My research

I have several ongoing research projects.

- 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
- 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

List of selected Publications:

Submitted/Preprint:

• L.M. Lui, K.C. Lam, T.W. Wong, X.F. Gu, Beltrami representation and its applications to texture and video compression, under revision
• L.M. Lui, K.C. Lam, S.T. Yau, X.F. Gu, Teichmuller mapping (T-Map) and its applications to landmark matching registrations, submitted
• T.C. Ng, X.F. Gu, L.M. Lui, Teichmuller extremal map of multiply-connected domains using Beltrami holomorphic flow, submitted
  
• R. Lai,  Z. Wen, W. Yin, X.F. Gu, L.M. Lui, Fast and Accurate Algorithms for Harmonic Energy
  Minimization on Genus-0 Surfaces, under revision

Published:

• L.M. Lui, W. Zeng, S.T. Yau, X.F. Gu, Shape analysis of planar multiply-connected objects using conformal welding, accepted, IEEE Transaction on Pattern Analysis and Machine Intelligence (2013)
  
• L.M. Lui, C.F. Wen, X.F. Gu, A conformal approach for surface inpainting, accepted, Journal of Inverse Problems and Imaging (2013)
• M. Zhang, F. Li, Y. He, L. Shi, D. Wang and  L.M. Lui, 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)
  
• T.W. Wong, L.M. Lui, P.M. Thompson and 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)
• W. Zeng, L.M. Lui, X.F. Gu, T.F. Chan and S.T. Yau, Quasiconformal Maps Using Discrete Curvature Flow,Numerische Mathematik , Volume 121, 671-703 (2012)
• L.M. Lui, 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)
• X.F. Gu, W. Zeng, L.M. Lui, F. Luo, S.T. Yau, Recent Development of Computational Conformal Geometry, AMS/IP Studies in Advanced Mathematics, Volume 51 , 515-560 (2012)
• L.M. Lui, T.W. Wong, W. Zeng, X.F. Gu, P.M. Thompson, T.F. Chan and S.T. Yau, Optimization of Surface Registrations using Beltrami Holomorphic Flow, Journal of Scientific Computing, 50(3), 557-585 (2012)
• T.W. Wong, X.F. Gu, T.F. Chan, L.M. Lui, Parallelizable Inpainting and Refinement of Diffeomorphisms using Beltrami Holomorphic Flow, in press, Proceedings of the International Conference of Computer Visions (ICCV) (2011)
• S. Xin, Y. He, P. Fu, L. Shi, D. Wang, W.C.W. Chu, J.C.K. Cheng, X.F. Gu, L.M. Lui, 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)
  
• W. Yang, L.M. Lui, 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)
• L.M. Lui, W. Zeng, X.F. Gu, T.F. Chan and 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)
• L.M. Lui, T.W. Wong, X.F. Gu, P.M. Thompson, T.F. Chan and 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)
• W. Zeng, L.M. Lui, 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)
  
• L.M. Lui, T.W. Wong, X.F. Gu, T.F. Chan and S.T. Yau, Compression of Surface Diffeomorphism using Beltrami coefficient, IEEE Computer Vision and Pattern Recognition(CVPR), 2839-2846 (2010)
• L.M. Lui, T.W. Wong, W. Zeng, X.F. Gu, P.M. Thompson, T.F. Chan and 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)
• L.M. Lui, S. Thiruvenkadam, Y. Wang, P.M. Thompson and T.F. Chan, Optimized Conformal Surface Registration with Shape-based Landmark Matching , SIAM Journal of Imaging Sciences, Volume 3, Issue 1, 52-78 (2010)
• L.M. Lui, X. Gu, T.F. Chan and 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)
• W. Zeng, L.M. Lui, X. Gu , S.-T. Yau, Shape Analysis by Conformal Modules, Journal of Methods and Applications of Analysis, Volume 15, Number 4, 539-556 (2008)
• L.M. Lui, Y. Wang, J. Kwan, and S. T. Yau, Computation of Curvatures using Conformal Parameterization, Communications in Information and Systems, Volume 8, Number 1, 1-16 (2008)
• L.M. Lui, S. Thiruvenkadam, Y. Wang, T.F. Chan, P.M. Thompson, Optimized Conformal Parameterization of Cortical Surfaces Using Shape Based Matching of Landmark Curves, IEEE Medical Image Computing and Computer Assisted Intervention(MICCAI), LNCS 5241, 494-502 (2008)
• L.M. Lui, 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)
• L.M. Lui, Y. Wang, T.F. Chan and P.M. Thompson, Landmark Constrained Genus Zero Surface Conformal Mapping and Its Application to Brain Mapping Research, Applied Numerical Mathematics 57, 847-858 (2007)
• Y. Wang, L. M. Lui, X. Gu, K.M. Hayashi, T.F. Chan, P.M. Thompson and S.-T. Yau, Brain Surface Conformal Parameterization using Riemann Surface Structure, IEEE Transaction of Medical Imaging, 26(6), 853-865 (2007)
• B. Gutman, Y. Wang, L.M. Lui, 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)
  
• L. M. Lui, Y. Wang, T.F. Chan and 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)
• B. Gutman, Y. Wang, L. M. Lui, T. F. Chan, and 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)
• L.M. Lui, 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)
• Y. Wang, L.M. Lui, T.F. Chan and P.M. Thompson, Optimization of Brain Conformal Mapping with Landmarks, IEEE Medical Image Computing and Computer Assisted Intervention(MICCAI), Part II, 675-683 (2005)