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A different contour search algorithm is presented in this paper that provides a faster convergence to the object contours than both the greedy snake algorithm (GSA) and the fast greedy snake (FGSA) algorithm. This new algorithm performs the search in an alternate skipping way between the even and odd nodes (snaxels) of a snake with different step sizes such that the snake moves to a likely local minimum in a twisting way. The alternative step sizes are adjusted so that the snake is less likely to be trapped at a pseudo-local minimum. The iteration process is based on a coarse-to-fine approach to improve the convergence. The proposed algorithm is compared with the FGSA algorithm that employs two alternating search patterns without altering the search step size. The algorithm is also applied in conjunction with the subband decomposition to extract face profiles in a hierarchical way.