An Algorithm Based on Augmented Lagrangian Method for Generalized Gradient Vector Flow Computation

  • Dongwei Ren
  • Wangmeng Zuo
  • Xiaofei Zhao
  • Hongzhi Zhang
  • David Zhang
Part of the Communications in Computer and Information Science book series (CCIS, volume 321)


We propose a novel algorithm for the fast computation of generalized gradient vector flow (GGVF) whose high cost of computation has restricted its potential applications on images with large size. We reformulate the GGVF problem as a convex optimization model with equality constraint. Our approach is based on a variable splitting method to obtain an equivalent constrained optimization formulation, which is then addressed with the inexact augmented Lagrangian method (IALM). To further enhance the computational efficiency, IALM is incorporated in a multiresolution approach. Experiments on a set of images with a variety of sizes show that the proposed method can improve the computational speed of the original GGVF by one or two order of magnitude, and is comparable with the multigrid GGVF (MGGVF) method in terms of the computational efficiency.


Generalized gradient vector flow convex optimization augmented Lagrangian method multiresolution method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Vision 1(4), 321–331 (1987)CrossRefGoogle Scholar
  2. 2.
    Xu, C., Prince, J.L.: Snakes, shapes, and gradient vector flow. IEEE Trans. Image Processing 7(3), 359–369 (1988)MathSciNetGoogle Scholar
  3. 3.
    Xu, C., Prince, J.L.: Generalized gradient vector flow external forces for active contours. Signal Processing 71(2), 13–139 (1998)CrossRefGoogle Scholar
  4. 4.
    Ray, N., Acton, S.T.: Motion gradient vector flow: An external force for tracking rolling leukocytes with shape and size constrained active contours. IEEE Trans. Medical Imaging 23(12), 1466–1478 (2004)CrossRefGoogle Scholar
  5. 5.
    Hassouna, M.S., Farag, A.A.: Variational curve skeletons using gradient vector flow. IEEE Trans. Pattern Analysis and Machine Intelligence 31(12), 2257–2274 (2009)CrossRefGoogle Scholar
  6. 6.
    He, L., Li, C., Xu, C.: Intensity statistics-based HSI diffusion for color photo denoising. In: IEEE International Conference on Computer Vision and Pattern Recognition, Anchorage, AK (2008)Google Scholar
  7. 7.
    Ghita, O., Whelan, P.F.: A new GVF-based image enhancement formulation for use in the presence of mixed noise. Pattern Recognition 43(8), 2646–2658 (2010)zbMATHCrossRefGoogle Scholar
  8. 8.
    Li, B., Acton, S.T.: Active contour external force using vector field convolution for image segmentation. IEEE Trans. Image Processing 16(8), 2096–2106 (2007)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ntalianis, K., Doulamis, N., Doulamis, A., Kollias, S.: Multiresolution gradient vector flow field: a fast implementation towards video object plane segmentation. In: 2001 IEEE International Conference on Multimedia and Expo, ICME 2001 (2001)Google Scholar
  10. 10.
    Boukerroui, D.: Efficient numerical schemes for gradient vector flow. In: 16th IEEE International Conference on Image Processing (ICIP 2009), pp. 4057–4060 (2009)Google Scholar
  11. 11.
    Han, X., Xu, C., Prince, J.L.: Fast numerical scheme for gradient vector flow computation using a multigrid method. IET Image Processing 1(1), 48–55 (2007)CrossRefGoogle Scholar
  12. 12.
    Wang, Y., Yang, J., Yin, W., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imag. Sci. 1, 248–272 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Afonso, M.V., Bioucas-Dias, J.M., Figueiredo, M.A.T.: Fast image recovery using variable splitting and constrained optimization. IEEE Trans. Image Processing 19(9), 2345–2356 (2010)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Liu, G., Lin, Z., Yu, Y.: Robust subspace segmentation by low-rank representation. In: International Conference on Machine Learning 2010, Haifa, Israel (2010)Google Scholar
  15. 15.
    Li, J., Zuo, W., Zhao, X., Zhang, D.: An augmented Lagrangian method for fast gradient vector flow computation. In: 18th IEEE International Conference on Image Processing, pp. 1557–1560 (2011)Google Scholar
  16. 16.
    Zuo, W., Lin, Z.: A Generalized Accelerated Proximal Gradient Approach for Total-Variation-Based Image Restoration. IEEE Trans. Image Processing 20(10), 2748–2759 (2011)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Ganesh, A., Lin, Z., Wright, J., Wu, L., Chen, M., Ma, Y.: Fast algorithms for recovering a corrupted low-rank matrix. In: International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (2009)Google Scholar
  18. 18.
    Lin, Z., Chen, M., Ma, Y.: The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices. Technical Report UILU-ENG-09-2215, UIUC (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dongwei Ren
    • 1
  • Wangmeng Zuo
    • 1
  • Xiaofei Zhao
    • 1
  • Hongzhi Zhang
    • 1
  • David Zhang
    • 1
    • 2
  1. 1.Biocomputing Research Centre, School of Computer Science and TechnologyHarbin Institute of TechnologyHarbinChina
  2. 2.Biometrics Research Centre, Department of ComputingThe Hong Kong Polytechnic UniversityKowloonHong Kong

Personalised recommendations