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Brain Surface Conformal Parameterization Using Riemann Surface Structure

Yalin Wang, Lok Ming Lui, Xianfeng Gu, Kiralee M. Hayashi, Tony F. Chan, Arthur W. Toga, Paul M. Thompson, Shing-Tung Yau
2007 IEEE Transactions on Medical Imaging  
Index Terms-Brain mapping, conformal parameterization, partial differential equation, Riemann surface structure.  ...  Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain.  ...  [12] implement a finite-element 0278-0062/$25.00 © 2007 IEEE approximation for parameterizing brain surfaces via conformal mappings.  ... 
doi:10.1109/tmi.2007.895464 pmid:17679336 pmcid:PMC3197830 fatcat:qe6uqvdavfcatnkv6acmkvjkky

Brain Surface Conformal Parameterization with Algebraic Functions [chapter]

Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-Tung Yau
2006 Lecture Notes in Computer Science  
Here we introduce a parameterization method based on algebraic functions. By solving the Yamabe equation with the Ricci flow method, we can conformally map a brain surface to a multi-hole disk.  ...  To illustrate the technique, we computed parameterizations of several types of anatomical surfaces in MRI scans of the brain, including the hippocampi and the cerebral cortices with various landmark curves  ...  Conclusion and Future Work In this paper, we present a brain surface conformal parameterization method based on algebraic functions.  ... 
doi:10.1007/11866763_116 fatcat:a7o36fv75ncebo42jpqluzpwnm

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.  ...  Secondly, we conformally parameterize each cortical surface to a parameter domain with a user-designed Gaussian curvature arrangement.  ...  [22] implemented a finite element approximation for parameterizing brain surfaces via conformal mappings.  ... 
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.  ...  Secondly, we conformally parameterize each cortical surface to a parameter domain with a user-designed Gaussian curvature arrangement.  ...  [22] implemented a finite element approximation for parameterizing brain surfaces via conformal mappings.  ... 
doi:10.1109/isbi.2007.357101 dblp:conf/isbi/WangGCTY07 fatcat:6zkrxwsiafayffrmddfxyslr2m

Brain surface conformal parameterization with the slit mapping

Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-Tung Yau
2008 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro  
Brain surface conformal mapping has been studied intensively.  ...  Preliminary experimental results parameterizing various brain anatomical surfaces are presented.  ...  This work continues our group's previous research on brain surface conformal parameterization.  ... 
doi:10.1109/isbi.2008.4541029 dblp:conf/isbi/WangGCTY08 fatcat:4vgbj65ko5dazh6azr7i4mggwm

Conformal Slit Mapping and Its Applications to Brain Surface Parameterization [chapter]

Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-Tung Yau
2008 Lecture Notes in Computer Science  
In this paper, we studied its application to brain surface parameterization.  ...  Preliminary experimental results parameterizing various brain anatomical surfaces are presented.  ...  [2] implemented a finite element approximation for parameterizing brain surfaces via conformal mappings.  ... 
doi:10.1007/978-3-540-85988-8_70 fatcat:2whbqpwdbjg7tgfkw3bcsmq3ge

Brain Surface Parameterization Using Riemann Surface Structure [chapter]

Yalin Wang, Xianfeng Gu, Kiralee M. Hayashi, Tony F. Chan, Paul M. Thompson, Shing-Tung Yau
2005 Lecture Notes in Computer Science  
To illustrate the technique, we computed conformal structures for several types of anatomical surfaces in MRI scans of the brain, including the cortex, hippocampus, and lateral ventricles.  ...  Based on Riemann surface structure, we can then canonically partition the surface into patches. Each of these patches can be conformally mapped to a parallelogram.  ...  Here we present a new method to parameterize brain surfaces based on their Riemann surface structure.  ... 
doi:10.1007/11566489_81 fatcat:wkmfqxh6frfp5ojdytwil5lwoq

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  
In this work, we find meaningful parameterizations of cortical surfaces utilizing prior anatomical information in the form of anatomical landmarks (sulci curves) on the surfaces.  ...  impairing conformality.  ...  (A) shows the brain surface 1. It is mapped to brain surface 2 under the conformal parameterization as shown in (B). (C) shows the result of matching under our proposed parameterization.  ... 
doi:10.1007/978-3-540-85988-8_59 fatcat:q5md63dxnnevret4z6klziubv4

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  
The proposed algorithm has been tested on 38 human brain surfaces.  ...  For genus-0 closed brain surfaces, the optimized spherical harmonic parameterization, which aligns landmarks to consistent locations on the sphere, has been widely used.  ...  First, we propose a fast and accurate method for spherical conformal parameterization of genus-0 closed brain surfaces.  ... 
doi:10.1137/130950008 fatcat:jfnt4ynrung25fu3zepxdfbiqu

Genus Zero Surface Conformal Mapping and Its Application to Brain Surface Mapping [chapter]

Xianfeng Gu, Yalin Wang, Tony F. Chan, Paul M. Thompson, Shing-Tung Yau
2003 Lecture Notes in Computer Science  
Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.  ...  We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and Yau, 2002),  ...  OPTIMIZE THE CONFORMAL PARAMETERIZATION BY USING LANDMARKS In order to compare two brain surfaces, it is desirable to adjust the conformal parameterization and match the geometric features on the brains  ... 
doi:10.1007/978-3-540-45087-0_15 fatcat:xxptcaiytbbjdcxuandqtkj2wm

Genus Zero Surface Conformal Mapping and Its Application to Brain Surface Mapping

X. Gu, Y. Wang, T.F. Chan, P.M. Thompson, S.-T. Yau
2004 IEEE Transactions on Medical Imaging  
Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.  ...  We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and Yau, 2002),  ...  OPTIMIZE THE CONFORMAL PARAMETERIZATION BY USING LANDMARKS In order to compare two brain surfaces, it is desirable to adjust the conformal parameterization and match the geometric features on the brains  ... 
doi:10.1109/tmi.2004.831226 pmid:15338729 fatcat:wzezjyymfze7jang2cxcsednie

Surface parameterization using Riemann surface structure

Yalin Wang, Xianfeng Gu, K.M. Hayashi, T.F. Chan, P.M. Thompson, Shing-Tung Yau
2005 Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1  
To illustrate the technique, we computed conformal structures for anatomical surfaces in MRI scans of the brain and human face surfaces.  ...  We propose a general method that parameterizes general surfaces with complex (possible branching) topology using Riemann surface structure.  ...  [7] implement a finite element approximation for parameterizing brain surfaces via conformal mappings. Gu et al.  ... 
doi:10.1109/iccv.2005.233 dblp:conf/iccv/WangGHCTY05 fatcat:uah4oshunffdneftiqymfayj5a

Conformal-Based Surface Morphing and Multi-Scale Representation

Ka Lam, Chengfeng Wen, Lok Lui
2014 Axioms  
Once we have the (λ, H) parameterization of the surface, post-processing of the surface can be done directly on the conformal parameter domain.  ...  We test the proposed algorithms on 3D human face data and MRI-derived brain surfaces.  ...  Figure 1d ,e shows the corresponding conformal factor, λ, and mean curvature, H, of the brain surface. Figure 1 . Conformal parameterization of a brain cortical surface.  ... 
doi:10.3390/axioms3020222 fatcat:etwyr5q7kzb2xhgt6c5w7ebaha

Mutual information-based 3D surface matching with applications to face recognition and brain mapping

Yalin Wang, Ming-Chang Chiang, P.M. Thompson
2005 Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1  
In brain imaging, surface-based registration is useful for tracking brain change, and for creating statistical shape models of anatomy.  ...  This finite-dimensional linear space generates all conformal reparameterizations of the surface.  ...  Figure 3 . 3 Shows a uniform (left panel) and a non-uniform (right panel) global conformal parameterization for the same surface, the lateral ventricles of the human brain.  ... 
doi:10.1109/iccv.2005.165 dblp:conf/iccv/WangCT05 fatcat:u5rqzjdymnbk5aa7whsea3caqq

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  
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.  ...  Here we propose a new method, based on a new energy functional, to optimize the conformal parameterization of cortical surfaces by using landmarks.  ...  [4] implemented a finite element approximation for parameterizing brain surfaces via conformal mappings.  ... 
doi:10.1007/11566489_83 fatcat:7hcppvfw7vg2llaunjq4bafhn4
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