离散曲线去噪的内在算法

An Intrinsic Algorithm for Discrete Curve Smoothing

对离散曲线采用一种内在表示方法,用曲线的内在几何量———边长和边与x轴正方向的夹角来表示点的位置.利用双边滤波的思想,对边与x轴夹角进行去噪声;然后以去噪后的角度作为一个约束条件,构造目标函数来反求曲线的顶点.该方法主要在于解决了去噪声方法中一般都会产生的收缩问题,并且能够保持曲线的基本特征.

In this paper we propose a new algorithm for curve smoothing by adopting an intrinsic representation for discrete curves. By this representation, a piecewise linear curve is defined by lengths of edges and angles between edges and the positive direction of x-axis. For a noisy curve, we first filter the angle sequence of the curve by bilateral filtering method. Then, we obtain the smoothed vertexes for the curve by solving an objective function under the constraint of the filtered angles. By this algorithm, not only can main features of the original curve be preserved well, but also the smoothed curve no longer suffer from shrinkage.