Combination of brain conformai, mapping and landmarks: A variational approach

Yalin Wang, Lok Ming Lui, Tony F. Chan, Paul M. Thompson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

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. It is well known that any genus zero Riemann surface can be mapped conformally to a sphere. Since the cortical surface of the brain is a genus zero surface, conformal mapping offers a convenient method to parameterize cortical surfaces without angular distortion, generating an orthogonal grid on the cortex that locally preserves the metric. To compare cortical surfaces more effectively, it is advantageous to adjust the conformal parameterizations to match consistent anatomical features across subjects. This matching of cortical patterns improves the alignment of data across subjects, although it is more challenging to create a consistent conformal (orthogonal) parameterization of anatomy across subjects when landmarks are constrained to lie at specific locations in the spherical parameter space. Here we propose a new method, based on a new energy functional, to optimize the conformal parameterization of cortical surfaces by using landmarks. Experimental results on a dataset of 40 brain hemispheres showed that the land-mark mismatch energy can be significant reduced while effectively preserving conformality. 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. We also examined how the parameterization changes with different weighting factors. As expected, the landmark matching error can be reduced if it is more heavily penalized, but conformality is progressively reduced.

Original languageEnglish (US)
Title of host publicationProceedings of the Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005
EditorsM.H. Hamza
Pages70-75
Number of pages6
StatePublished - Dec 1 2005
Externally publishedYes
EventEighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005 - Honolulu, HI, United States
Duration: Aug 15 2005Aug 17 2005

Publication series

NameProceedings of the Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005

Other

OtherEighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005
CountryUnited States
CityHonolulu, HI
Period8/15/058/17/05

Keywords

  • Brain mapping
  • Conformal mapping
  • Variational method

ASJC Scopus subject areas

  • Engineering(all)

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