基于内在表示的空间曲线去噪算法

An Intrinsic 3D Discrete Curve Smoothing Algorithm

介绍了一种对空间离散曲线进行去噪声的新的方法。不同于一般的顶点表示方法,这里对离散曲线采用一种新的内在表示方法,用曲线的内在几何量——边长和边与x轴正方向、z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轴正方向、z轴正方向夹角进行去噪声。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。该方法的优点主要在于解决了去噪声方法中一般都会产生的收缩问题,并且能够保持基本的特征。

In this paper, we propose a new method for 3D discrete curve smoothing by adopting an intrinsic representation for discrete curves. With this representation, a piecewise 3D curve is defined by lengths of edges, angles between edges and the positive x-axis, and angles between edges and the positive z-axis. For a noisy curve, we first filter the two angle sequences of the curve by bilateral filtering method. Then, we obtain the smoothed vertexes of the curve by solving an objective function under the constraint of the two angle sequences. By this algorithm, not only can main features of the original curve be preserved well, but also the smoothed curve no longer suffers from shrinkage.