Conformal Mapping via Metric Optimization with Application for Cortical Label Fusion

  • Yonggang Shi
  • Rongjie Lai
  • Arthur W. Toga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7917)


In this paper we develop a novel approach for computing conformal maps between anatomical surfaces with the ability of aligning anatomical features and achieving greatly reduced metric distortion. In contrast to conventional approaches that focused on conformal maps to the sphere or plane, our method computes the conformal map between surfaces in the embedding space formed the intrinsically defined Laplace-Beltrami (LB) eigenfunctions. Utilizing the power of LB eigenfunctions as informative descriptors of global geometry, the conformal maps computed by our method can effectively align anatomical features on cortical surfaces. By computing such feature-aware conformal maps to a group-wisely optimal atlas surface, which is also computed with metric optimization in the LB embedding space, we develop a fully automated system for cortical labeling with the fusion of labels on a large number of atlas surfaces. In our experiments, we build our system with 40 labeled surfaces and demonstrate its excellent performance with leave-one-out cross validation. We also applied the automated labeling system to cortical surfaces reconstructed from MR scans of 50 patients with Alzheimer’s disease (AD) and 50 normal controls (NC) to illustrate its robustness and effectiveness in clinical data analysis.


Cortical Surface Right Hemisphere Label Surface Anatomical Surface Gyral Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yonggang Shi
    • 1
  • Rongjie Lai
    • 2
  • Arthur W. Toga
    • 1
  1. 1.Lab of Neuro ImagingUCLA School of MedicineLos AngelesUSA
  2. 2.Dept. of MathematicsUniversity of Southern CaliforniaLos AngelesUSA

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