Affine Coordinate-Based Parametrized Active Contours for 2D and 3D Image Segmentation | SpringerLink
Skip to main content
Springer Nature Link
Log in

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

  • Conference paper
  • First Online:
Computer Vision, Imaging and Computer Graphics - Theory and Applications (VISIGRAPP 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 550))

  • 629 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Similar content being viewed by others

References

  1. Barbosa, D., Dietenbeck, T., Schaerer, J., D’hooge, J., Friboulet, D., Bernard, O.: B-spline explicit active surfaces: an efficient framework for real-time 3D region-based segmentation. IEEE Trans. Image Process. 21(1), 241–251 (2012)

    Article  MathSciNet  Google Scholar 

  2. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis. 22, 61–79 (1997)

    Article  Google Scholar 

  3. Chan, T., Vese, L.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)

    Article  Google Scholar 

  4. Coquillart, S.: Extended free-form deformation: a sculpturing tool for 3d geometric modeling. SIGGRAPH 24(4), 187–196 (1990)

    Article  Google Scholar 

  5. Faloutsos, P., van de Panne, M., Terzopoulos, D.: Dynamic free-form deformations for animation synthesis. IEEE Trans. Visual. Comput. Graph. 3(3), 201–214 (1997)

    Article  Google Scholar 

  6. Floater, M.S.: Mean value coordinates. Comput. Aided Geom. Des. 20(1), 19–27 (2003)

    Article  MathSciNet  Google Scholar 

  7. Getreuer, P.: Chan-vese segmentation. Image Processing On Line (2012)

    Google Scholar 

  8. Gouraud, H.: Continuous shading of curved surfaces. IEEE Trans. Comput. C–20(6), 623–629 (1971)

    Article  Google Scholar 

  9. Hormann, K., Floater, M.: Mean value coordinates for arbitrary planar polygons. ACM Trans. Graph. 25(4), 1424–1441 (2006)

    Article  Google Scholar 

  10. Hormann, K., Greiner, G.: Continuous shading of curved surfaces. In: Curves and Surfaces Proceedings, pp. 152–163, Saint Malo, France (2000)

    Google Scholar 

  11. Jacob, M., Blu, T., Unser, M.: Efficient energies and algorithms for parametric snakes. IEEE Trans. Image Process. 13(9), 1231–1244 (2004)

    Article  Google Scholar 

  12. Joschi, P., Meyer, M., DeRose, T., Green, B., Sanocki, T.: Harmonic coordinates for character articulation. In: SIGGRAPH (2007)

    Google Scholar 

  13. Ju, T., Schaefer, S., Warren, J.: Mean value coordinates for closed triangular meshes. Proc. ACM SIGGRAPH 24, 561–566 (2005)

    Article  Google Scholar 

  14. Kalmoun, M., Garrido, K., Caselles, V.: Line search multilevel optimization as computational methods for dense optical flow. SIAM J. Imaging Sci. 4(2), 695–722 (2011)

    Article  MathSciNet  Google Scholar 

  15. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J. Comput. Vis. 1(4), 321–331 (1988)

    Article  Google Scholar 

  16. Lankton, S., Tannenbaum, A.: Localizing region-based active contours. IEEE Trans. Image Process. 17(11), 2029–2039 (2008)

    Article  MathSciNet  Google Scholar 

  17. Lipman, Y., Kopf, J., Cohen-Or, D., Levin, D.: GPU-assisted positive mean value coordinates for mesh deformations. In: Eurographics Symposium on Geometry Processing (2007)

    Google Scholar 

  18. Lipman, Y., Levin, D., Cohen-Or, D.: Green coordinates. In: SIGGRAPH (2008)

    Google Scholar 

  19. Michailovich, O., Rathi, Y., Tannenbaum, A.: Image segmentation using active contours driven by the Bhattacharyya gradient flow. IEEE Trans. Image Process. 16(11), 2787–2801 (2007)

    Article  MathSciNet  Google Scholar 

  20. Rousson, M., Deriche, R.: A variational framework for active and adaptative segmentation of vector valued images. In: Proceedings of the Workshop on Motion and Video Computing, pp. 56–61. IEEE Computer Society (2002)

    Google Scholar 

  21. Rueckert, D., Sonoda, L., Hayes, C., Hill, D., Leach, M., Hawkes, D.: Nonrigid registration using free-form deformations: application to breast MR images. IEEE Trans. Med. Imaging 18(8), 712–721 (1999)

    Article  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Analysis, Univerity of Barcelona, Gran Via de les Corts Catalanes 585, 08007, Barcelona, Spain

    Qi Xue, Laura Igual, Albert Berenguel & Luis Garrido

  2. Department of Mathematics, Tongji University, Shanghai, China

    Qi Xue

  3. Computer Vision Center, Edificio O, Campus UAB, Bellaterra (Cerdanyola), 08193, Barcelona, Spain

    Laura Igual, Albert Berenguel & Luis Garrido

  4. Department of Computer Science and Applied Mathematics, Univerity of Girona, Girona, Spain

    Marité Guerrieri

Authors
  1. Qi Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laura Igual
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Albert Berenguel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marité Guerrieri
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Luis Garrido
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laura Igual .

Editor information

Editors and Affiliations

  1. Dip. di Matematica e Informatica, Università di Catania, Catania, Catania, Italy

    Sebastiano Battiato

  2. Inria/ZIRST, Saint Ismier, France

    Sabine Coquillart

  3. INRIA-Rennes/MimeTIC Tean, Rennes cedex, France

    Julien Pettré

  4. Swansea University, Swansea, UK

    Robert S. Laramee

  5. Computer Science, Linnaeus University, Växjö, Sweden

    Andreas Kerren

  6. do IPS, Escola Superior de Tecnologia, Setúbal, Portugal

    José Braz

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Xue, Q., Igual, L., Berenguel, A., Guerrieri, M., Garrido, L. (2015). Affine Coordinate-Based Parametrized Active Contours for 2D and 3D Image Segmentation. In: Battiato, S., Coquillart, S., Pettré, J., Laramee, R., Kerren, A., Braz, J. (eds) Computer Vision, Imaging and Computer Graphics - Theory and Applications. VISIGRAPP 2014. Communications in Computer and Information Science, vol 550. Springer, Cham. https://doi.org/10.1007/978-3-319-25117-2_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25117-2_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25116-5

  • Online ISBN: 978-3-319-25117-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation