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Conformal invariants for multiply connected surfaces: Application to landmark curve-based brain morphometry analysis

Jie Shi, Wen Zhang, Miao Tang, Richard J. Caselli, Yalin Wang
2017 Medical Image Analysis  
Landmark curves were widely adopted in neuroimaging research for surface correspondence computation and quantified morphometry analysis.  ...  With the surface Ricci flow method, we can conformally map a multiply connected surface to the Poincaré disk.  ...  to RJC) and the National Science Foundation (DMS-1413417 to YW, IIS-1421165 to WZ and YW).  ... 
doi:10.1016/j.media.2016.09.001 pmid:27639215 pmcid:PMC5099092 fatcat:qczplwszpzdppanhoom5wiwvaa

Shape Analysis with Conformal Invariants for Multiply Connected Domains and its Application to Analyzing Brain Morphology

Y. Wang, X. Gu, T.F. Chan, A.W. Toga, P.M. Thompson
2009 NeuroImage  
Conformal invariants, which are shape indices that can be defined intrinsically on a surface, may be used to identify which surfaces are conformally equivalent, and they can also be used to measure surface  ...  Here we propose to compute a conformal invariant, or shape index, that is associated with the perimeter of the inner concentric circle in the hyperbolic parameter plane. SPLTRAK Abstract Submission  ...  Methods: With the surface Ricci flow method, we can conformally map a multiply connected domain to a multi-hole disk and this conformal map can preserve the values of the conformal invariant.  ... 
doi:10.1016/s1053-8119(09)70848-1 fatcat:nxvovvfqujhupolllj2hkzzzqi

Shape analysis with conformal invariants for multiply connected domains and its application to analyzing brain morphology

Yalin Wang, Xianfeng Gu, T.F. Chan, P.M. Thompson
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
Conformal invariants, which are shape indices that can be defined intrinsically on a surface, may be used to identify which surfaces are conformally equivalent, and they can also be used to measure surface  ...  Here we propose to compute a conformal invariant, or shape index, that is associated with the perimeter of the inner concentric circle in the hyperbolic parameter plane. SPLTRAK Abstract Submission  ...  Methods: With the surface Ricci flow method, we can conformally map a multiply connected domain to a multi-hole disk and this conformal map can preserve the values of the conformal invariant.  ... 
doi:10.1109/cvprw.2009.5206578 fatcat:g7wrmon4grhgfmvykqt65ot3iy

Shape analysis with conformal invariants for multiply connected domains and its application to analyzing brain morphology

Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
Conformal invariants, which are shape indices that can be defined intrinsically on a surface, may be used to identify which surfaces are conformally equivalent, and they can also be used to measure surface  ...  Here we propose to compute a conformal invariant, or shape index, that is associated with the perimeter of the inner concentric circle in the hyperbolic parameter plane. SPLTRAK Abstract Submission  ...  Methods: With the surface Ricci flow method, we can conformally map a multiply connected domain to a multi-hole disk and this conformal map can preserve the values of the conformal invariant.  ... 
doi:10.1109/cvpr.2009.5206578 dblp:conf/cvpr/WangGCT09 fatcat:xuc7fq5tyffwnkw5vthz3mjkbm

Brain Surface Conformal Parameterization With the Ricci Flow

Yalin Wang, Jie Shi, Xiaotian Yin, Xianfeng Gu, Tony F. Chan, Shing-Tung Yau, A. W. Toga, P. M. Thompson
2012 IEEE Transactions on Medical Imaging  
In brain mapping research, parameterized 3D surface models are of great interest for statistical comparisons of anatomy, surface-based registration and signal processing.  ...  First, we convert a cortical surface model into a multiple boundary surface by cutting along selected anatomical landmark curves.  ...  invariants for multiply connected domain, which may be useful for longitudinal image data analysis; (3).  ... 
doi:10.1109/tmi.2011.2168233 pmid:21926017 pmcid:PMC3571860 fatcat:euvzr6tlsfak5kfxcfs6k5euuy

BRAIN SURFACE CONFORMAL PARAMETERIZATION WITH THE RICCI FLOW

Yalin Wang, Xianfeng Gu, Tony Chan, Paul Thompson, Shing-tung Yau
2007 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro  
In brain mapping research, parameterized 3D surface models are of great interest for statistical comparisons of anatomy, surface-based registration and signal processing.  ...  First, we convert a cortical surface model into a multiple boundary surface by cutting along selected anatomical landmark curves.  ...  invariants for multiply connected domain, which may be useful for longitudinal image data analysis; (3).  ... 
doi:10.1109/isbi.2007.357101 dblp:conf/isbi/WangGCTY07 fatcat:6zkrxwsiafayffrmddfxyslr2m

Applying tensor-based morphometry to parametric surfaces can improve MRI-based disease diagnosis

Yalin Wang, Lei Yuan, Jie Shi, Alexander Greve, Jieping Ye, Arthur W. Toga, Allan L. Reiss, Paul M. Thompson
2013 NeuroImage  
Here we develop a new approach to apply tensor-based morphometry to parametric surface models for diagnostic classification.  ...  First, with holomorphic 1-forms, we compute an efficient and accurate conformal mapping from a multiply connected mesh to the so-called slit domain.  ...  , can parameterize brain cortical surfaces with boundaries, i.e. multiply connected surfaces.  ... 
doi:10.1016/j.neuroimage.2013.02.011 pmid:23435208 pmcid:PMC3641904 fatcat:axpvzsnryfedhe7gitxb4sps3q

From a projective invariant to some new properties of algebraic hypersurfaces

ZhongXuan Luo, XinChen Zhou, David XianFeng Gu
2014 Science China Mathematics  
Brain morphometry on congenital hand deformities based on Teichmüller space theory. Computer-Aided Design 58: 84-91 (2015) 25.  ...  Genus Zero Surface Conformal Mapping and Its Application to Brain Surface Mapping. IEEE Transaction on Medical Imaging (TMI), 23(8):949-958, August 2004. 119.  ...  Lui, Landmark Constrained Genus-one Surface Teichmüller Map Applied to Surface Registration in Medical Imaging, accepted, Medical Image Analysis (2015) 34.  ... 
doi:10.1007/s11425-014-4877-0 fatcat:rxfzuf55rvd4lmxmnva3pzzha4

Hyperbolic Ricci Flow and Its Application in Studying Lateral Ventricle Morphometry [chapter]

Jie Shi, Paul M. Thompson, Yalin Wang
2012 Lecture Notes in Computer Science  
For lateral ventricular surface registration, we further convert the parameterization to the Klein model where a convex polygon is guaranteed for a multiply connected surface.  ...  Here we propose a novel method to compute surface hyperbolic parameterization for studying brain morphology with the Ricci flow method.  ...  Overall, it provides an intrinsic and stable way to compute surface conformal structure based shape index for further morphometry study.  ... 
doi:10.1007/978-3-642-33530-3_6 fatcat:6tz3cvzoxvhlleelcq5tsvq74q

Metric Optimization for Surface Analysis in the Laplace-Beltrami Embedding Space

Yonggang Shi, Rongjie Lai, Danny J. J. Wang, Daniel Pelletier, David Mohr, Nancy Sicotte, Arthur W. Toga
2014 IEEE Transactions on Medical Imaging  
In this paper, we present a novel approach for the intrinsic mapping of anatomical surfaces and its application in brain mapping research.  ...  Using the Laplace-Beltrami eigen-system, we represent each surface with an isometry invariant embedding in a high dimensional space.  ...  localization of subtle perturbations to brain morphometry in population studies.  ... 
doi:10.1109/tmi.2014.2313812 pmid:24686245 pmcid:PMC4079755 fatcat:h26iimhxyndeznz75tw24lzlza

Mindboggling morphometry of human brains

Arno Klein, Satrajit S. Ghosh, Forrest S. Bao, Joachim Giard, Yrjö Häme, Eliezer Stavsky, Noah Lee, Brian Rossa, Martin Reuter, Elias Chaibub Neto, Anisha Keshavan, Dina Schneidman
2017 PLoS Computational Biology  
and shape information for further analysis.  ...  Brain image morphometry shows great potential for providing much-needed biological markers for diagnosing, tracking, and predicting progression of mental health disorders.  ...  Arno Klein would like to thank Deepanjana and Ellora for their continued patience and support, and dedicates this project to his mother and father, Karen and Arnold Klein.  ... 
doi:10.1371/journal.pcbi.1005350 pmid:28231282 pmcid:PMC5322885 fatcat:lsqa2kigtzfivlkqzrnmkri37u

Deformation similarity measurement in quasi-conformal shape space

Vahid Taimouri, Jing Hua
2014 Graphical Models  
Energy functional of the deformation curve is minimized to calculate the geodesic curve connecting two shapes on the shape space manifold.  ...  This paper presents a novel approach based on the shape space concept to classify deformations of 3D models.  ...  Completely invariant to the conformal transformations, a conformal structure based on the period matrix and related algorithms to calculate the period matrix for manifolds with arbitrary topologies are  ... 
doi:10.1016/j.gmod.2013.12.001 fatcat:5xgxag4d6fa4nlmdm52o4xcsdu

Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors

N. Lepore, C. Brun, Yi-Yu Chou, Ming-Chang Chiang, R.A. Dutton, K.M. Hayashi, E. Luders, O.L. Lopez, H.J. Aizenstein, A.W. Toga, J.T. Becker, P.M. Thompson
2008 IEEE Transactions on Medical Imaging  
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM).  ...  In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in  ...  To help estimate anatomical correspondences, features such as point, curve, and surface landmarks present in both datasets can be used, [58] or, more commonly, intensity-based cost functions are used  ... 
doi:10.1109/tmi.2007.906091 pmid:18270068 pmcid:PMC2832297 fatcat:y7n5w44m6jbdngl6a2xkg4rg74

A framework for computational anatomy

Paul M. Thompson, Arthur W. Toga
2002 Computing and Visualization in Science  
We present some novel mathematical strategies for computational anatomy, focusing on the creation of population-based brain atlases.  ...  Additional maps have been developed to represent neuronal connectivity and circuitry (Van Essen and Maunsell, 1983), based on compilations of empirical evidence (Brodmann, 1909; Berger, 1929; Penfield  ...  of Mental Health (NINDS/NIMH NS38753), and by a Human Brain Project grant to the International Consortium for Brain Mapping, funded jointly by NIMH and NIDA (P20 MH/DA52176).  ... 
doi:10.1007/s00791-002-0084-6 fatcat:cla6fnu5ybbpngc2gjmcijzavi

Subpopulation Brain Atlases [chapter]

Paul M. Thompson, Michael S. Mega, Arthur W. Toga
2002 Brain Mapping: The Methods  
of Mental Health (NINDS/NIMH NS38753), and by a Human Brain Project grant to the International Consortium for Brain Mapping, funded jointly by NIMH and NIDA (P20 MH/DA52176).  ...  Special thanks go to Neal Jeffries for his advice on longitudinal random effects models, and to our colleagues Katherine Narr, Jay Giedd, Judith Rapoport, Tyrone Cannon, Elizabeth Sowell, Christine Vidal  ...  Tensor-Based Morphometry.  ... 
doi:10.1016/b978-012693019-1/50030-7 fatcat:jyb3d46vhbbp7nfqw3yothneia
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