My research

I have several ongoing research projects.

-  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 constrait

List of selected Publications:

Submitted/Preprint:

• T.W. Wong, L.M. Lui, P.M. Thompson, T.F. Chan and S.T. Yau, Instrinic feature extraction and Hippocampal Surface Registration using Harmonic eigenmap, submitted
• W. Zeng, L.M. Lui, X.F. Gu, T.F. Chan and S.T. Yau, Quasiconformal Maps Using Discrete Curvature Flow, submitted
• L.M. Lui, T.W. Wong, W. Zeng, X.F. Gu, T.F. Chan and S.T. Yau, Optimization of Surface Registrations using Beltrami Holomorphic Flow, to be submitted
• L.M. Lui, J.S. Liu, X.F. Gu and S.T. Yau, Computation of Teichmuller extremal map using Quadratic differentials, to be submiited
  

Published:

• 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, ECCV, in press (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, IEEE Medical Image Computing and Computer Assisted Intervention(MICCAI), in press, (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, IEEE Medical Image Computing and Computer Assisted Intervention(MICCAI), in press, (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), in press, (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)