. Tai, A Level Set Method for Solving Free Boundary Problems Associated with Obstacles, International J. Numer. Anal. Modelling, vol. 1, no.2, pp.157-172, 2004. (Also as UCLA, Applied Mathematics, CAM-report-03-69, November 2003.) Blue Point Download pdf file
  31. Xue-Cheng Tai and Tony F. Chan, A survey on Multiple Level Set Methods with Applications for Identifying Piecewise Constant Functions, International J. Numer. Anal. Modelling, vol. 1, no.1, pp.25-48, 2004. (Also as UCLA, Applied Mathematics, CAM-report-03-68, November 2003.) Blue Point Download pdf file
  32. Marius Lysaker, Stanley Osher, Xue-Cheng Tai, Noise Removal Using Smoothed Normals and Surface Fitting, January 2003. IEEE Transection on image processing, vol. 13, no. 10, oct. 2004, pp. 1345-1457. (Also UCLA, Applied Mathematics, CAM-report-03-03.) Blue Point Download pdf file
  33. Tony F. Chan and Xue-Cheng Tai, Level Set And Total Variation Regularization For Elliptic Inverse Problems With Discontinuous Coefficients, Journal of Computational Physics, Vol. 193 (2003), pp. 40-66. Blue Point Download pdf file Blue Point Download ps file
  34. Tony F. Chan and Xue-Cheng Tai, Identification of Discontinuous Coefficients from Elliptic Problems Using Total Variation Regularization. SIAM J. Sci. Comput.., Vol. 25, No. 3, pp. 881-­904, 2003. Blue Point Download pdf file Blue Point Download ps file Blue Point See abstract.
  35. M. Lysaker, A. Lundervold and X.-C. Tai, Noise Removal Using Fourth-Order Partial Differential Equations with Applications to Medical Magnetic Resonance Images in Space and Time. IEEE Transection on image processing, vol. 12, no. 12, pp. 1579-1590, 2003. (Also UCLA, Applied Mathematicsd, CAM-report-02-44). Blue Point Download pdf file Blue Point Download ps file
  36. Lori Badea, Xue-Cheng Tai and Junping Wang, Convergence rate analysis of a multiplicative Schwarz method for variational inequalities. SIAM J. Numer. Anal.., vol. 41, no. 3, pp. 1052-1073, 2003. Blue Point Download pdf file Blue Point Download ps file Blue Point See abstract.
  37. T. K. Nilssen and T. Mannseth and X.-C. Tai, Permeability estimation with the augmented Lagrangian method for a nonlinear diffusion equation, Comput. Geosci. , 7:27-47, 2003. (Also report-155, Department of Mathematics, University of Bergen, 2001.) Abstract. Download pdf file.
  38. Xue-Cheng Tai, Rate of convergence for some constraint decomposition methods for nonlinear variational inequalities, Numer. Math., 2003, 93:755-786, 2003. (Also report-150, Department of Mathematcis, University of Bergen, 2000.) Blue Point Download pdf file and ( a related paper ) Blue Point Download ps file Blue Point See abstract
  39. K. A. Mardal and X.-C. Tai and R. Winther, A robust finite element method for Darcy-stokes flow, SIAM J. Numer. Anal., vol. 40, no. 5, pp. 1605--1631, 2002. Aslo report-154, Department of Mathematics, University of Bergen, 2001. Blue Point Download pdf file Blue Point Download ps file Blue Point See abstract.
  40. Bjorn-ove Heimsund, Xue-Cheng Tai and Junping Wang, Superconvergence for the gradient of finite element approximations by L2-projections, SIAM J. Numer. Anal., vol. 40, no. 4, pp. 1263--1280, 2002. Blue Point Download pdf file Blue Point Download ps file Blue Point See abstract.
  41. X.-C. Tai and P. Tseng, Convergence rate analysis of an asynchronous space decomposition method for convex minimization Math. Comp., vol. 71, pp. 1105-1135, 2001. (Report No. 120, Department of Mathematics, University of Bergen, August, 1998.) Blue Point Download pdf file Blue Point Download ps file Blue Point See abstract.
  42. X.-C. Tai, B. Heimsund and J. Xu: Rate of Convergence for Parallel Subspace Correction Methods for nonlinear variational inequalities. "Thirteenth international domain decomposition conference", 2001, pp. 127--138, CIMNE, Barcelona, Spain 2002. Available online at: https://cdcsp.univ-lyon1.fr/dd13/indexproc.html. Blue Point Download pdf file Blue Point Download ps fil
  43. Xue-Cheng Tai, Convergence rate analysis of domain decomposition methods for obstacle problems, East-West J. Numer. Anal., vol. 9, n0. 3, pp. 233-252, 2001. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  44. X.-C. Tai and J. Xu, Global convergence of subspace correction methods for convex optimization problems Math. Comp., vol. 71, no. 237, pp. 105-124, May 2001. (A longer and detailed version: Report No. 114 , Department of Mathematics, University of Bergen, August, 1998. ) Blue Point Download pdf file Blue Point Download ps file Blue Point See abstract.
  45. O. Rognes and X.-C. Tai, Subspace correction methods for nonsymmetric parabolic problems, Linear Algebra and its Applications, vol. 332/334, pp. 205-234 , 2001. Blue Point Download dvi file Blue Point Download pdf file Blue Point See abstract.
  46. T. K. Nilssen, X.-C. Tai and R. Winther, A robust nonconforming H2-element, Math. Comp. , vol. 70, pp. 489-505, 2001. (Also Universiyt of Bergen, Department of Mathematics, Norway, 1999, Report-125. ) Blue Point Download pdf file Blue Point Download ps file Blue Point See abstract.
  47. Lai, C.-H.; Ierotheou, C.S.; Palansuriya, C.J.; Pericleous, K.A.; Espedal, M.S.; Tai, X.-C. Accuracy of a domain decomposition method for the recovering of discontinuous heat sources in metal sheet cutting. Comput. Vis. Sci., vol. 2, No.2-3, pp. 149-152, 1999.
  48. M. Espedal, X.-C. Tai and N. Yan , A hybrid domain decomposition method for advection-diffusion problems. Numerical Algorithms, vol. 18, 1998, pp. 321--336. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  49. X.-C. Tai and M. Espedal, Applications of a space decomposition method to linear and nonlinear elliptic problems. Numer. Meth. for Part. Diff. Equat., vol. 14, pp. 717-737, 1998. Blue Point Download dvi file Blue Point Download pdf file Blue Point See abstract.
  50. X.-C. Tai, A space decomposition method for parabolic problems. Numer. Method for Part. Diff. Equat., vol. 14, no.1, pp. 27--46, 1998. (ALso Report No. 106, Department of Mathematics, University of Bergen, 1997. ) Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  51. X.-C. Tai and M. Espedal, Rate of convergence of some space decomposition methods for linear and nonlinear problems. SIAM J. Numer. Anal., vol. 35, no. 4, pp. 1558--1570, 1998. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  52. K. Kunisch and X.-C. Tai, Sequential and parallel splitting methods for bilinear control problems in Hilbert spaces. SIAM J. Numer. Anal., vol. 34, no. 1, pp. 91 - 118, 1997. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  53. Xue-Cheng Tai, Parallel function and space decomposition methods -- Part II. Space decomposition. Beijing Mathematics. vol.1, part 2, pp. 135--152, 1995. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  54. Xue-Cheng Tai, Parallel function and space decomposition methods -- Part I. Function decomposition. Beijing Mathematics. vol.1, part 2, pp. 104--134, 1995. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  55. X.-C. Tai and T. Karkainen, Identification of a nonlinear parameter in a parabolic equation from a linear equation. Comp. Appl. Mat., vol. 14, no. 2, pp. 157-184, 1995. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  56. Xue-Cheng Tai, Global extrapolation with a parallel splitting method. Numerical Algorithms, vol. 3, pp. 427-440, 1992. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  57. Xue-Cheng Tai and Pekka Neittaanmaki, Error estimates for numerical identification of distributed parameters. J. Comp. Math., vol. 10, supplementary issue, 1992, pp. 66-78. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  58. T. Lu, P. Neittaanmaki and X-C Tai, A parallel splitting up method for partial differential equations and its application to Navier-Stokes equations. RAIRO Math. Model. and Numer. Anal., vol. 26, no.6, pp. 673--708, 1992. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  59. T. Lu, P. Neittaanmaki and X-C Tai, A parallel splitting up method and its application to Navier-Stokes equations. Applied Mathematics Letters, Vol. 4, No. 2, pp.25-29, 1991. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract
  60. Xue-Cheng Tai and Pekka Neittaanmaki, A parallel finite element splitting-up methods for parabolic problems. Numerical Methods for Partial Differential Equations, Vol. 7, 1991, pp.209--225. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  61. Xue-Cheng Tai, Finite element methods used in one and two dimensional distributed parameter identification problems of parabolic type. Mathematica Numerica Sinica (Ji Suan Shu Xue, Chinese Version), Vol. 12, No.1, 1990, pp. 1-8. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.

Proceedings

  1. Xue-Cheng Tai and Pekka Neittaanmaki. A FE-splitting-up method and its application to distributed parameter identification of parabolic type. In "Approximation, Optimisation and Computing. Theory and Applications (A. G. Law and C. L. Wang eds)", Elsevier Science Publishers, B. V. (North Holland), 1990, pp.185-188. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  2. Xue-Cheng Tai and Pekka Neittaanmaki A linear approach for the nonlinear distributed parameter identification. In "Numerical methods for free boundary problems, proceeding of a conference held at the Department of Mathematics, University of Jyvaskyla, Finland, July 23-27, 1990 (P. Neittaanmaki ed)". International series of numerical mathematics, vol. 99, Birkhauser Verlag Basel,1991, pp. 401-411. (Math. Review number CMP: 91 16) Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  3. Xue-Cheng Tai and Pekka Neittaanmaki On the numerical solution of the distributed parameter parameter identification problem. In " Control and estimation of distributed parameter systems". International series of numerical mathematics, Vol. 100, Birkhauser Verlag Basel, 1991, pp.317-329. Proceeding of the international conference on control and estimation of distributed parameter systems, Vorau, July 8-14, 1990. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  4. Xue-Cheng Tai Parallel computing with splitting-up methods and the distributed parameter identification problems. Doctoral thesis. Report 50, University of Jyvaskyla, Department of Mathematics, 1991. 94 pages. (Math. Review number CMP: 91 11).
  5. Xue-Cheng Tai Parallel function and space decomposition methods with applications to optimisation, splitting and domain decomposition methods. Technical report of Technical University of Graz, No. 231--1992, September, 1992. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  6. X.-C. Tai Domain decomposition for linear and nonlinear elliptic problems via function or space decomposition. in "Domain decomposition methods in scientific and engineering computing (Proc. of the 7th international conference on domain decomposition, Penn. State University, 1993)", D. Keyes and J. Xu eds, American Mathematical Society, 1995, pp. 355-360. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  7. X.-C. Tai Parallel function and space decomposition methods. In "The Finite element Method: Fifty years of the Courant Element", lecture notes in pure and applied mathematics, vol. 164, pp. 421--432, 1994, Marcel Dekker. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  8. X-C Tai, T. O. W. Johansen, H. K. Dahle, M. S. Espedal A characteristic domain splitting method. In "Domain decomposition methods in science and engineering, 8th international conference, Beijing, China, (R. Glowinski, J. Periaux, Z.-C. Shi and O. Widlund eds)", 1997, pp. 308--317, John Wiley and Sons, England. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  9. Xue-Cheng Tai and Pekka Neittaanmaki. Pointwise error estimates for distributed parameter identification. in "Proceedings of the seventh international colloqium on differential equations (D. Bainov and V. Covachev ed)", 1997, pp. 455--468, International Science Publishers, The Netherlands. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  10. X.-C. Tai and M. Espedal A space decomposition method for minimization problems. In "Domain decomposition methods in science and engineering (P. Bjorstad, M. Espedal and D. Keyes eds)", 9th international conference Bergen, Norway, published by ddm.org, 1998, pp. 509--516. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  11. K. Kunisch and X.-C. Tai Nonoverlapping Domain Decomposition Methods for Inverse Problems. In "Domain decomposition methods in science and engineering (P. Bjorstad, M. Espedal and D. Keyes eds)", 9th international conference Bergen, Norway, published by ddm.org, 1998, pp. 517--524. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  12. H. K. Dahle, T. O. Johansen, T. Bone and X.-C. Tai A characteristic domain decomposition method for modelling the flow in a coastal aquifer. In "Domain decomposition methods in science and engineering (P. Bjorstad, M. Espedal and D. Keyes eds)", 9th international conference Bergen, Norway, published by ddm.org, 1998, pp. 698--705. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  13. M. Espedal, X.-C. Tai and N. Yan A Hybrid Domain Decomposition Method For Convection Dominated Problems. In "Domain decomposition methods in science and engineering (P. Bjorstad, M. Espedal and D. Keyes eds)", 9th international conference Bergen, Norway, published by ddm.org, 1998, pp. 230--236. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  14. T. F. Chan and X.-C. Tai Augmented Lagrangian and Total Variation Methods for Recovering Discontinuous Coefficients from Elliptic Equations, In "Computational Science for the 21st Century", M. Bristeau, G. Etgen, W. Fitzgibbon, J. L. Lions, J. Periaux and M. F. Wheeler (eds), pp. 597--607, J. Wiley & Sons, 1997, and Report No. CAM-97-2, Department of Mathematics, University of California, Los Angeles, 1997. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  15. X.-C. Tai Parallel function decomposition methods and numerical applications. In "Iterative methods in scientific computation", J. Wang, M. B. Allen, B. M. Chen and T. Mathew eds, IMACS, Series in Compputational and Allped Mathematics, vol. 4, 1998, pp. 231-238. And also Report No. 111, Department of Mathematics, University of Bergen, 1997. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  16. X.-C. Tai, J. Froyen, M. S. Espedal and T. F. Chan Overlapping domain decomposition and multigrid methods for inverse problems. In "Domain decomposition method 10, the tenth international conference on domain decomposition methods, August 10-14, 1997, Boulder", J. Mandel, C. Farhat and X. Cai eds, Contemporary Mathematics vol. 218, American Mathematical Society, 1998, pp. 523--529; and Report No. 113, Department of Mathematics, University of Bergen, 1997. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  17. X.-C. Tai and J. Xu, Global convergence of subspace correction methods for convex optimization problems. Report No. 114, Department of Mathematics, University of Bergen, 1998. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  18. X.-C. Tai and J. Xu, Subspace correction methods for convex optimization problems, In "Domain decomposition methods in sciences and engineering, 11th international conference, London, UK", C. Lai, P. E. Bjorstad and O. B. Widlund eds, Domain decomposition Press, Bergen, Norway, p. 128--137, 1999. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  19. X.-C. Tai and P. Tseng, An asynchronous space decomposition method, In "Domain decomposition methods in sciences and engineering, 11th international conference, London, UK", C. Lai, P. E. Bjorstad and O. B. Widlunc eds, Domain decomposition Press, Bergen, Norway, p. 343--353, 1999. Blue Point Download dvi file Blue Point Download ps file Blue Point See abstract.
  20. X.-C. Tai, B. Heimsund and J. Xu: Rate of Convergence for Parallel Subspace Correction Methods for nonlinear variational inequalities. "Thirteenth international domain decomposition conference", 2001, pp. 127--138, CIMNE, Barcelona, Spain 2002. Available online at: https://cdcsp.univ-lyon1.fr/dd13/indexproc.html. Blue Point Download pdf file Blue Point Download ps file
  21. Xue-Cheng Tai, Some new domain decomposition and multigrid methods for variational inequalities. In "Domain decomposition methods in Science and Engineering, 14th international conference on domain decomposition methods, Cocoyoc, , Maxico", I. Herrera, D. Keyes, O. Widlund and R. Yates editors, published by National Autonomous University of Maxico (UNAM), 2003, pp. 323-330. Blue Point Download pdf file Blue Point Download ps file
  22. Xue-Cheng Tai, Domain decomposition and multigrid methods for obstacle problems, in "Computationa Science-ICCS 2002", Lecture notes in Computer science, Springer, P. Sloot, C. J. Tan, J. Dongarra and A. Hoekstra eds, pp. 345-352.
  23. B. Heimsund, T.F. Chan, T.K. Nilssen and X.-C. Tai, Level Set Methods and Augmented Lagrangian for a Parameter Identification Problem, in book: "Analysis and optimization of differential systems", V.Barbu, I.Lasiecka, D.Tiba and C.Varsan editors, Kluwer Academic Publishers, Boston/Dordrecht/London, p. 189-200, 2003.
  24. X.-C.Tai, Nonlinear positive interpolation operators for analysis with multilevel grids, in "Domain Decomposition Methods in Science and Engineering", Lecture Notes in Computational Science and Engineering , Vol. 40, Kornhuber, R.; Hoppe, R.; Périaux, J.; Pironneau, O.; Widlund, O.; Xu, J. (Eds.), Springer-Verlag, Heidelberg, p. 477-486, 2005.
  25. J. Lie, M. Lysaker and X.-C. Tai, Piecewise Constant Level Set Methods and Image Segmentation, in "Scale Space and PDE Methods in Computer Vision: 5th International Conference, Scale-Space 2005, Hofgeismar, Germany, April 7-9, 2005". Lecture Notes in Computer Science, vol. 3459, Editors: Ron Kimmel, Nir Sochen, Joachim Weickert., Springer-Verlag, Heidelberg, p. 573-584, 2005. Download pdf file..
  26. Heimsund, Bjørn-Ove; Tai, Xue-Cheng A two-mesh superconvergence method for mesh adaptivity. Recent advances in adaptive computation, 225--238, Contemp. Math., 383, Amer. Math. Soc., Providence, RI, 2005.
  27. Hongwei Li and Xue-Cheng Tai; Piecewise constant level set method for interface problems. In " Free boundary problems: theory and applications", I. Figueiredi, J. Rodrigues and L. Santos eds, Birkhauser, 2006.
  28. Xue-Cheng Tai, Stanlery Osher and Randi Holm, Image inpainting using a TV-Stokes equation , in " Image Processing based on partial differential equations", Springer. Heidelberg, 2006.
  29. Oddvar Christiansen and Xue-Cheng Tai, Fast Implementation of Piecewise constant level set methods , in " Image Processing based on partial differential equations", Springer. Heidelberg, 2006.
  30. Tony. F. Chan, K. Chen and Xue-Cheng Tai, Nonlinear multilevel schemes for solving the total variation image minimization problem , in "Image Processing based on partial differential equations", Springer. Heidelberg, 2006.
  31. Xue-Cheng Tai and Changhui Yao , Fast Piecewise Constant Level Set Methods (PCLSM) with Newton Updating , in "Image Processing based on partial differential equations", Springer. Heidelberg, 2006. Download pdf file.
  32. Lars Kristian Nielsen, Xue-Cheng Tai, Sigurd Ivar Aanonsen and Magne Espedal, Reservoir Description using a Binary Level Set Model, in "Image Processing based on partial differential equations", Springer. Heidelberg, 2006.
  33. X.-C. Tai, E. Hodneland, J. Weickert, N. Bukoreshtliev, A. Lundervold and H. Gerdes, Level set methods for watershed image segmentation , p. 178-190, 2007. In "Scale space and variational methods in Computer vision", F. Sgallari, A. Murli and N. Paragios eds, Springer, 2007. Download pdf file.
  34. T. Rahman, X.-C. Tai and S. Osher, A TV-Stokes denoising algorithm, p. 473-482, 2007. In "Scale space and variational methods in Computer vision", F. Sgallari, A. Murli and N. Paragios eds, Springer, 2007. Download pdf file.
  35. A. Losnegaard, O. Christiansen and X.-C. Tai, Piecewise constant level set method for 3D image segmentation , p. 687-696, 2007. In "Scale space and variational methods in Computer vision", F. Sgallari, A. Murli and N. Paragios eds, Springer, 2007. Download pdf file.
  36. E. Bae and X.-C. Tai, Graph cuts for the multiphase Mumford-Shah model using piecewise constant level set methods. p. 127-135, 2008. In "Proceedings of the National Institute for Mathematical Sciences", K. Jun, C. Keem, H. Lee and J. Choi eds, NIMS, Korea 2008. Download pdf.

Preprints (submitted and under review)