基于Franklin函数的数字曲线多边形逼近

摘要

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.%针对数字曲线多边形逼近中存在计算复杂度高、容易受噪声影响等问题,提出一种基于Franklin函数系的数字曲线多边形逼近算法.通过对原始数字曲线在Franklin函数系下进行正交分解,选取少量较大的、反映了原始数字曲线主要特征的分解系数进行重构,所得结果即为数字曲线的逼近多边形.实例结果表明,该算法计算复杂度低、对噪声有较强的鲁棒性,不仅可以实现对原始数字曲线的多层次的最佳平方逼近,而且还保留了原始数字曲线的整体特征.