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Compactly supported radial basis functions based collocation method for level-set evolution in image segmentation.

Amaud Gelas1, Olivier Bernard, Denis Friboulet

  • 1CREATIS-LRMN, INSA, UCB, CNRS UMR 5220, 69621 Villeurbanne Cedex, France. arnaud.gelas@creatis.insa-lyon.fr

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 4, 2007
PubMed
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This study introduces a novel radial basis function (RBF) collocation method for level-set segmentation, offering continuous representations and avoiding reinitialization. This approach enhances topological flexibility in image segmentation, particularly for medical imaging applications.

Area of Science:

  • Medical Imaging
  • Computational Mathematics
  • Image Segmentation

Background:

  • Level-set evolution is typically solved using finite differences schemes.
  • Existing methods often require a reinitialization step, limiting topological flexibility.

Purpose of the Study:

  • To propose an alternative, more flexible level-set evolution scheme using radial basis functions (RBFs).
  • To investigate the use of compactly supported RBFs (CSRBFs) for efficient and topologically flexible image segmentation.

Main Methods:

  • A novel RBF collocation scheme for solving the partial differential equation of level-set evolution.
  • Utilizing compactly supported RBFs (CSRBFs) for continuous representation and reduced computation.
  • Employing a kd-tree strategy for neighborhood representation and avoiding the reinitialization step by constraining the l1-norm of CSRBF parameters.

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Main Results:

  • The proposed CSRBF collocation method provides a continuous representation of the implicit function and its zero level set.
  • Computation cost is reduced through CSRBFs and kd-tree-based neighborhood representation.
  • Avoiding reinitialization leads to topologically flexible solutions capable of developing new contours.

Conclusions:

  • The RBF collocation method offers a viable and advantageous alternative to finite differences for level-set segmentation.
  • This approach demonstrates superior topological flexibility, particularly beneficial for complex medical image segmentation tasks.
  • The method was successfully validated on 3-D CT bone and echocardiographic ultrasound images.