Affine Coordinate-Based Parametrized Active Contours for 2D and 3D Image Segmentation

  • Qi Xue
  • Laura Igual
  • Albert Berenguel
  • Marité Guerrieri
  • Luis Garrido
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 550)


In this paper, we present a new framework for image segmentation based on parametrized active contours. The contour and the points of the image space are parametrized using a set of reduced control points that form a closed polygon in two dimensional problems and a closed surface in three dimensional problems. The active contour evolves by moving the control points. The parametrization, that uses mean value coordinates, stems from the techniques used in computer graphics to animate virtual models. The proposed framework allows to easily formulate region-based energies as the one proposed by Chan and Vese in both two and three dimensional segmentation problems. We show the usefulness of our approach with several experiments.


Active contours Affine coordinates Mean value coordinates 



Q. Xue would like to acknowledge support from Erasmus Mundus BioHealth Computing, L. Igual and L. Garrido from MICINN projects, reference TIN2012-38187- C03-01, MTM2012-30772 and TIN2013-43478-P, and from Catalan Government award 2014-SGR-1219.


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Copyright information

© Springer International Publishing Switzerland 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Qi Xue
    • 1
    • 2
  • Laura Igual
    • 1
    • 3
  • Albert Berenguel
    • 1
    • 3
  • Marité Guerrieri
    • 4
  • Luis Garrido
    • 1
    • 3
  1. 1.Department of Applied Mathematics and AnalysisUniverity of BarcelonaBarcelonaSpain
  2. 2.Department of MathematicsTongji UniversityShanghaiChina
  3. 3.Computer Vision CenterBarcelonaSpain
  4. 4.Department of Computer Science and Applied MathematicsUniverity of GironaGironaSpain

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