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In this paper, we present a complete and practical algorithm for the approximation of level-set-based curve evolution suitable for real-time implementation. In particular, we propose a two-cycle algorithm to approximate level-set-based curve evolution without the need of solving partial differential equations (PDEs). Our algorithm is applicable to a broad class of evolution speeds that can be viewed as composed of a data-dependent term and a curve smoothness regularization term. We achieve curve evolution corresponding to such evolution speeds by separating the evolution process into two different cycles: one cycle for the data-dependent term and a second cycle for the smoothness regularization. The smoothing term is derived from a Gaussian filtering process. In both cycles, the evolution is realized through a simple element switching mechanism between two linked lists, that implicitly represents the curve using an integer valued level-set function. By careful construction, all the key evolution steps require only integer operations. A consequence is that we obtain significant computation speedups compared to exact PDE-based approaches while obtaining excellent agreement with these methods for problems of practical engineering interest. In particular, the resulting algorithm is fast enough for use in real-time video processing applications, which we demonstrate through several image segmentation and video tracking experiments.