Selected Publication

Submitted/Preprint

            1. (with H. Zhang, Q. Chen) Deformation-invariant Neural Network and Its Applications in Distorted Image Restoration and Analysis, under revision
            2. (with D. Zhang, X.C. Tai) A Registration-Based Star-Shape Segmentation Model and Fast Algorithms, submitted
            3. (with Y. Guo, H. Cao) Deep Learning-Based Quasi-Conformal Surface Registration for Partial 3D Faces Applied to Facial Recognition , submitted
            4. (with Z. Lyu, P.T. Choi) Ellipsoidal Density-Equalizing Map for Genus-0 Closed Surfaces, submitted
            5. (with G. Li, D. Qiu) A deep neural network framework for dynamic multi-valued mapping problems and its applications, submitted

Published

            1. (with H. Zhang, D. Zhang) QIS: Quasiconformal Interactive Segmentation via Quasiconformal Mappings, accepted, SIAM Journal on Imaging Sciences (2024)
            2. (with Z.Y. Lyu, G.P.T. Choi) Spherical Density-Equalizing Map for Genus-0 Closed Surfaces, accepted, SIAM Journal on Imaging Sciences (2024)
            3. (with H. Zhang) A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings, accepted, Neurocomputing (2024)
            4. (with H.L. Chan, H.M. Yuen, C.T. Au, C.C. Chan, A.M. Li) Classification of the Obstructive Sleep Apnea based on X-ray images analysis by Quasi-conformal Geometry, accepted, Pattern Recognition (2024)
            5. (with Z.Y. Lyu, G.P.T. Choi) Bijective Density-Equalizing Quasiconformal Map for Multiply-Connected Open Surfaces, accepted, SIAM Journal on Imaging Sciences (2024)
            6. (with Q. Chen, Z. Li) A Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry applied to Imaging, SIAM Journal on Imaging Sciences, 17(1), 501-539 (2024)
            7. (with H.L. Chan, Y. Luo, L. Shi) QC-SPHRAM: Quasi-conformal Spherical Harmonics Based Geometric Distortions on Hippocampal Surfaces for Early Detection of the Alzheimer's Disease, accepted, Annals of Mathematical Sciences and Applications (AMSA) (2024)
            8. (with H. Yang, J.C. Li, S. Ying, J. Shi, T. Zeng) Double Transformer Super-Resolution for Breast Cancer ADC Images, accepted in IEEE Journal on Biomedical and Health Informatics (2023)
            9. (with Y.C. Guo Q. Chen, G.P.T. Choi) Automatic Landmark Detection and Registration of Brain Cortical Surfaces via Quasi-Conformal Geometry and Convolutional Neural Networks, Computers in Biology and Medicine, 163, 107185 (2023)
            10. (with H. Yang, J.C. Li, S. Ying, J. Shi, T. Zeng) Fast MRI Reconstruction via Edge Attention, Communications in Computational Physics, 33, 1409-1431 (2023)
            11. (with M.H. Wong, M. Li, K.M. Tam, H.M. Yuen, C.T. Au, C.C. Chan, A.M. Li) A Quasiconformal-based Geometric model for Craniofacial Analysis and its application, Axioms 12(4), 393, 1-28 (2023)
            12. (with Q.C. Chen, Z. Lyu) A two-stage algorithm for combined quasiconformal and optimal mass transportation spherical parameterization, Journal of Mathematics, Computation and Geometry of Data, 3(1), 29-57 (2023)
            13. (with C. Lin) Harmonic Beltrami Signature: A Novel 2D Shape Representation for Object Classification, SIAM Journal on Imaging Sciences, 15(4), 1851-1893 (2022)
            14. (with Z.P. Zhu, G.P.T. Choi) Parallelizable global QC parameterization of multiply-connected surfaces, SIAM Journal on Imaging Sciences, 15(4), 1765-1807 (2022)
            15. (with D.P. Zhang, G.P.T. Choi, J.P. Zhang) A unifying framework for $n$-dimensional quasi-conformal mappings, SIAM Journal on Imaging Sciences, 15(2), 960-988 (2022)
            16. (with H. Zhang) Non-deterministic Deformation Analysis using Computational Quasiconformal Geometry, Proceeding of ICIP (2022)
            17. (with H. Zhang) A New Framework for Deformation Analysis with Uncertainties using Beltrami Fourier Descriptor, Journal of Mathematics, Computation and Geometry of Data, 2(1), 67-88 (2022)
            18. (with H. Law, P.T. Choi, K.C. Lam) CNN-Driven Quasiconformal Model for Large Deformation Image Registration, Journal of Inverse Problem and Imaging, doi: 10.3934/ipi.2022010 (2022)
            19. (with D.P. Zhang, X.C. Tai) Topology- and Convexity-Preserving Image Segmentation Based On Image Registration, Applied Mathematics Modelling, 100, 218-239 (2021)
            20. (with D. Qiu) Modal Uncertainty Estimation for Medical Image Understanding, MICCAI: Uncertainty for Safe Utilization of Machine Learning in Medical Imaging, 3-14 (2021)
            21. (with Y.C. Liu, P.T. Choi) Free-boundary conformal parameterization of point clouds, Journal of Scientific Computing, 90(1):14, (2021)
            22. (with H. Law) Decomposition of Longitudinal Deformations via Beltrami Descriptors, accepted, Journal of Scientific Computing, 89(1): 6 (2021)
            23. (with D.P. Zhang) Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization, Journal of Scientific Computing,  87, 74 (2021)
            24. (with H. Zhang) Quasi-Conformal Neural Network (QC-net) with Applications to Shape Matching, Journal on Mathematics of Computation, Geometry and Data, 1(2), 165-206 (2021)
            25. (with W.H. Chak, C.P. Lau) Subsampled Turbulence Removal Network, Journal on Mathematics, Computation and Geometry of Data, 1(1), 1-33, (2021)
            26. (with N. Lei, K. Su, C. Li, S. Zhao, S. Chen; X.F. Gu) Comparison Between Variational Optimal Mass Transportation and Lie Advection, Journal on Mathematics, Computation, Geometry of Data, 1(1), 99-130, (2021)
            27. (with G.P.T. Choi, D. Qiu) Shape analysis via inconsistent surface registration, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2242), 20200147, (2020)
            28. (with C.Y. Siu, H.L. Chan) Image segmentation with partial convexity prior using discrete conformality structures, SIAM Journal on Imaging Sciences, 13(4), 2105-2139 (2020)
            29. (with Q. Di) Inconsistent Surface Registration via Optimization of Mapping Distortions,Journal of Scientific Computing, 83(64) (2020)
            30. (with P.T. Choi, Y.L Liu, X.F. Gu) Parallelizable global conformal parameterization of simply-connected surfaces via partial welding, SIAM Journal on Imaging Sciences, 13(3), 1049-1083 (2020)
            31. (with H.L. Chen) Recent Development of Medical Shape Analysis Via Computational Quasi-Conformal Geometry, accepted, Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging (2020)
            32. (with H.L. Chan, T.C. Yam) Automatic characteristic-calibrated registration (ACC-REG): Hippocampal surface registration using eigen-graphs, Pattern Recognition, 103, 107142 (2020)
            33. (with P.T. Choi, H.L. Chan, R. Yong, K. Chen, A. Brook, G. Townsend) Tooth morphometry using quasi-conformal theory, accepted, Pattern Recognition, 99, 107064 (2020)
            34. (with K. Chen and J. Modersitzki) Image and Surface Registration, Processing, Analyzing and Learning of Images, Shapes, and Forms, Handbook of Numerical Analysis, 20, 579-611 (2019)
            35. (with D. Syl, K.C. Lam) Computing Quasiconformal Folds, SIAM Journal on Imaging Sciences, 12(3), 1392-1424 (2019)
            36. (with C.P. Lau, Y.H. Lai) Restoration of Atmospheric Turbulence-distorted Images via RPCA and Quasiconformal Maps, Journal of Inverse Problems, 35(7), 1-33 (2019)
            37. (with C.P. Lau, Y.H. Lai) Variational models for joint subsampling and reconstruction of turbulence-degraded images, Journal of Scientific Computing, https://doi.org/10.1007/s10915-018-0833-4 (2018)
            38. (with C.P. Lau, C.P. Yung) Image retargeting via Beltrami representation, IEEE Transaction on Image Processing, 27(12), 5787-5801 (2018)
            39. (with C.P. Yung, P.T. Choi, K. Chen) Efficient Feature-based Image Registration by Mapping Sparsified Surfaces, Journal of Visual Communication and Image Representation, 55, 561-571 (2018)
            40. (with T.W. Meng) PCBC: Quasiconformality of Point Cloud Mappings, Journal of Scientific Computing, 77(1), 597-633 (2018)
            41. (with H.L. Chan, Y. Shi, X.C. Tai) Topology Preserving Image Segmentation by Beltrami Signature of Images, Journal of Mathematical Imaging and Vision, 60(3), 401-421 (2018)
            42. (with K.C. Lam) Optimized Conformal Parameterization with Controllable Area Distortions, Communications in Mathematical Sciecnes, 15(7), 2027-2054 (2017)
            43. (with P.T. Choi, Y. Chen, B. Chiu) Conformal mapping of carotid vessel wall and plaque thickness measured from three-dimensional ultrasound images, Journal of Medical and Biological Engineering and Computing, 55(12), 2183-2195 (2017)
            44. (with C.P. Choi, X.F. Gu) Subdivision Connectivity Remeshing via Teichmuller extremal map, Journal of Inverse Problems and Imaging, 11(5), 825-855 (2017)
            45. (with P.T. Choi) A Linear Algorithm for Disk Conformal Parameterization of Simply-Connected Open Surface, Advances in Computational Mathematics, 44(1), 87–114 (2017)
            46. (with T.C. Ng, K.C. Lam) Multi-scale Representation of Deformations via Wavelet Transform on Beltrami coefficients, SIAM Journal on Multiscale Modeling and Simulation, 15(2), 864–891 (2017)
            47. (with T.W. Meng, P.T. Choi) TEMPO: Feature-Endowed Teichmuller Extremal Mappings of Point Clouds, SIAM Journal on Imaging Sciences, 9(4), 1922–1962 (2016)
            48. (with P.T. Choi, K.T. Ho) Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing, SIAM Journal on Imaging Sciences, 9(4), 1582–1618 (2016)
            49. (with H.L. Chan, H.F. Li) Quasi-conformal Statistical Shape Analysis of Hippocampal Surfaces for Alzheimer Disease Analysis, Journal of Neurocomputing, 175(A), 177–187 (2016)
            50. (with Y.T. Lee, K.C. Lam) Large deformation registration via n-dimensional quasi-conformal maps, Journal of Scientific Computing, 67(3), 926–954 (2016)
            51. (with K.T. Ho) QCMC: Quasi-conformal Parameterization for Multiply-connected domains, Advances in Computational Mathematics, 42(2), 279–312 (2016)
            52. (with P.T. Choi, H.Y. Man) Fast Spherical Quasiconformal Parameterization of Genus-0 Closed Surfaces with Application to Adaptive Remeshing, accepted, Journal of Geometry, Imaging and Computing (2016)
            53. (with K.C. Lam) Quasi-Conformal Hybrid Multi-modality Image Registration and Its Application to Medical Image Fusion, Advances in Visual Computing, 9474, 809-818 (2015)
            54. (with K.C. Lam, X.F. Gu) Landmark Constrained Genus-one Surface Teichmuller Map Applied to Surface Registration in Medical Imaging, Medical Image Analysis, 25(1), 45-55 (2015)
            55. (with C.F. Wen, D.F. Wang, L. Shi, W.C.W. Chu, J.C.Y. Cheng) Landmark Constrained Registration of High-genus Surfaces Applied to Vestibular System Morphometry, Computerized Medical Imaging and Graphics, Vol. 44, 1-12 (2015)
            56. (with P.T. Choi) Fast Disk Conformal Parameterization for Simply-connected Open Surfaces, Journal of Scientific Computing, 65(3), 1065-1090 (2015)
            57. (with P.T. Choi, K.C. Lam) FLASH: Fast Landmark Aligned Spherical Harmonic Parameterization for Genus-0 Closed Brain Surfaces, SIAM Journal on Imaging Sciences, 8(1), 67-94 (2015)
            58. (with T.C. Ng) A Splitting method for diffeomorphism optimization problem using Beltrami coefficients, Journal of Scientific Computing, 63(2), 573-611 (2015)
            59. (with H.L Chan, H.Y. Hung) Hooke's Optimization for 3D Triangular Mesh, Journal of Geometry, Imaging and Computing, 2(2) (2015)
            60. (with X.F. Gu, S.T. Yau) Convergence analysis of an iterative algorithm for Teichmuller maps via harmonic energy optimization, Mathematics of Computation, 84, 2823-2842  (2015)
            61. (with K.C. Lam) Landmark and intensity based registration with large deformations via quasi-conformal maps, SIAM Journal on Imaging Sciences, 7(4), 2364-2392 (2014)
            62. (with H.L. Chan) Detection of n-dimensional deformities using n-dimensional quasi-conformal maps, Journal of Geometry, Imaging and Computing, 1(4) (2014)
            63. (with K.C. Lam, C.F. Wen) Conformal-based Surface Morphing and Multi-scale representation, Axioms (SI: Discrete Differential Geometry and its Applications to Imaging and Graphics), Vol. 2, 222-243; (2014)
            64. (with K.C. Lam, X.F. Gu) Genus-One Surface Registration via Teichmuller Extremal Mapping, Medical Image Computing and Computer Machine Intelligence(MICCAI), Volume 8675, 25-32  (2014)
            65. (with W. Zeng, X.F. Gu) Surface Registration by Optimization in Constrained Diffeomorphism Space, Computer Visions and Pattern Recognition(CVPR), 4169-4176  (2014)
            66. (with X.F. Gu, W. Zeng, S.T. Yau) Beltrami representation for diffeomorphisms and its Applications, accepted, AMS/IP Studies in Advanced Mathematics (2014)
            67. (with C.F. Wen) Geometric registration of high-genus surfaces, SIAM Journal on Imaging Sciences, 7(1), 337–365 (2014)
            68. (with M. Zhang, F. Li, X. Wang, Z. Wu, S.Q. Xin, L. Shi, D.F. Wang, Y. He) Automatic registration of vestibular systems with exact landmark correspondence, Graphical Models, 76(5), 532–541 (2014)
            69. (with K.C. Lam, S.T. Yau, X.F. Gu) Teichmuller mapping (T-Map) and its applications to landmark matching registrations, SIAM Journal on Imaging Sciences, 7(1), 391–426 (2014)
            70. (with T.C. Ng, X.F. Gu), Teichmuller extremal map of multiply-connected domains using Beltrami holomorphic flow, Journal of Scientific Computing, 60(2), 249-275 (2013)
            71. (with K.C. Lam, T.W. Wong, X.F. Gu) Texture map and video compression using Beltrami representation, SIAM Journal on Imaging Sciences, Vol. 6, No. 4, 1880–1902 (2013)
            72. (with R. Lai,  Z. Wen, W. Yin, X.F. Gu) Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization, Journal of Scientific Computing, 58(3), 705-725 (2013)
            73. (with W. Zeng, S.T. Yau, X.F. Gu) Shape analysis of planar multiply-connected objects using conformal welding, IEEE Transaction on Pattern Analysis and Machine Intelligence, 36(7), 1384 - 1401 (2013)
            74. (with C.F. Wen, X.F. Gu) A conformal approach for surface inpainting, Journal of Inverse Problems and Imaging, 7(3), 863-884 (2013)
            75. (with M. Zhang, F. Li, Y. He, L. Shi, D. Wang) Registration of Brainstem Surfaces in Adolescent Idiopathic Scoliosis Using Discrete Ricci Flow, Medical Image Computin and Computer Assisted Intervention (MICCAI), Part II, LNCS 7511, 146-154 (2012)
            76. (with T.W. Wong, P.M. Thompson, T.F. Chan) Instrinic feature extraction and Hippocampal Surface Registration using Harmonic eigenmap,SIAM Journal of Imaging Sciences, Volume 5, Issue 2, 746-768 (2012)
            77. (with W. Zeng, X.F. Gu, T.F. Chan, S.T. Yau) Quasiconformal Maps Using Discrete Curvature Flow,Numerische Mathematik , Volume 121, 671-703 (2012)
            78. (with T.W. Wong, W. Zeng, P.M. Thompson, T.F. Chan, S.T. Yau) A Survey on Recent Development in Computational Quasi-conformal Geometry and its Applications, AMS/IP Studies in Advanced Mathematics, Volume 51 , 697-717 (2012)
            79. (with X.F. Gu, W. Zeng, F. Luo, S.T. Yau) Recent Development of Computational Conformal Geometry, AMS/IP Studies in Advanced Mathematics, Volume 51 , 515-560 (2012)
            80. (with T.W. Wong, W. Zeng, X.F. Gu, P.M. Thompson, T.F. Chan, S.T. Yau) Optimization of Surface Registrations using Beltrami Holomorphic Flow, Journal of Scientific Computing, 50(3), 557-585 (2012)
            81. (with T.W. Wong, X.F. Gu, T.F. Chan) Parallelizable Inpainting and Refinement of Diffeomorphisms using Beltrami Holomorphic Flow, in press, Proceedings of the International Conference of Computer Visions (ICCV) (2011)
            82. (with S. Xin, Y. He, P. Fu, L. Shi, D. Wang, W.C.W. Chu, J.C.K. Cheng, X.F. Gu) Euclidean Geodesic Loops on High-genus Surfaces Applied to the Morphometry of Vestibular Systems, Medical Image Computin and Computer Assisted Intervention (MICCAI), 384-392 (2011)
            83. (with W. Yang, J.H. Gao, T.F. Chan, S.T. Yau) R.A. Sperlinge and X. Huang, Independent component analysis-based classification of Alzheimer’s MRI data, Journal of Alzheimer's Disease (JAD), Volume 24, Number 4, 615-637 (2011)
            84. (with W. Zeng, X.F. Gu, T.F. Chan, S.T. Yau) Shape Analysis of Planar Objects with Arbitrary Topologies using Conformal Geometry, Proceedings of the 11th European conference on Computer vision, 672-686 (2010)
            85. (with T.W. Wong, X.F. Gu, P.M. Thompson, T.F. Chan, S.T. Yau) Hippocampal Shape Registration using Beltrami Holomorphic flow, Medical Image Computing and Computer Assisted Intervention(MICCAI), Part II, LNCS 6362, 323-330 (2010)
            86. (with W. Zeng, L. Shi, D. Wang, W.C.W. Chu, J.C.K. Cheng, X.F. Gu, S.T. Yau) Shape Analysis of Vestibular Systems in Adolescent Idiopathic Scoliosis Using Geodesic Spectra, Medical Image Computing and Computer Assisted Intervention(MICCAI), Part III, LNCS 6363, 538-546 (2010)
            87. (with T.W. Wong, X.F. Gu, T.F. Chan, S.T. Yau) Compression of  Surface Diffeomorphism using Beltrami coefficient, IEEE Computer Vision and Pattern Recognition(CVPR), 2839-2846 (2010)
            88. (with T.W. Wong, W. Zeng, X.F. Gu, P.M. Thompson, T.F. Chan, S.T. Yau) Detecting Shape Deformations using Yamabe Flow and Beltrami Coefficents,  Journal of Inverse Problem and Imaging (IPI), Volume 4, Number 2, 311-333 (2010)
            89. (with S. Thiruvenkadam, Y. Wang, P.M. Thompson, T.F. Chan) Optimized Conformal Surface Registration with Shape-based Landmark Matching , SIAM Journal of Imaging Sciences, Volume 3, Issue 1, 52-78 (2010)
            90. (with L.M. Lui, X. Gu, T.F. Chan, S.-T. Yau) Variational Method on Riemann Surfaces using Conformal Parameterization and its Applications to Image Processing, Journal of Methods and Applications of Analysis, Volume 15, Number 4, 513-538 (2008)
            91. (with W. Zeng, X. Gu , S.-T. Yau) Shape Analysis by Conformal Modules,  Journal of Methods and Applications of Analysis, Volume 15, Number 4, 539-556 (2008)
            92. (with Y. Wang, J. Kwan, S. T. Yau) Computation of Curvatures using Conformal Parameterization, Communications in Information and Systems, Volume 8, Number 1, 1-16 (2008)
            93. (with S. Thiruvenkadam, Y. Wang, T.F. Chan, P.M. Thompson) Optimized Conformal Parameterization of Cortical Surfaces Using Shape Based Matching of Landmark Curves, Medical Image Computing and Computer Assisted Intervention(MICCAI), LNCS 5241, 494-502 (2008)
            94. (with Y. Wang, T.F. Chan, and P.M. Thompson) Brain Anatomical Feature Detection by Solving Partial Differential Equations on General Manifolds, Discrete and Continuous Dynamical Systems B, 7(3), 605-618 (2007)
            95. (with Y. Wang, T.F. Chan, P.M. Thompson) Landmark Constrained Genus Zero Surface Conformal Mapping and Its Application to Brain Mapping Research, Applied Numerical Mathematics 57, 847-858 (2007)
            96. (with Y. Wang, X. Gu, K.M. Hayashi, T.F. Chan, P.M. Thompson, S.-T. Yau) Brain Surface Conformal Parameterization using Riemann Surface Structure, IEEE Transaction of Medical Imaging, 26(6), 853-865 (2007)
            97. (with B. Gutman, Y. Wang, T.F. Chan, P.M. Thompson) Hippocampal Surface Discrimination via Invariant Descriptors of Spherical Conformal Maps, IEEE International Symposium on Biomedical Imaging - From Nano to Macro (ISBI), Washington D.C., USA, 1316-1319 (2007)
            98. (with Y. Wang, T.F. Chan, P.M. Thompson) Automatic Landmark Tracking and Its Application to the Optimization of Brain Conformal Mapping, IEEE Computer Vision and Pattern Recognition(CVPR), Vol. 2, 1784-1792 (2006)
            99. (with B. Gutman, Y. Wang, T. F. Chan, P.M. Thompson) Hippocampal Surface Analysis Using Spherical Harmonic Function Applied to Surface Conformal Mapping, Proceeding of 8th International Conference on Pattern Recognition (ICPR), Hong Kong, China, Vol. 3, 964-967 (2006)
            100. (with Y. Wang, T.F. Chan) PDE on manifold using global conformal parametrization, Variational, Geometric, and Level Set Methods in Computer Vision: Third International Workshop, VLSM 2005, Beijing, China, 307-319 (2005)
            101. (with Y. Wang, T.F. Chan, P.M. Thompson) Optimization of Brain Conformal Mapping with Landmarks, Medical Image Computing and Computer Assisted Intervention(MICCAI), Part II, 675-683 (2005)