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A Landmark-Based Brain Conformal Parametrization with Automatic Landmark Tracking Technique [chapter]

Lok Ming Lui, Yalin Wang, Tony F. Chan, Paul M. Thompson
2006 Lecture Notes in Computer Science  
In this paper, we present algorithms to automatically detect and match landmark curves on cortical surfaces to get an optimized brain conformal parametrization.  ...  Based on the global conformal parametrization of a cortical surface, our method adjusts the landmark curves iteratively on the spherical or rectangular parameter domain of the cortical surface along its  ...  Fig. 5 . 5 Optimization of brain conformal mapping using automatic landmark tracking. In (A) and (B), two different cortical surfaces are mapped conformally to the sphere.  ... 
doi:10.1007/11866763_38 fatcat:ge2nhc6vfbgltooknmuomz33oi

Optimization of Brain Conformal Mapping with Landmarks [chapter]

Yalin Wang, Lok Ming Lui, Tony F. Chan, Paul M. Thompson
2005 Lecture Notes in Computer Science  
The key advantage of this conformal parameterization approach is that any local adjustments of the mapping to match landmarks do not affect the conformality of the mapping significantly.  ...  To compare and integrate brain data, data from multiple subjects are typically mapped into a canonical space. One method to do this is to conformally map cortical surfaces to the sphere.  ...  Based on this fact, we can compute the conformal mapping by a variational approach, which minimizes the harmonic energy.  ... 
doi:10.1007/11566489_83 fatcat:7hcppvfw7vg2llaunjq4bafhn4

Optimized Conformal Surface Registration with Shape-based Landmark Matching

Lok Ming Lui, Sheshadri Thiruvenkadam, Yalin Wang, Paul M. Thompson, Tony F. Chan
2010 SIAM Journal of Imaging Sciences  
We propose a variational method to minimize a compound energy functional that measures the harmonic energy of the parameterization maps and the shape dissimilarity between mapped points on the landmark  ...  An application of our model to medical imaging research is shown, using experiments on brain cortical surfaces, with anatomical (sulcal) landmarks delineated, which show that our computed maps give a shape-based  ...  We propose a variational approach by minimizing a compounded energy that measures the harmonic energy of the parameterizations and the shape dissimilarity between mapped points on the landmark curves.  ... 
doi:10.1137/080738386 fatcat:ioo4f2ynh5d3bnfqudj44txgzq

Landmark constrained genus zero surface conformal mapping and its application to brain mapping research

Lok Ming Lui, Yalin Wang, Tony F. Chan, Paul Thompson
2007 Applied Numerical Mathematics  
In order to compare and integrate brain data more effectively, data from multiple subjects are typically mapped into a canonical space.  ...  The key advantage of these conformal parameterization approaches is that any local adjustments of the mapping to match landmarks do not affect the conformality of the mapping significantly.  ...  Fig. 8(a) shows the average maps of the optimal Möbius transformation approach. Fig. 8(b) shows the average map of the variational approach.  ... 
doi:10.1016/j.apnum.2006.07.031 fatcat:ayvvohfowjgq3iarwy36kromqi

Landmark and Intensity Based Registration with Large Deformations via Quasi-conformal Maps [article]

Lam Ka Chun, Lok Ming Lui
2013 arXiv   pre-print
The basic idea is to minimize an energy functional involving a Beltrami coefficient term, which measures the distortion of the quasi-conformal map.  ...  The obtained registration is guaranteed to be diffeomorphic (1-1 and onto), even with a large deformation or large number of landmark constraints.  ...  Note that a T , b T , c T and d T can be written as a linear combination of the x-coordinates and y-coordinate of the desired quasi-conformal map f .  ... 
arXiv:1310.1710v1 fatcat:yeuiazpnw5bstkritcm4xnbwt4

Landmark-free geometric methods in biological shape analysis

Patrice Koehl, Joel Hass
2015 Journal of the Royal Society Interface  
We take as input a pair of triangulated genus zero surfaces that are topologically equivalent to spheres with no holes or handles, and construct a discrete conformal map f between the surfaces.  ...  The conformal map is chosen to minimize a symmetric deformation energy E sd ( f ) which we introduce. This measures the distance of f from an isometry, i.e. a non-distorting correspondence.  ...  and m is a bijective conformal map of the sphere to itself.  ... 
doi:10.1098/rsif.2015.0795 pmid:26631331 pmcid:PMC4707851 fatcat:wi2rfudehfh6vlv3bhgzk5sepq

Optimized Conformal Parameterization of Cortical Surfaces Using Shape Based Matching of Landmark Curves [chapter]

Lok Ming Lui, Sheshadri Thiruvenkadam, Yalin Wang, Tony Chan, Paul Thompson
2008 Lecture Notes in Computer Science  
We propose a variational energy that measures the harmonic energy of the parameterization maps, and the shape dissimilarity between mapped points on the landmark curves.  ...  We achieve this by intrinsically modelling our search space of maps as flows of smooth vector fields that do not flow across the landmark curves, and by using the local surface geometry on the curves to  ...  We propose a variational approach by minimizing an energy that measures the harmonic energy of the parameterization maps, and the shape dissimilarity between mapped points on the landmark curves.  ... 
doi:10.1007/978-3-540-85988-8_59 fatcat:q5md63dxnnevret4z6klziubv4

Landmark- and Intensity-Based Registration with Large Deformations via Quasi-conformal Maps

Ka Chun Lam, Lok Ming Lui
2014 SIAM Journal of Imaging Sciences  
The basic idea is to minimize an energy functional involving a Beltrami coefficient term, which measures the distortion of the quasi-conformal map.  ...  The obtained registration is guaranteed to be diffeomorphic (1-1 and onto), even with a large deformation or large number of landmark constraints.  ...  Note that a T , b T , c T and d T can be written as a linear combination of the x-coordinates and y-coordinate of the desired quasi-conformal map f .  ... 
doi:10.1137/130943406 fatcat:rr3ey32ornegzm42r3usdaqata

Surface Matching and Registration by Landmark Curve-Driven Canonical Quasiconformal Mapping [chapter]

Wei Zeng, Yi-Jun Yang
2014 Lecture Notes in Computer Science  
The mapping exists and is unique and intrinsic to surface and landmark geometry. The novel shape representation provides a conformal invariant shape signature.  ...  The key idea of the canonical mapping is to minimize the harmonic energy with the landmark curve straightening constraints and generate a quasi-holomorphic 1-form which is zero in one parameter along landmark  ...  This work is partially supported by NSFC-61202146 and the Outstanding Young Scientist Research Award Fund of Shandong Province of China (BS2012DX014).  ... 
doi:10.1007/978-3-319-10590-1_46 fatcat:skzrilmddjefdiumpwrx7fndli

Optimal landmark distributions for statistical shape model construction

Tobias Heimann, Ivo Wolf, Hans-Peter Meinzer, Joseph M. Reinhardt, Josien P. W. Pluim
2006 Medical Imaging 2006: Image Processing  
A drawback of the current approach is that the user has no influence on the final landmark positions, which often do not represent the modeled shape adequately.  ...  To compare our remeshed models with the original approach, we generalize the established generalization and specificity measures to be independent of the underlying landmark distribution.  ...  ACKNOWLEDGMENTS We would like to thank Tomos Williams from the Div. of Imaging Science, University of Manchester, UK for the data of the diffusion mapping parameterization in Fig. 2 .  ... 
doi:10.1117/12.653294 dblp:conf/miip/HeimannWM06 fatcat:r5dspoaumbgcrkrhmf3c42hmyi

FLASH: Fast Landmark Aligned Spherical Harmonic Parameterization for Genus-0 Closed Brain Surfaces

Pui Tung Choi, Ka Chun Lam, Lok Ming Lui
2015 SIAM Journal of Imaging Sciences  
This approach is limited by the loss of bijectivity under large deformations and the slow computation.  ...  Also, by adjusting the Beltrami differential of the mapping, a diffeomorphic (1-1, onto) spherical parameterization can be effectively obtained.  ...  [16] introduced a variational approach to obtain shape-based landmark-matching optimized conformal parameterizations of simply connected open brain surfaces.  ... 
doi:10.1137/130950008 fatcat:jfnt4ynrung25fu3zepxdfbiqu

Landmark-matching Transformation with Large Deformation via n-dimensional Quasi-conformal Maps [article]

Lee Yin Tat, Lam Ka Chun, Lui Lok Ming
2015 arXiv   pre-print
The generalized conformality term K(f) enforces the bijectivity of the optimized mapping and minimizes its local geometric distortions even with large deformations.  ...  Given a set of feature correspondences, our algorithm searches for an optimal folding-free mapping that satisfies the prescribed landmark constraints.  ...  Most of the existing landmark-based registration models are variational approaches.  ... 
arXiv:1402.6908v2 fatcat:dur3teuu35ewrav4wqkqvni7bi

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  
The novel conformal invariant shape indices may offer a new sensitive biomarker and enrich our brain imaging analysis toolset for studying diagnosis and prognosis of AD.  ...  With the surface Ricci flow method, we can conformally map a multiply connected surface to the Poincaré disk.  ...  Data collection and sharing for this project was funded by the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense  ... 
doi:10.1016/j.media.2016.09.001 pmid:27639215 pmcid:PMC5099092 fatcat:qczplwszpzdppanhoom5wiwvaa

Landmarks and Frontiers in Biological Fluid Dynamics [article]

John O. Dabiri
2019 arXiv   pre-print
Rather than attempt a comprehensive review of the literature, this article highlights a limited selection of classic and recent work.  ...  While this growth is exciting, it can present a barrier to researchers seeking a concise introduction to key challenges and opportunities for progress in the field.  ...  This presents the opportunity to use a powerful suite of tools from complex analysis, especially conformal mapping, which are most appropriate in the limit of inviscid, potential flows.  ... 
arXiv:1904.13013v1 fatcat:omajxgmfcrd4ti46frmtcfa2ky

Landmark-Guided Surface Matching and Volumetric Warping for Improved Prostate Biopsy Targeting and Guidance [chapter]

Steven Haker, Simon K. Warfield, Clare M. C. Tempany
2004 Lecture Notes in Computer Science  
The novelty of this approach is that it allows for the exact matching of pre-specified corresponding landmark points on the two surfaces to be matched.  ...  We present a composite method for landmark-guided surface matching and volumetric non-rigid registration, with an application to prostate biopsy.  ...  This work was funded by NIH grants R01 AG 19513-03 and P41 RR13218-06.  ... 
doi:10.1007/978-3-540-30135-6_104 fatcat:kqgmkpdxxffsjamzwf3ss3pgei
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