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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