Improving Image Segmentation Performance via Edge Preserving Regularization

This paper presents an improved image segmentation model with edge preserving regularization based on the piecewise-smooth Mumford-Shah functional. A level set formulation is considered for the Mumford-Shah functional minimization in segmentation, and the corresponding partial difference equations are solved by the backward Euler discretization. Aiming at encouraging edge preserving regularization, a new edge indicator function is introduced at level set frame. In which all the grid points which is used to locate the level set curve are considered to avoid blurring the edges and a nonlinear smooth constraint function as regularization term is applied to smooth the image in the isophote direction instead of the gradient direction. In implementation, some strategies such as a new scheme for extension of u+ and u- computation of the grid points and speedup of the convergence are studied to improve the efficacy of the algorithm. The resulting algorithm has been implemented and compared with the previous methods, and has been proved efficiently by several cases.

Authors:

• Ying-jie Zhang
• Li-ling Ge

Keywords:

• Energy minimization
• image segmentation
• level sets
• edge regularization.

References:

[1] D. Mumford and J. Shah, "Optimal approximations by piecewise smooth
functions and associated variational problems," Commun. Pure Appl.
Math., vol. 42, pp. 577-685, May. 1989.
[2] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour
models," International Journal of Computer Vision, vol. 1, no. 4, pp.
321-331, 1988.
[3] P. Perona and J. Malik, "Scale space and edge detection using
anisotropic diffusion," IEEE Transactions on Pattern Analysis and
Machine Intelligence, vol. 12, no. 8,pp. 629-639, 1990.
[4] L. Ambrosis, and V. M. Tortorelli, On the approximation of functionals
depending on Jumps by quadratic elliptic functionals. Bull. Un. Mat. Ital.
1992
[5] Jayant Shah, "A common framework for curve evolution, segmentation
and anisotropic diffusion," in IEEE Proc. Conf. Computer Vision and
Pattern Recognition, San Francisco, CA, Jun. 1996, pp. 136-142.
[6] S. Teboul, L. B. Féraud, G. Aubert, and M. Barlaud, "Variational
approach for edge-preserving regularization using coupled PDE-s," IEEE
Trans. Image Processing, vol.7, no.3, pp.387-397, Mar. 1998.
[7] J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving
interfaces in computational geometry, fluid mechanics, computer vision
and material science. Cambridge Univ. Press, 1999.
[8] T. F. Chan and L. A. Vese, "A Level Set Algorithm for Minimizing the
Mumford-Shah Functional in Image Processing," IEEE Comput. Soc.
Proc. of the First IEEE Workshop on Variational and Level Set Methods
in Computer Vision, pp. 161-168, 2001.
[9] T. F. Chan and L. A. Vese, "Active Contours without edges," IEEE
Transactions on Image Processing, vol. 10, no. 2, pp. 266-277, 2001.
[10] L. A. Vese and T. F. Chan, "A multiphase level set framework for image
segmentation using the Mumford and Shah model," International Journal
of Computer Vision, vol. 50, no. 3, pp. 271-293, 2002.
[11] J. Weickert, K. J. Zuiderveld, B. M. ter Haar Romeny, W. J. Niessen,
"Parallel implementations of AOS schemes: A fast way of nonlinear
diffusion filtering," in Proc. IEEE Conf. Image Processing, Mar.1997,
pp.396-399.
[12] A. Tsai, A. J. Yezzi, and A. S. Willsky, "Curve evolution implementation
of the Mumford-Sshah functional for image segmentation, denoising,
interpolation, and magnification," IEEE Trans. Image Processing, vol.10,
pp. 1169-1186, Aug. 2001.
[13] S. Osher and J. A. Sethian, "Fronts propagating with curvature
dependent speed: Algorithms based on hamilton-jacobi formulation,"
Journal of Computational Physics, vol. 79, pp. 12-49, 1988.
[14] S. Osher and R. Fedkiw, Level set methods and dynamic implicit surfaces,
New York, Springer-Verlag, 2003.
[15] S. Geman, and D. Geman, "Stochastic relaxation, Gibbs distribution and
the Bayesian restoration of images," IEEE Trans. Pattern Anal. Machine
Intell., vol. PAMI-6, pp.721-741, Nov. 1984.
[16] S. Geman and D. E. Mcclure, "Bayesian image analysis: An application to
single photon emission tomography," Proc. Stat. Comput. Sect.
Washington, DC: Amer. Stat. Assoc. pp. 12-18, 1985.
[17] S. Ji and H. Park, "Image segmentation of color image based on region
coherency," in Proceedings 1998 International Conference on Image
Processing, vol. 1, Chicago, IL, USA, pp. 80-83,1998.
[18] S. Kichenassamy, A. Kumar, P. Oliver, A. Tannenbaum, and A. Yezzi,
"Conformal curvature flows: from phase transitions to active vision,"
Archive for Rational Mech. and Anal., vol. 134, pp. 275-301, 1996.
[19] C. Xu and J. Prince, "Snakes, shapes, and gradient vector flow," IEEE
Transactions on Image Processing, vol. 7, pp. 359-369, March 1998.
[20] Choi, G. Kim, P. Park, G. Wang, and S. Kim, "Efficient PDE-based
segmentation algorithms and their application to CT images," Journal.
Korean Institute of Plant Engineering, pp. 1-17, 2003.
[21] J. Haddon and J. Boyce, "Image segmentation by unifying region and
boundary information," IEEE Transactions on Pattern Analysis and
Machine Intelligence, vol. 12, no. 10, pp. 929-948, 1990.
[22] K. Haris, S. Efstratiadis, N. Maglaveras, and A.Katsaggelos, "Hybeid
image segmentation using watersheds and fast region merging," IEEE
Transactions on Image Processing, vol. 7, no. 12, pp. 1684-1699, 1998.
[23] D. Marr and E. Hildreth, "Theory of edge detection," Proc. R. Soc. Lond.,
vol. B207, pp. 187-217, 1980.
[24] P. Hill, C. Canagarajah, and D. Bull, "Texture gradient based watershed
segmentation," IEEE International Conference on Acoustics, Speech, and
Signal Processing, vol. 4, Orlando, FL, USA, pp. 3381-3384,2002.