This Article 
 Bibliographic References 
 Add to: 
A Bayesian Approach to Dynamic Contours Through Stochastic Sampling and Simulated Annealing
October 1994 (vol. 16 no. 10)
pp. 976-986

In many applications of image analysis, simply connected objects are to be located in noisy images. During the last 5-6 years active contour models have become popular for finding the contours of such objects. Connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations. These approaches do however have several disadvantages. The numerical algorithms that are in use constrain the models that can be used. Furthermore, in many cases only local minima can be achieved. In this paper, the author discusses a method for curve detection based on a fully Bayesian approach. A model for image contours which allows the number of nodes on the contours to vary is introduced. Iterative algorithms based on stochastic sampling is constructed, which make it possible to simulate samples from the posterior distribution, making estimates and uncertainty measures of specific quantities available. Further, simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented. In theory, no restrictions on the models are made. In practice, however, computational aspects must be taken into consideration when choosing the models. Much more general models than the one used for active contours may however be applied. The approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain, and show promising results.

[1] A. A. Amini, S. Tehrani, and T. E. Weymouth, "Using dynamic programming for minimizing the energy of active contours in the presence of hard constraints," inProc. Second Int. Conf. Computer Vision, Tarpon Springs, FL, Dec. 1988, pp. 95-99.
[2] A. A. Amini, T. E. Weymouth, and R. C. Jain, "Using dynamic programming for solving variational problems in vision,"IEEE Trans. Pattern Anal. Machine Intell., vol. 12, no. 9, pp. 855-867, 1990.
[3] J. Besag, "Towards Bayesian image analysis,"J. Anal. Statist., vol. 16, no. 3, pp. 395-407, 1989.
[4] O. Cantoni, "Rough large deviation estimates for simulated annealing: Application to exponential schedules,"Ann. Probab., vol. 20, no. 3, pp. 1109-1146, 1992.
[5] I. Cohen, L. D. Cohen, and N. Ayache, "Using deformable surfaces to segment 3-D images and infer differential structures,"CVGIP: Image understanding, vol. 56, no. 2, pp. 242-263, 1992.
[6] T. E. Dufresne and A. P. Dhawan, "A structured approach to edge clustering and extrapolation," inIEEE Int. Conf. on Systems Engineering, Fairborn: OH, Aug. 1991, pp. 262-65.
[7] N. Friedland and D. Adam, "Automatic cavity boundary detection from sequential ultrasound images using simulated annealing,"IEEE Trans. Med. Imaging, vol. 8, pp. 344-353, 1989.
[8] A. E. Gelfand and A. F. M. Smith, "Sampling-based approaches to calculating marginal densities,"J. Amer. Statist. Assoc., vol. 85, no. 410, pp. 398-409, 1990.
[9] S. Geman and D. Geman, "Stochastic relaxation, Gibbs distribution, and Bayesian restoration of images,"IEEE Trans. Pattern Anal. Machine Intell., vol. 6, no. 6, pp. 721-741, 1984.
[10] B. Hajek, "Cooling schedules for optimal annealing,"Math. Oper. Res., vol. 13, no. 2, pp. 311-329, May 1988.
[11] W. K. Hastings, "Monte Carlo sampling methods using Markov chains and their applications,"Biometrika, vol. 57, no. 1, pp. 97-109, 1970.
[12] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models,"Int. J. Comput. Vision, vol. 1, no. 4, pp. 321-331, 1988.
[13] F. Leitner, I. Marque, S. Lavallée, and P. Cinquin, "Dynamic segmentation: Finding the edge with snake splines," inCurves and Surfaces, P. J. Laurent, A. Le Méhauté, and L. Schumaker, Eds. Boston, MA: Academic Press, 1991, pp. 279-284.
[14] A. Lundervold and G. Storvik, "Brain tissue and csf segmentation in multispectral MRI," submitted to theIEEE Trans. Medical Imaging, 1994.
[15] A. Lundervold and T. Taxt, "Automatic detection of left ventricular cardiac boundary," inNOBIM Conf., Tromsø, May 1990.
[16] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, "Equations of state calculations by fast computing machines,"J. Chem. Phys., vol. 21, pp. 1087-1092, 1953.
[17] E. Persoon and K. S. Fu, "Shape discrimination using Fourier descriptors,"IEEE Trans. Syst., Man. Cybern., vol. 7, pp. 171-179, 1977.
[18] B. D. R. Ripley,Stochastic Simulation. New York: Wiley, 1987.
[19] G. Storvik, "A Bayesian approach to dynamic contours through stochastic sampling and simulated annealing," Tech. Rep. 1, Inst. of Math., Univ. of Oslo, 1994.
[20] G. Storvik and A. Lundervold, "Segmentation of brain parenchyma and CSF in multispectral MR images of the head," in8th SCIA Conf., May 1993.
[21] G. Storvik and P. Switzer, "Space-time modeling of simply connected objects: An application to detection of left ventricular cardiac boundaries from ultrasound images," inInterface'92, TX, Mar. 1992.
[22] H. L. Tan, S. B. Gelfand, and E. J. Delp, "A cost minimisation approach to edge detection using simulated annealing,"IEEE Trans. Pattern Anal. Machine Intell., vol. 14, no. 1, pp. 3-17, 1991.
[23] V. Venkateswar and R. Chellappa, "Extraction of straight lines in aerial images,"IEEE Trans. Pattern Anal. Machine Intell., vol. 14, no. 11, pp. 1111-1114, 1992.
[24] D. J. Williams and M. Shah, "A fast algorithm for active contours and curvature estimation,"CVGIP: Image understanding, vol. 55, no. 1, pp. 14-26, 1992.
[25] C. T. Zahn and R. Z. Roskies, "Fourier descriptors for plane closed contour,"IEEE Trans. Comput., vol. C-21, pp. 269-281, 1972.

Index Terms:
simulated annealing; Bayes methods; iterative methods; biomedical NMR; brain; biomedical ultrasonics; cardiology; Bayesian approach; dynamic contours; stochastic sampling; simulated annealing; image analysis; simply connected objects; noisy images; active contour models; iterative algorithms; minimizing energy curves; numerical algorithms; local minima; curve detection; image contours; posterior distribution; uncertainty measures; global minimum energy configuration; ultrasound images; left ventricle; magnetic resonance images; human brain
G. Storvik, "A Bayesian Approach to Dynamic Contours Through Stochastic Sampling and Simulated Annealing," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 10, pp. 976-986, Oct. 1994, doi:10.1109/34.329011
Usage of this product signifies your acceptance of the Terms of Use.