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Object Segmentation Using Growing Neural Gas and Generalized Gradient Vector Flow in the Geometric Algebra Framework

  • Jorge Rivera-Rovelo
  • Silena Herold
  • Eduardo Bayro-Corrochano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4225)

Abstract

In this paper we present a method based on self-organizing neural networks to extract the shape of a 2D or 3D object using a set of transformations expressed as versors in the conformal geometric algebra framework. Such transformations, when applied to any geometric entity of this geometric algebra, define the shape of the object. This approach was tested with several images, but here we show its utility first using a 2D magnetic resonance image to segment the ventricle. Then we present some examples of an application for the case of 3D objects.

Keywords

Final Shape Geometric Algebra Volumetric Data Object Segmentation Neural Unit 
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.

References

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    Rosenhahn, B., Sommer, G.: Pose Estimation in Conformal Geometric Algebra., Christian-Albrechts-University of Kiel, Technical Report No. 0206, pp. 13–36 (2002)Google Scholar
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    Fritzke, B.: A growing neural gas network learns topologies. Advances in Neural Information Processing Systems 7. MIT Press, Cambridge (1995)Google Scholar
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    Xu, C.: Deformable models with applications to human cerebral cortex reconstruction from magnetic resonance images., Ph.D. Thesis, Johns Hopkins University, pp. 14–63 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jorge Rivera-Rovelo
    • 1
  • Silena Herold
    • 2
  • Eduardo Bayro-Corrochano
    • 1
  1. 1.CINVESTAV Unidad GuadalajaraJaliscoMéxico
  2. 2.Universidad de OrienteCuba

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