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The geodesic active contour is a recent geometric approach for image segmentation, which is motivated by previous snake and geometric models. Segmentation in this model is performed by a dynamic curve which minimizes several internal and external forces. These forces smooth the curve and attract it to the boundaries of objects. The conventional framework for computing geodesic active contours is the level-set method, where the evolving contour is represented as a levelset of a surface. This gives a stable solution, which naturally handles segmentation of several objects in one image. To overcome the relatively high computational requirements of this approach, an implicit formulation is proposed, which reduces the required number of timesteps drastically. An efficient adaptive multigrid algorithm is developed and implemented for the solution of the resulting nonlinear system.