Selected Publications

  • Dissertation: Variational Problems for Maps of Riemannian Manifolds, 1985, under the supervision of Professor Richard Schoen, UC Berkeley.
  1. A Regularity Theorem for Harmonic Maps with Small Energy, G. Liao, The Journal of Differential Geometry, Vol. 22, 1985, pp. 233-241. Conference Papers and Book Chapters
  2. A Study of the Regularity Problem of Harmonic maps, G. Liao, The Pacific Journal of Mathematics, Vol. 131, No. 2, 1988, pp. 291-302. 
  3. On Removability of a Singular Submanifold for Weakly Harmonic Maps, G. Liao and D. Costa, The Journal of the Faculty of Science, the University of Tokyo, Sec. IA, Mathematics, Vol. 35, No. 2, 1988, p. 321-344.
  4. An Application of Fokker-Planck Equations to Josephson Junction, G. Liao, and A. Lawrence, Acta Mathematica Scientia, Vol. 9, No. 1, 1989, p. 109-120
  5. A Variational Approach to Grid Generation, G. Liao, Numerical Methods for Partial Differential Equations, Vol. 8, p. 143-147, 1992
  6. A New Approach to Grid Generation, G. Liao and D. Anderson, Applicable Analysis, Vol. 44, p. 285-298, 1992
  7. Grid Generation via Deformation, G. Liao and J. Su, Applied Mathematics Letters, 5:3, p. 27-29, 1992
  8. A Direct Method in Dacorogna-Moser’s Approach of Grid Generation Problems, G. Liao and J. Su, Applicable Analysis, an International Journal, March-April 1993, p. 73-84.   
  9. A Numerical Grid Generator Based on Moser’s Deformation  Method, T. Pan, J. Su and G. Liao, Numerical Methods for Partial Differential Equations, Vol. 10, p. 20-31, 1994.
  10. On the Compactness of a Class of Riemannian Manifolds, Z. Gao and G. Liao, The Pacific J. of Mathematics, Vol. 166, No. 1, p. 23-41, 1994
  11. A Moving Grid Method for 1+1 Dimension, G. Liao and J. Su, Applied Mathematics Letters, Vol. 8, No. 4, p. 47-49, 1995
  12. A Moving Grid Finite Element Method Using Grid Deformation, W. Semper and G. Liao, Numer. Methods for Partial Differential Equations, vol. 11, 603-615, 1995
  13. A Note on Harmonic Maps, H. Liu and G. Liao, Appl. Math. Letters, Vol. 9, No. 4, p. 95-97, 1996
  14. Analysis and Computation of Adaptive Moving Grids by Deformation, P. Bochev, G. de la Pena, and G. Liao, Numerical Methods for Partial Differential Equations, Vol. 12, p. 489-506, 1996
  15. An Adaptive Grid Method and its Application to Steady Euler Flow Calculations, F. Liu, S. Ji, and G. Liao, SIAM (Society for Industrial and Applied Mathematics) Journal for Scientific Computing, Vol. 20, No. 3, p. 811-825, 1998
  16. A Deformation Method for Moving Grids, G. Liao and G. de la Pena, Proceedings of the 8th International Meshing Roundtable, Sponsored by the Sandia National Laboratory, p. 155-162, 1999.
  17. Level Set Based Deformation Methods for Adaptive Grids, G. Liao, F. Liu, G. de la Pena, D. Pang, and S. Osher, Journal of Computational Physics, vol. 159, p. 103-122, 2000
  18. Deformation Method in Grid Generation, Theory and Applications: Qualitative Behavior, G. Liao, W. Pan, G. de la Pena, and J. Su. Communications of Nonlinear Analysis, Volume 9, Number 2, 19-30, (2002)
  19. Adaptive Grids for Resolution Enhancement, G. Liao, Z. Lei and G. de la Pena, vol. 12, p.153-156, Shock Waves (2002)
  20. A Moving Finite Difference Method for Partial Differential Equations,  G. de la Pena, D. Anderson, J. Su and G. Liao, Studia Univ. “Babes-Bolyai”, Mathematica, Volume XLIX, Number 2, June 2004, Romania.
  21. Adaptive Grid Generation Based on the Least Square Finite Element Method, X. Cai, D. Fleitas, B. Jiang and G. Liao, Computers and Mathematics 48 (2004) 1077-1085.
  22. The Least-Squares Finite Element Method on Overlapping Elements, Fleitas, D., X. Cai, G. Liao, B. Jiang, Journal of Computational Systems, 1:2 (2005), 203-213.
  23. Moving Meshes by the Deformation Method, Liao, G., and J. Xue, Special issue: The International Symposium on Computing and Information, Journal of Computational and Applied Mathematics, Volume 195, Issue 1, pp. 83-92, 10/2006.
  24. Unexpected Shape Changes of Encapsulated Oblate Spheroids in Response to Equatorial Traction, R A Schachar, G G Liao, R D Kirby, F Kamagar, J H Savoie, A Abolmaali and G. Rosensteel, J. Phys. A: Math. Theor. 41 (2008) (9pp)
  25. Optimal Control Approach to Data Alignment, G. Liao, X. Cai, D. Fleitas, X. Luo, J. Wang, J. Xue, Volume 21, Issue 9, September 2008, Pages 898-905, Applied Mathematics Letters
  26. Adaptive Grid Generation Based Non-Rigid Image Registration Using Mutual Information for Breast MRI, Mei-Yi Chu, Hua-Mei Chen, Chih-Yao Hsieh, Ting-Hung Lin, Hsi-Yue Hsiao, Guojun Liao, and Qi Peng, Journal of Signal Process System (2009) 54:45–63
  27. Construction of differentiable transformations, Guojun Liao, Xianxing Cai, Jie Liu, Xiaonan Luo, Jianmin Wang, Jiaxing Xue, 22 (2009) 1543-1548, Applied Math. Letters
  28. Novel explanation for the shape of the lenticular galaxy bulge and its implication for red spiral galaxy evolution, R. A. Schachar1, G. G. Liao, R. D. Kirby, F. Kamangar, Z. E. Musielak, and G. Rosensteel, 505, 613–623 (2009), Astronomy & Astrophysics
  29. New Development of Nonrigid Registration, Hsiao, H-Y., Hsieh, C-Y., Chen, X., Gong, Y., Luo, X. and Liao, G. ANZIAM Journal, Vol. 55, pp. 289-297, 2014, Australian Mathematics Association
  30. A comparison between local h-refinement and a novel r-refinement method, J. R. Grisham, N. Vijayakumar, G. Liao, B. H. Dennis, and F. K. Lu, ser. AIAA SciTech. AIAA, Jan 2015, AIAA 2015-2040.
  31. [Chen and Liao 2015] New Variational Method of Grid Generation with Prescribed Jacobian determinant and Prescribed Curl, Chen, X. and Liao, G. https://arxiv.org/pdf/1507.03715.pdf, 2015.
  32. [Chen and Liao 2016] New method of averaging diffeomorphisms based on Jacobian determinant and curl vector, Chen, X. and Liao, G. https://arxiv.org/pdf/1611.03946.pdf, 2016
  33. [Zhou et al. 2017] Uniqueness of Transformation Based on Jacobian Determinant and Curl Vector, Zicong Zhou, Xi Chen, Xian Xin Cai, Guojun Liao, arXiv: 1712.03443: 11 pages, 8 figures
  34. [Zhu et al. 2019a] Effects of Differential Geometry Parameters on Grid Generation and Segmentation of MRI Brain Image, Yongpei Zhu, Zicong Zhou, Guojun Liao, Qianxi Yang, Kehong Yuan, IEEE ACCESS, 7(1), 68529-68539(2019).SCI(IF=4.098)
  35. [Zhu et al. 2019b] The Generation and Application of Medical Image Grid Based on Differential Geometric Features, Zhu, Yongpei and Zhou, Zicong and Liao, Guojun and Yang, Qianxi and Yuan, Kehong, CoRR Journal, 2019  https://scholar.google.com/citations?user=tKsFXboAAAAJ&hl=en
  36. [Zhu et al. 2019c] Learning rate based on Jacobian determinant and modified U-net for medical brain image segmentation, Zhu, Yongpei and Zhou, Zicong and Liao, Guojun and Yang, Qianxi and Yuan, Kehong, BASIC CLINICAL PHARMACOLOGY TOXICOLOGY, Volume 125, Pages 3 – 4, 2019, WILEY 111 RIVER ST, HOBOKEN 07030-5774, NJ USA  https://scholar.google.com/citations?user=tKsFXboAAAAJ&hl=en
  37. [Zhu et al. 2020a] New Loss Functions for Medical Image Registration Based on VoxelMorph, Yongpei Zhu, Zicong Zhou, Guojun Liao, Kehong Yuan,  Proc. SPIE 11313, Medical Imaging 2020: Image Processing, 113132E (10 March 2020).
  38. [Zhu et al. 2020b]  Y. Zhu, Z. Zhou, G. Liao, and K. Yuan, “Csrgan: Medical Image Super-Resolution Using A Generative Adversarial Network,” 2020 IEEE 17th International Symposium on Biomedical Imaging Workshops (ISBI Workshops), Published 1 April 2020, pp. 1-4
  39. [Zhu et al. 2021a]  Yongpei Zhu, Zicong Zhou, Guojun Liao, Kehong Yuan, “A novel unsupervised learning model for diffeomorphic image registration,” Proc. SPIE 11596, Medical Imaging 2021: Image Processing, 115960M (15 February 2021). https://doi.org/10.1117/12.2580815
  40. [Zhu et al. 2021b]  Y. Zhu, Z. Zhou, G. Liao, and K. Yuan, “A New Unsupervised Learning Method for 3D Deformable Medical Image Registration,” 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI), 25 May 2021, pp. 908-912, DOI: 10.1109/ISBI48211.2021.9433835.
  41. [Zicong Zhou and Guojun Liao 2021] A Novel Approach to form Normal Distribution of Medical Image Segmentation based on Multiple Doctors’ Annotations, to be presented at SPIE Image Processing, February 2022, San Diego, California (accepted for poster presentation on October 16, 2021)
  42. [Zicong Zhou and Guojun Liao 2022a] Construction of Diffeomorphisms with Prescribed Jacobian Determinant and Curl, International Congress of Geometry and Graph (ICGG 2022)
  43. [Zicong Zhou and Guojun Liao 2022b] Recent Developments of an Optimal Control approach to Nonrigid Image Registration, the 10th Workshop on Biological Image Registration, (WBIR 2022)
  44. [Zhou and Liao 2022] RECENT INSIGHTS ON THE UNIQUENESS PROBLEM OF DIFFEOMORPHISMS DETERMINED BY PRESCRIBED JACOBIAN DETERMINANT AND CURL, arXiv:2207.13053v1 [cs.CG] 26 Jul 2022