Personal Site

My research

I have been working on the following research projects.

- Restoration of turbulence-distorted images via RPCA and Quasi-conformal Maps
- Image retargeting via Beltrami representation
- Topology Preserving Image Segmentation by Beltrami Signature of Shapes
- Large Deformation Diffeomorphic Registration via n-Dimensional Quasi-conformal Maps
- A Splitting Method for Diffeomorphism Optimization Problem using Beltrami Coefficients
- FLASH: Fast landmark aligned spherical harmonic parameterization
- Q-Fibra: Feature and intensity based registration via quasi-conformal maps
- Geometric registration of high-genus surfaces
- Teichmuller mapping of Multiply-connected domains using Beltrami holomorphic flow
- A conformal approach for surface inpainting
- Teichmuller mapping (T-Map) and its applications to landmark matching registrations
- Beltrami Inpainting and Refinement of Diffeomorphisms
- Hippocampal Shape Registration using Beltrami Holomorphic flow
- Instrinic feature extraction and Hippocampal Surface Registration using Harmonic eigenmap
- Shape Analysis of Vestibular Systems in Adolescent Idiopathic Scoliosis by Geodesic Spectra
- Compression of Surface Diffeomorphism using Beltrami coefficient
- Shape Analysis of Planar Objects with Arbitrary Topologies using Conformal Geometry
- Computation of Quasi-conformal map using discrete Curvature flow
- Computation of Teichmuller extremal map using Quadratic differentials
- Representation and Optimization of Surface Diffeomorphisms using Beltrami Coefficients
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Shape Analysis by Conformal Modules
- Detecting Abnormal Shape Deformations using Yamabe Flow and Beltrami Coefficents
- Accurate estimation of curvatures using the conformal structure
- Shape based landmark matching differeomphism between brain cortical surfaces
- Automatics sulcal landmark tracking on the brain cortical surface
- Variational problem and Image processing on surfaces using conformal parameterization
-
Optimized brain conformal parameterization using landmark constraints


Press release
Our research on medical morphometry was reported on the newspaper (
信報
): Link

List of selected Publications:

Submitted/Preprint:

  1. (with K.C. Lam) Optimized Conformal Parameterization with Controllable Area Distortions, under revision
  2. (with T.W. Meng) The Theory of Computational Quasi-conformal Geometry on Point Clouds, submitted
  3. (with C.P. Choi, X.F. Gu) Subdivision Connectivity Remeshing via Teichmuller extremal map, under revision
  4. (with C.P. Yung, P.T. Choi, K. Chen) TRIM: Triangulating Images for Efficient Registration, submitted
  5. (with P.T. Choi, H.Y. Man) Fast Spherical Quasiconformal Parameterization of Genus-0 Closed Surfaces with Application to Adaptive Remeshing, submitted

Published:

  1. (with P.T. Choi) A Linear Algorithm for Disk Conformal Parameterization of Simply-Connected Open Surface, accepted, Advances in Computational Mathematics (2017)
  2. (with T.C. Ng, K.C. Lam) Multi-scale Representation of Deformations via Wavelet Transform on Beltrami coefficients, accepted, SIAM Journal on Multiscale Modeling and Simulation (2017)
  3. (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)
  4. (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)
  5. (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)
  6. (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)
  7. (with K.T. Ho) QCMC: Quasi-conformal Parameterization for Multiply-connected domains, Advances in Computational Mathematics, 42(2), 279–312 (2016)
  8. (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)
  9. (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)
  10. (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)
  11. (with P.T. Choi) Fast Disk Conformal Parameterization for Simply-connected Open Surfaces, Journal of Scientific Computing, 65(3), 1065-1090 (2015)
  12. (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)
  13. (with T.C. Ng) A Splitting method for diffeomorphism optimization problem using Beltrami coefficients, Journal of Scientific Computing, 63(2), 573-611 (2015)
  14. (with H.L Chan, H.Y. Hung) Hooke's Optimization for 3D Triangular Mesh, Journal of Geometry, Imaging and Computing, 2(2) (2015)
  15. (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)
  16. (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)
  17. (with H.L. Chan) Detection of n-dimensional deformities using n-dimensional quasi-conformal maps, Journal of Geometry, Imaging and Computing, 1(4) (2014)
  18. (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)
  19. (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)
  20. (with W. Zeng, X.F. Gu) Surface Registration by Optimization in Constrained Diffeomorphism Space, Computer Visions and Pattern Recognition(CVPR), 4169-4176  (2014)
  21. (with X.F. Gu, W. Zeng, S.T. Yau) Beltrami representation for diffeomorphisms and its Applications, accepted, AMS/IP Studies in Advanced Mathematics (2014)
  22. (with C.F. Wen) Geometric registration of high-genus surfaces, SIAM Journal on Imaging Sciences, 7(1), 337–365 (2014)
  23. (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)
  24. (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)
  25. (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)
  26. (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)
  27. (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)
  28. (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)
  29. (with C.F. Wen, X.F. Gu) A conformal approach for surface inpainting, Journal of Inverse Problems and Imaging, 7(3), 863-884 (2013)
  30. (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)
  31. (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)
  32. (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)
  33. (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)
  34. (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)
  35. (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)
  36. (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)
  37. (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)
  38. (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)
  39. (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)
  40. (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)
  41. (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)
  42. (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)
  43. (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)
  44. (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)
  45. (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)
  46. (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)
  47. (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)
  48. (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)
  49. (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)
  50. (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)
  51. (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)
  52. (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)
  53. (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)
  54. (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)
  55. (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)
  56. (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)