Segmentation of Vertebrae from 3D Spine Images by Applying Concepts from Transportation and Game Theories

  • Bulat IbragimovEmail author
  • Boštjan Likar
  • Franjo Pernuš
  • Tomaž Vrtovec
Conference paper
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 17)


We describe a landmark-based three-dimensional (3D) segmentation framework, in which the shape representation of the object of interest is based on concepts from transportation theory. Landmark-based shape representation relies on a premise that considering spatial relationships for every pair of landmarks is redundant, therefore landmarks are first separated into clusters. Landmarks within each cluster form a complete graph of connections, while landmarks within any two clusters are connected in a one-to-one manner by applying a concept from transportation theory called the optimal assignment. The resulting optimal assignment-based shape representation captures the most descriptive shape properties and therefore represents an adequate balance among rigidity, elasticity and computational complexity, and is combined with a 3D landmark detection algorithm that is based on concepts from game theory. The framework was applied to segment 50 lumbar vertebrae from 3D computed tomography images, and the resulting symmetric surface distance of \(0.76 \pm 0.10\,\text {mm}\) and Dice coefficient of \(93.5 \pm 1.0\,\%\) indicate that accurate segmentation can be obtained by the described framework. Moreover, when compared to the complete graph, the computational time was reduced by a factor of approximately nine in the case of optimal assignment-based shape representation.


Complete Graph Cooperative Game Target Image Azimuth Angle Grand Coalition 
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.



This work has been supported by the Slovenian Research Agency under grants P2-0232, J7-2264, L2-7381, and L2-2023.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Bulat Ibragimov
    • 1
    Email author
  • Boštjan Likar
    • 1
  • Franjo Pernuš
    • 1
  • Tomaž Vrtovec
    • 1
  1. 1.Faculty of Electrical EngineeringUniversity of LjubljanaLjubljanaSlovenia

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