Abstract: A novel algorithm based on Franklin function is proposed to improve complexity and robustness in digital curve approximation.The original digital curve is projected orthogonally on the Franklin functions system,and a few of large scale decomposition coefficients are selected to reconstruct a piecewise linear approximation polygon,which can reflect important features of original digital curve.The experimental results show that the proposed algorithm is of low complexity and robust to noise.The method achieves not only the best square approximation to the original digital curve hierarchically,but also inherits the global features of the original curve.