Area- and Angle-Preserving Parameterization for Vertebra Surface Mesh

  • Shoko MiyauchiEmail author
  • Ken’ichi Morooka
  • Tokuo Tsuji
  • Yasushi Miyagi
  • Takaichi Fukuda
  • Ryo Kurazume
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 20)


This paper proposes a parameterization method of vertebra models by mapping them onto the parameterized surface of a torus. Our method is based on a modified Self-organizing Deformable Model (mSDM) [1], which is a deformable model guided by competitive learning and an energy minimization approach. Unlike conventional mapping methods, the mSDM finds the one-to-one mapping between arbitrary surface model and the target surface with the same genus as the model. At the same time, the mSDM can preserve geometrical properties of the original model before and after mapping. Moreover, users are able to control mapping positions of the feature vertices in the model. Using the mSDM, the proposed method maps the vertebra model onto a torus surface through an intermediate surface with the approximated shape of the vertebra. The use of the intermediate surface results in the stable mapping of the vertebra to a torus compared with the direct mapping from the model to the torus.


Feature Vertices Intermediate Surface Vertebral Model Target Surface Tor Surface 
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This work was supported by Foundation of Kyushu University, JSPS KAKENHI Grant Number 26560262, 24390345 and the Ministry of Health, Labour and Welfare(2010241 71A).


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Shoko Miyauchi
    • 1
    Email author
  • Ken’ichi Morooka
    • 1
  • Tokuo Tsuji
    • 1
  • Yasushi Miyagi
    • 2
  • Takaichi Fukuda
    • 3
  • Ryo Kurazume
    • 1
  1. 1.Graduate School of Information Science and Electrical EngineeringKyushu UniversityFukuokaJapan
  2. 2.Department of NeurosurgeryKaizuka HospitalFukuokaJapan
  3. 3.Graduate School of Medical SciencesKumamoto UniversityKumamotoJapan

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