Journal of Combinatorial Optimization

, Volume 15, Issue 3, pp 257–275 | Cite as

Shape analysis for automated sulcal classification and parcellation of MRI data

  • Monica K. Hurdal
  • Juan B. Gutierrez
  • Christian Laing
  • Deborah A. Smith


We describe geometric invariants that characterize the shape of curves and surfaces in 3D space: curvature, Gauss integrals and moments. We apply these invariants to neuroimaging data to determine if they have application for automatically classifying and parcellating cortical data. The curves of sulci and gyri on the cortical surface can be obtained by reconstructing cortical surface representations of the human brain from magnetic resonance imaging (MRI) data. We reconstructed gray matter surfaces for 15 subjects, traced 10 sulcal curves on each surface and computed geometric invariants for each curve. These geometric features were used classify the curves into sulcal and hemispheric classes. The best classification results were obtained when moment-based features were computed on the sulcal curves in native space. Gauss integral measures showed that they were useful for differentiating the hemispheric location of a single sulcus. These promising results may indicate that moment invariants are useful for characterizing shape on a global scale. Gauss integral invariants are potentially useful measures for characterizing cortical shape on a local, rather than global scale. Gauss integrals have found biological significance in characterizing proteins so it is worthwhile to consider their possible application to neuroscientific data.


Geometric invariants Shape descriptors Curvature Gauss integrals Moments Data mining Pattern classification MRI data Sulcal curves Cortical shape 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Monica K. Hurdal
    • 1
  • Juan B. Gutierrez
    • 1
  • Christian Laing
    • 1
  • Deborah A. Smith
    • 1
  1. 1.Department of MathematicsFlorida State UniversityTallahasseeUSA

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