Hyperbolic Harmonic Brain Surface Registration with Curvature-Based Landmark Matching

  • Rui Shi
  • Wei Zeng
  • Zhengyu Su
  • Yalin Wang
  • Hanna Damasio
  • Zhonglin Lu
  • Shing-Tung Yau
  • Xianfeng Gu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7917)


Brain Cortical surface registration is required for inter-subject studies of functional and anatomical data. Harmonic mapping has been applied for brain mapping, due to its existence, uniqueness, regularity and numerical stability. In order to improve the registration accuracy, sculcal landmarks are usually used as constraints for brain registration. Unfortunately, constrained harmonic mappings may not be diffeomorphic and produces invalid registration. This work conquer this problem by changing the Riemannian metric on the target cortical surface to a hyperbolic metric, so that the harmonic mapping is guaranteed to be a diffeomorphism while the landmark constraints are enforced as boundary matching condition. The computational algorithms are based on the Ricci flow method and hyperbolic heat diffusion. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic, with higher qualities in terms of landmark alignment, curvature matching, area distortion and overlapping of region of interests.


Harmonic Mapping Cortical Surface Dynamic Time Warping Ricci Flow Surface Registration 
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

  • Rui Shi
    • 1
  • Wei Zeng
    • 2
  • Zhengyu Su
    • 1
  • Yalin Wang
    • 3
  • Hanna Damasio
    • 4
  • Zhonglin Lu
    • 5
  • Shing-Tung Yau
    • 6
  • Xianfeng Gu
    • 1
  1. 1.Department of Computer ScienceStony Brook UniversityUSA
  2. 2.School of Computing & Information SciencesFlorida International UniversityUSA
  3. 3.School of Computing, Informatics, and Decision Systems EngineeringArizona State UniversityUSA
  4. 4.NeuroscienceUniversity of Southern CaliforniaUSA
  5. 5.Department of PsychologyOhio State UniversityUSA
  6. 6.Mathematics DepartmentHarvard UniversityUSA

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