International Journal of Computer Vision

, Volume 85, Issue 3, pp 223–236 | Cite as

3D Topology Preserving Flows for Viewpoint-Based Cortical Unfolding

  • Kelvin R. RochaEmail author
  • Ganesh Sundaramoorthi
  • Anthony J. Yezzi
  • Jerry L. Prince


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.


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


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Kelvin R. Rocha
    • 1
    Email author
  • Ganesh Sundaramoorthi
    • 1
  • Anthony J. Yezzi
    • 1
  • Jerry L. Prince
    • 2
  1. 1.School of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Electrical and Computer EngineeringJohns Hopkins UniversityBaltimoreUSA

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