This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
September 1996 (vol. 18 no. 9)
pp. 884-900

Abstract—We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and combines aspects of snakes/balloons and region growing. Indeed the classic snakes/balloons and region growing algorithms can be directly derived from our approach. We provide theoretical analysis of region competition including accuracy of boundary location, criteria for initial conditions, and the relationship to edge detection using filters. It is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images, color images and texture images. The novel color model allows us to eliminate intensity gradients and shadows, thereby obtaining segmentation based on the albedos of objects. It also helps detect highlight regions.

[1] R. Adams and L. Bischof, “Seeded Region Growing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 6, pp. 641-647, June 1994.
[2] J.R. Beveridge et al., "Segmenting Images Using Localizing Histograms and Region Merging," Int'l J. Compt. Vision, vol. 2, 1989.
[3] A. Blake and A. Zisserman, Visual Reconstruction. MIT Press, 1987.
[4] J. Canny, “A Computational Approach to Edge Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 679-698, June 1986.
[5] A. Chakraborty, L.H. Staib, and J.S. Duncan, "Deformable boundary finding influenced by region homogeneity," Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR),Seattle, pp. 624-627, June 1994.
[6] L.D. Cohen and I. Cohen, "A Finite Element Method Applied to New Active Contour Models and 3D Reconstruction From Cross Sections," Proc. Third Int'l Conf. Computer Vision ICCV90,Osaka, Japan, 1990.
[7] L. D. Cohen,“On active contour models and balloons,” Computer Vision, Graphics, and Image Processing, vol. 53, No. 2, pp. 211-218, March 1991.
[8] K. Fukunaga, Introduction to Statistical Pattern Recognition, second edition. Academic Press, 1990.
[9] D. Geiger and A. Yuille, "A Common Framework for Image Segmentation," Int'l J. Computer Vision, vol. 6, pp. 227-243, 1991.
[10] S. Geman and D. Geman, "Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, pp. 721-741, 1984.
[11] D. Geman,S. Geman,C. Graffigne,, and P. Dong,“Boundary detection by constrained optimization,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 609-628, July 1990.
[12] M. Grayson, "The Heat Equation Shrinking Convex Plane Curves," J. Differential Geometry, vol. 23, pp. 285-314, 1987.
[13] M.D. Greenberg, Foundations of Applied Mathematics.Englewood Cliffs, N.J.: Prentice Hall, 1978.
[14] R.J. Hathaway, "Another Interpretation for the EM Algorithm for Mixture Distributions," Stat. Prob. Lett., vol. 4, pp. 53-56, 1986.
[15] G. Healey,“Segmenting images using normalized color,” IEEE Trans. Systems, Man, and Cybernetics, vol. 22, pp. 64-73, Jan. 1992.
[16] T.H. Hong and A. Rosenfeld, "Compact Region Extraction Using Weighted Pixel Linking in a Pyramid," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 2, pp. 222-229, Mar. 1984.
[17] R.A. Johnson and D.W. Wichern,Applied multivariate statistical analysis, Prentice Hall, 1988.
[18] T. Kanungo, B. Dom, W. Niblack, and D. Steele, "A Fast Algorithm for MDL-Based Multi-Band Image Segmentation," Proc. Comp. Vision and Patt. Recognition, CVPR, 1994.
[19] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active Contour Models," Proc. Int'l Conf. Computer Vision, ICCV87,London, 1987.
[20] K. Keeler, "Map Representations and Coding-Based Priors for Segmentation," IEEE Conf. Computer Vision and Pattern Recognition, pp. 420-425, 1991.
[21] G. Klinker, S. Shafer, and T. Kanade, “A Physical Approach to Color Image Understanding,” Int'l J. Computer Vision, vol. 4, pp. 7-38, 1990.
[22] G. Koepfler, C. Lopez, and J.-M. Morel, “A Multiscale Algorithm for Image Segmentation by Variational Method,” SIAM J. Numerical Analysis, vol. 31, pp. 282-299, 1994.
[23] Y.G. Leclerc, "Constructing Simple Stable Descriptions for Image Partitioning," Int'l J. Computer Vision, vol. 3, pp. 73-102, 1989.
[24] Y.G. Leclerc, "Region Growing Using the MDL Principle," DARPA Image Understanding Workshop, 1990.
[25] H.C. Lee, E.J. Breneman, and C.P. Schulte, Modeling Light Reflection for Computer Color Vision IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, pp. 402-409, 1990.
[26] A. Leonardis, A. Gupta, and R. Bajcsy, “Segmentation of Range Images as the Search for Geometric Parametric Models,” Int'l J. Computer Vision, vol. 14, no. 3, pp. 253-277, 1995.
[27] J.-M. Morel and S. Solimini, Variational Methods in Image Segmentation. Birkhäuser, 1995.
[28] D. Mumford and J. Shah, "Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems," Comm. Pure Appl. Math., vol. 42, pp. 577-684, 1989.
[29] A.P. Pentland,“Automatic extraction of deformable part models,” Int’l J. Computer Vision, vol. 4, pp. 107-126, 1990.
[30] J. Rissanen, "Modelling by Shortest Data Description," Automatica, vol. 14, pp. 465-471, 1978.
[31] J. Rissanen, Stochastic Complexity in Statistical Inquiry. World Scientific Series in Computer Science, vol. 15, 1989.
[32] R. Ronfard, “Region-Based Strategies for Active Contour Models,” Int'l J. Computer Vision, vol. 13, no. 2, 1994.
[33] T.-Y. Philips, A. Rosenfeld, and A.C. Sher, "O(log n) Bimodality Analysis," Pattern Recognition, vol. 22, pp. 741-746, 1989.
[34] K.-K. Sung, "A Vector Signal Processing Approach to Color," MIT Artificial Intelligence Laboratory, Technical Report 1349, 1992.
[35] Y. Wang, "Existence and Regularity of Solutions to a Variational Problem of Mumford and Shah," SIAM J. Optimization, 1991.
[36] R. Wilson and G. Granlund, "The Uncertainty Principle in Image Processing," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 6, Nov. 1984.
[37] G. Xu, E. Segawa, and S. Tsuji, "Robust Active Contours With Insensitive Parameters," Pattern Recognition, vol. 27, no. 7, pp. 879-884, 1994.
[38] S.C. Zhu and A.L. Yuille, “FORMS: A Flexible Object Recognition and Modeling System,” Int'l J. Computer Vision, vol. 20, no. 3, Dec. 1996
[39] S.C. Zhu, Y. Wu, and D. Mumford, “Filters, Random Fields and Maximum Entropy (FRAME)—Towards a Unified Theory for Texture Modeling,” Int'l J. Computer Vision, vol. 27, no. 2, 1998.
[40] S.C. Zhu and D.B. Mumford, "Learning and Sampling the Prior Distribution for Visual Computation," Harvard Robotics Laboratory Technical Report 95-3, 1995.
[41] S.C. Zhu and A.L. Yuille, "A Unified Theory for Image Segmentation: Region Competition and Its Analysis," Harvard Robotics Laboratory Technical Report 95-7, 1995.

Index Terms:
Image segmentation, region growing, snakes, minimum description length, Bayes statistics, uncertainty principle, color model.
Citation:
Song Chun Zhu, Alan Yuille, "Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 9, pp. 884-900, Sept. 1996, doi:10.1109/34.537343
Usage of this product signifies your acceptance of the Terms of Use.