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Active contour and surface models, also known as deformable models, constitute a class of powerful segmentation techniques. Geometric deformable models implemented via level-set methods have advantages over parametric ones due to their intrinsic behavior, parameterization independence, and ease of implementation. However, a long claimed advantage of geometric deformable models, the ability to automatically handle topology changes, turns out to be a liability in applications where the objects to be segmented have a known topology that must be preserved. In this paper, we present a geometric deformable model that preserves topology using the simple point concept from digital topology. This algorithm maintains the other advantages of standard geometric deformable models including sub-pixel accuracy and production of nonintersecting curves (or surfaces). Several experiments on simulated and real data are provided to demonstrate the performance of the proposed algorithm.