基于角度滤波的平面图形光顺算法

基于角度滤波的思想给出了一有效的平面图形光顺算法.离散曲线伸缩内在量表示中的有向转角既整体反映了曲线的走向及弯曲程度,又局部反映了曲线的光滑程度,对其借用图像去噪算法中双边滤波的思想进行光滑,然后利用光滑之后的伸缩内在量来重构曲线.其中曲线的重构转化为一个稀疏线性方程组的求解,可以由现成的程序库快速求解,重构过程中还可以加入一些线性约束来满足实际应用中的不同要求.该方法很容易推广得到对平面树状图形和三角网格图形的去噪算法.该算法是线性的,复杂度低,而且大量实例都表明,该方法可以得到较好的去噪效果,既能避免去噪过程中经常出现的收缩现象,又能较好地保持原曲线的形状．

Angle-filtering based smoothing algorithm for planar graphs

For a noisy discrete curve, the orientation angles of scaling invariant intrinsic variables reflect its bended degree. So first the orientation angle sequence of original curve is filtered by bilateral filtering method. Then the vertex coordinates of the smoothed curve are reconstructed by the filtered scaling invariant variables. The reconstruction of the smoothed curve is formulated as a sparse linear system, which can be easily solved by some solver library. Furthermore, the different requests in practical applications can be satisfied by adding linear constraints in the linear system. This method can  be easily generalized to the planar tree graph and triangular mesh. The proposed approach is simple and fast and can obtain satisfied results by presenting some experimental examples, not only avoiding shrinkage, but also preserving the features of the original curve．