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Watersnakes: Energy-Driven Watershed Segmentation
March 2003 (vol. 25 no. 3)
pp. 330-342

Abstract—The watershed algorithm from mathematical morphology is powerful for segmentation. However, it does not allow incorporation of a priori information as segmentation methods that are based on energy minimization. In particular, there is no control of the smoothness of the segmentation result. In this paper, we show how to represent watershed segmentation as an energy minimization problem using the distance-based definition of the watershed line. A priori considerations about smoothness can then be imposed by adding the contour length to the energy function. This leads to a new segmentation method called watersnakes, integrating the strengths of watershed segmentation and energy based segmentation. Experimental results show that, when the original watershed segmentation has noisy boundaries or wrong limbs attached to the object of interest, the proposed method overcomes those drawbacks and yields a better segmentation.

[1] D. Mumford and J. Shah, “Optimal Approximation by Piecewise Smooth Functions and Associated Variational Problems,” Comm. Pure and Applied Math., vol. 42, pp. 577-684, 1989.
[2] S.C. Zhu and A. Yuille, “Region Competition: Unifying Snakes, Region Growing and Bayes/MDL for Multiband Image Segmentation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, pp. 884-900, 1996.
[3] Y.G. Leclerc, “Constructing Simple Stable Descriptions for Image Partitioning,” Int'l J. Computer Vision, vol. 3, no. 1, pp. 73-102, 1989.
[4] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models,” Int'l J. Computer Vision, vol. 1, no. 4, pp. 321-331, 1987.
[5] V. Caselles, R. Kimmel, and G. Sapiro, “Geodesic Active Contours,” Int'l J. Computer Vision, vol. 22, no. 1, pp. 61-79, 1997.
[6] S. Osher and J.A. Sethian, “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” J. Computing in Physics, vol. 79, pp. 12-49, 1988.
[7] H. Tek and B.B. Kimia, Image Segmentation by Reaction-Diffusion Bubbles Proc. Int'l Conf. Computer Vision, pp. 156-162, 1995.
[8] S. Geman and D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721-741, Nov. 1984.
[9] S. Beucher and F. Meyer, “The Morphological Approach of Segmentation: The Watershed Transformation,” Mathematical Morphology in Image Processing, E. Dougherty, ed., chapter 12, pp. 43-481, New York: Marcel Dekker, 1992.
[10] L. Vincent and P. Soille, "Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, pp. 583-598, 1991.
[11] F. Meyer and S. Beucher, “Morphological Segmentation,” J. Visual Comm. and Image Representation, vol. 1, no. 1, pp. 21-46, Sept. 1990.
[12] P. Salembier, “Morphological Multiscale Segmentation for Image Coding,” Signal Processing, vol. 38, no. 3, pp. 359-386, Sept. 1994.
[13] L. Najman and M. Schmitt, “Watershed for a Continuous Function,” Signal Processing, vol. 38, no. 1, pp. 99-112, July 1994.
[14] L. Najman and M. Schmitt, “Geodesic Saliency of Watershed Contours and Hierarchical Segmentation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 12, pp. 1163-1173, Dec. 1996.
[15] F. Meyer, “Topographic Distance and Watershed Lines,” Signal Processing, vol. 38, no. 1, pp. 113-125, July 1994.
[16] F. Preteux, “On a Distance Function Approach for Gray-Level Mathematical Morphology,” Mathematical Morphology in Image Processing, E. Dougherty, ed., pp. 323-350, New York: Marcel Dekker, 1992.
[17] G. Borgefors, “Distance Transforms in Digital Images,” Computer Vision, Graphics, and Image Processing, vol. 34, pp. 344-371, 1986.
[18] H.T. Nguyen, M. Worring, and R. van den Boomgaard, “Watersnakes: Energy-Driven Watershed Segmentation,” Technical Report 12, Intelligent Sensory Information Systems Group, Univ. of Amsterdam, 2000, available athttp://www.science.uva.nl/research/reports-isis/ 2000ISISreport12.ps.
[19] J. Serra, Image Analysis and Mathematical Morphology. New York: Academic Press, 1982.
[20] P.L. Lions, Generalized Solutions of Hamilton-Jacobi Equations. Boston: Pitman, 1982.
[21] P.L. Lions, E. Rouy, and A. Tourin, “Shape-from-Shading, Viscosity Solutions and Edges,” Numerische Mathematik, vol. 64, pp. 323-353, 1993.
[22] A.D. Jepson and M. Black, “Mixture Models for Optical Flow Computation,” Proc. Computer Vision and Pattern Recognition, pp. 760-761, June 1993.
[23] F. Meyer, “Flooding and Segmentation,” Mathematical Morphology and Its Application to Image and Signal Processing, J. Goutsias, L. Vincent, and D.S. Bloomberg, eds., pp. 189-198, Kluwer, 2000.
[24] P. Maragos and M.A. Butt, “Advances in Differential Morphology: Image Segmentation via Eikonal PDE and Curve Evolution and Reconstruction via Constrained Dilation Flow,” Mathematical Morphology and Its Application to Image and Signal Processing, H. Heijmans and J. Roerdink, eds., pp. 167-174, 1998.
[25] D.G. Lowe, “Organization of Smooth Image Curves at Multiple Scales,” Proc. Int'l Conf. Computer Vision, pp. 558-567, 1988.
[26] M. Pardas and P. Salembier, “Time-Recursive Segmentation of Image Sequences,” Proc. European Assoc. Signal, Speech, and Image Processing, pp. 18-21, 1994.
[27] B. Marcotegui and F. Meyer, “Bottom Up Segmentation of Image Sequences for Coding,” Annals of Telecommunications, vol. 52, no. 7-8, pp. 397-407, 1997.
[28] P.B. Chou and C.M. Brown, “The Theory and Practice of Bayesian Image Labeling,” Int'l J. Computer Vision, vol. 4, no. 3, pp. 185-210, 1990.
[29] R. Adams and L. Bischof, “Seeded Region Growing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 6, pp. 641-647, June 1994.
[30] L. Vincent, “Morphological Gray Scale Reconstruction in Image Analysis: Applications and Efficient Algorithms,” IEEE Trans. Image Processing, vol. 2, pp. 176-201, 1993.

Index Terms:
Watershed segmentation, energy-based segmentation, topographical distance, snakes.
Citation:
Hieu Tat Nguyen, Marcel Worring, Rein van den Boomgaard, "Watersnakes: Energy-Driven Watershed Segmentation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 3, pp. 330-342, March 2003, doi:10.1109/TPAMI.2003.1182096
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