In this paper, we present a novel non-parametric polygonal approximation algorithm for planar curves. The proposed algorithm first selects all the breakpoints on the contour. From this set, a smaller set of high curvature points, cut-points, are obtained. An optimization procedure adaptively finds the best fitting polygonal approximation. Our algorithm adaptively locates segments of the contour with different levels of details. The proposed algorithm follows the contour more closely where the level of details on the curve is high. Experimental results demonstrate that the proposed algorithm is robust for noisy, real-life contours and compares favorably with other algorithms.