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Statistical Region Snake-Based Segmentation Adapted to Different Physical Noise Models
November 1999 (vol. 21 no. 11)
pp. 1145-1157

Abstract—Algorithms for object segmentation are crucial in many image processing applications. During past years, active contour models (snakes) have been widely used for finding the contours of objects. This segmentation strategy is classically edge-based in the sense that the snake is driven to fit the maximum of an edge map of the scene. In this paper, we propose a region snake approach and we determine fast algorithms for the segmentation of an object in an image. The algorithms developed in a Maximum Likelihood approach are based on the calculation of the statistics of the inner and the outer regions (defined by the snake). It has thus been possible to develop optimal algorithms adapted to the random fields which describe the gray levels in the input image if we assume that their probability density function family are known. We demonstrate that this approach is still efficient when no boundary's edge exists in the image. We also show that one can obtain fast algorithms by transforming the summations over a region, for the calculation of the statistics, into summations along the boundary of the region. Finally, we will provide numerical simulation results for different physical situations in order to illustrate the efficiency of this approach.

[1] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models,” International Journal of Computer Vision, vol. 1, pp. 321-331, 1988.
[2] L. D. Cohen,“On active contour models and balloons,” Computer Vision, Graphics, and Image Processing, vol. 53, No. 2, pp. 211-218, March 1991.
[3] D.J. Williams and M. Shah,“A fast algorithm for active contours and curvature estimation,” Computer Vision, Graphics, Image Processing, vol. 55, pp. 14-26, 1992.
[4] G.I. Chiou and J.-N. Hwang, A Neural Network-Based Stochastic Active Contour Model (nns-snake) for Contour Finding of Distinct Features IEEE Trans. Image Processing, vol. 4, pp. 1407-1416, 1995.
[5] C. Xu and J. Prince, Snakes, Shapes, and Gradient Vector Flow IEEE Trans. Image Processing, vol. 7, pp. 359-369, 1998.
[6] L.H. Staib and J.S. Duncan, “Boundary Finding with Parametrically Deformable Models,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 11, pp. 1,061-1,075, Nov. 1992.
[7] V. Caselles, R. Kimmel, and G. Sapiro, "Geodesic Active Contours," Proc. IEEE ICCV-95, pp. 694-699, 1995.
[8] R. Malladi, J. Sethian, and B.C. Vemuri, "Shape Modeling with Front Propagation: A Level Set Approach," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, pp. 158-175, 1995.
[9] Y. Amit, U. Grenander, and M. Piccioni, “Structural Image Restoration through Deformable Templates,” J. Am. Statistical Assoc., vol. 86, pp. 376-387, 1991.
[10] T. Cootes, A. Hill, C.J. Taylor, and J. Haslam, “Use of Active Models for Locating Structure in Medical Images,” Image and Vision Computing, vol. 12, pp. 355-365, 1994.
[11] C. Kervrann and F. Heitz, “A Hierarchical Statistical Framework for the Segmentation of Deformable Objects in Image Sequences,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 724-728, June 1994.
[12] T.F. Cootes, C.J. Taylor, D.H. Cooper, and J. Graham, "Active Shape Models—Their Training and Application," Computer Vision and Image Understanding, vol. 61, no. 1, pp. 38-59, Jan. 1995.
[13] R. Ronfard, “Region-Based Strategies for Active Contour Models,” Int'l J. Computer Vision, vol. 13, no. 2, 1994.
[14] G. Storvik, "A Bayesian approach to dynamic contours through stochastic sampling and simulated annealing," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 10, pp. 976-986, Oct. 1994
[15] A.K. Jain, Y. Zhong, and S. Lakshmanan, Object Matching Using Deformable Templates IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 3, pp. 267-278, Mar. 1996.
[16] M.T. de Figueiredo and J.M.N. Leitão, “Bayesian Estimation of Ventricular Contours in Angiographic Images,” IEEE Trans. Medical Imaging, vol. 11, 1992.
[17] O. Germain and P. Réfrégier, “Optimal Snake-Based Segmentation of a Random Luminance Target on a Spatially Disjoint Background,” Optical Letters, vol. 21, pp. 1,845-1,847, 1996.
[18] M.B. Jose Dias and M.N. Jose Leitao, “Wall Position and Thickness Estimation from Sequences of Echocardiographis Images,” IEEE Trans. Medical Imaging, vol. 15, pp. 25-38, 1996.
[19] P. Réfrégier, O. Germain, and T. Gaidon, “Optimal Snake Segmentation of Target and Background with Independent Gamma Density Probabilities, Application to Speckled and Preprocessed Images,” Optics Comm., vol. 137, pp. 382-388, 1997.
[20] M. Figueiredo, J. Leitão, and A.K. Jain, Adaptative Parametrically Deformable Contours Energy Minimization Methods in Computer Vision and Pattern Recognition, M. Pellilo and E. Hancock, eds., pp. 35-50, Springer-Verlag, 1997.
[21] A.L. Reno, D.F. Gillies, and D.M. Booth, “Deformable Models for Object Recognition in Aerial Images,” Proc. SPIE Conf. Automatic Target Recognition VIII, vol. 3,371, pp. 322-333, Orlando, Fla., 1998.
[22] C. Chesnaud and P. Réfrégier, “Optimal Snake Region-Based Segmentation for Different Physical Noise Model and Fast Algorithm Implementation, France,” Proc. First Int'l Symp. Physics in Signal and Image Processing, pp. 3-10, 1999.
[23] A. Azzalini, Statistical Inference—Based on the Likelihood. New York: Chapman and Hall, 1996.
[24] B.J. Slocumb and D.L. Syndner, “Maximum Likelihood Estimation Applied to Quantum Limited Optical Position Sensing,” Acquisition, Tracking, and Pointing IV, S. Gowrinathan, ed., SPIE, pp. 165-176, 1990.
[25] A.C. Bovik, On Detecting Eges in Speckle Imagery IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 36, no. 10, pp. 1618-1627, Oct. 1988.
[26] J.W. Goodman, “Laser Speckle and Related Phenomena,” Statistical Properties of Laser Speckle Patterns, pp. 9-75, Heidelberg: Springer-Verlag, 1975.
[27] C.J. Oliver, I. McConnell, D. Blacknell, and R.G. White, “Optimum Ddge Detection in SAR,” Proc. Conf. Satellite Remote Sensing, pp. 152-163, Paris, 1995.
[28] O. Germain and P. Réfrégier, “Edge Detection and Localisation in SAR Images: A Comparative Study of Global Filtering and Active Contour Approaches,” Proc. EurOpto Conf. Image and Signal Processing for Remote Sensing, pp. 111-121, Barcelona, 1998.
[29] C. Chesnaud, V. Pagé, and P. Réfrégier, “Robustness Improvement of the Statistically Independent Region Snake-Based Segmentation Method,” Optical Letters, vol. 23, pp. 488-490, 1998.
[30] C.P. Robert, The Bayesian Choice—A Decision-Theoretic Motivation. New York: Springer-Verlag, 1996.

Index Terms:
Image processing, statistical theory of estimation, segmentation, active contour.
Christophe Chesnaud, Philippe Réfrégier, Vlady Boulet, "Statistical Region Snake-Based Segmentation Adapted to Different Physical Noise Models," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 11, pp. 1145-1157, Nov. 1999, doi:10.1109/34.809108
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