3D topology preserving flows for viewpoint-based cortical unfolding

Kelvin R. Rocha, Ganesh Sundaramoorthi, Anthony J. Yezzi, Jerry L. Prince

Research output: Contribution to journalArticlepeer-review


We present a variational method for unfolding of the cortex based on a user-chosen point of view as an alternative to more traditional global flattening methods, which incur more distortion around the region of interest. Our approach involves three novel contributions. The first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface with respect to a given viewpoint. The second is an additional energy function and flow designed to preserve the 3D topology of the evolving surface. The third is a method that dramatically improves the computational speed of the 3D topology preservation approach by creating a tree structure of the 3D surface and using a recursion technique. Experiments results show that the proposed approach can successfully unfold highly convoluted surfaces such as the cortex while preserving their topology during the evolution.

Original languageEnglish (US)
Pages (from-to)223-236
Number of pages14
JournalInternational Journal of Computer Vision
Issue number3
StatePublished - Dec 2009
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported by the grants NSF CCR-0133736 and NIH/NINDS R01-NS-037747.


  • Active polyhedron
  • Area preservation
  • Cortex
  • Surface flattening
  • Surface unfolding
  • Topology preservation
  • Variational method
  • Visibility
  • Visibility maximization

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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