Quasi-conformal Flat Representation of Triangulated Surfaces for Computerized Tomography

  • Eli Appleboim
  • Emil Saucan
  • Yehoshua Y. Zeevi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4241)


In this paper we present a simple method for flattening of triangulated surfaces for mapping and imaging. The method is based on classical results of F. Gehring and Y. Väisälä regarding the existence of quasi-conformal and quasi-isometric mappings between Riemannian manifolds. A random starting triangle version of the algorithm is presented. A curvature based version is also applicable. In addition the algorithm enables the user to compute the maximal distortion and dilatation errors. Moreover, the algorithm makes no use to derivatives, hence it is robust and suitable for analysis of noisy data. The algorithm is tested on data obtained from real CT images of the human brain cortex and colon, as well as on a synthetic model of the human skull.


Riemannian Manifold Quasiconformal Mapping Angle Dilatation Circle Packing Triangulate Surface 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Eli Appleboim
    • 1
  • Emil Saucan
    • 1
  • Yehoshua Y. Zeevi
    • 1
  1. 1.Electrical Engineering DepartmentTechnionHaifaIsrael

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