• Received : 2014.04.25
  • Accepted : 2014.05.26
  • Published : 2014.06.25


We propose a variational segmentation model based on statistical information of intensities in an image. The model consists of both a local region-based energy and a global region-based energy in order to handle misclassification which happens in a typical statistical variational model with an assumption that an image is a mixture of two Gaussian distributions. We find local ambiguous regions where misclassification might happen due to a small difference between two Gaussian distributions. Based on statistical information restricted to the local ambiguous regions, we design a local region-based energy in order to reduce the misclassification. We suggest an algorithm to avoid the difficulty of the Euler-Lagrange equations of the proposed variational model.


  1. R. C. Gonzalez and R. E. Woods. Digital image processing. Prentice-Hall, New Jersey, 2002.
  2. A. K. Jain. Fundamentals of digitial image processing. Prentice-Hall, New Jersey, 2003.
  3. J. Canny. A computational approach to edge detection. IEEE Trans. Pattern Anal. Machine Intell., 8:679-698, 1986.
  4. M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. Int. J. Comput. Vis., 1:321-331, 1988.
  5. V. Caselles, F. Catte, T. Coll, and F. Dibos. A geometric model for active contours in image processing. Numer. Math., 66:1-31, 1993.
  6. V. Caselles, R. Kimmel, and G. Sapiro. Geodesic active contours. Int. J. Comput. Vis., 22:61-79, 1997.
  7. C. Xu, A. Yezzi, and J. L. Prince. On the relationship between parametric and geometric active contours. Proc. of 34th Asilomar Conference on Signals, Systems, and Computers, 1:483-489, 2000.
  8. S. J. Osher and J. A. Sethian. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys, 79:12-49, 1988.
  9. J. A. Sethian. Level set methods. Cambridge University Press, New York, 1996.
  10. R. Adams and L. Bischof. Seeded region growing. IEEE Trans. Pattern Anal. Machine Intell., 16:641-647, 1994.
  11. T. Chan and L. Vese. Active contours without edges. IEEE Trans. Image Processing, 10:266-277, 2001.
  12. S. C. Zhu and A. Yuille. Region competition: unifying snakes, regions growing, and Bayes/MDL for multiband image segmentation. IEEE Trans. Pattern Anal. Machine Intell., 18:884-900, 1996.
  13. N. Paragios and R. Deriche. Geodesic active regions and level set methods for supervised texture segmentation. Int. J. Comput. Vis., 46:223-247, 2002.
  14. N. Paragios and R. Deriche. Geodesic active regions: A new framework to deal with frame partition problems in computer vision. J. Vis. Commun. and Image Represent., 13:249-268, 2002.
  15. X. Xie and M. Mirmehdi. RAGS: Region-aided geometric snake. IEEE Trans. Image Processing, 13:640-652, 2004.
  16. D. Comaniciu and P. Meer. Mean shift: A robust approach toward feature space analysis. IEEE Trans. Pattern Anal. Machine Intell., 24:603-619, 2002.
  17. G. Aubert and P. Kornprobst. Upwind differencing schemes for hyperbolic conservation laws with source terms. Springer-Verlag, New York, 2002.
  18. M. Sussman, P. Smereka, and S. Osher. A level set approach for computing solutions to incompressible twophase flow. J. Comput. Phys., 114:146-159, 1994.