一种基于MQ拟插值的自适应边缘检测方法

摘要

MQ拟插值方法在进行微分方程数值解时具有精度高、稳定性好且节点移动灵活等特点.基于此提出一种使用MQ拟插值模拟几何活动轮廓模型(GAC)的自适应算法.将几何流表示为参数形式,首先在空间方向用MQ拟插值及其导数来逼近函数及其空间导数,然后通过节点移动方程移动节点使得节点几乎均匀分布在轮廓线上,最后在时间方向用向前差分法离散得到下一个时间层的函数逼近.该算法可使用较少的点达到较好的拟合效果,节省计算量,在进行具有大曲率大变化图像的边缘检测时更加精确、高效.最后给出几个实例,说明了该方法的有效性.%This paper proposes an adaptive method for simulating one kind of geometric active contours (GAC) applying multiquadric (MQ) quasi-interpolation. The geometric flow is presented in its parametric form. Then the numerical scheme is obtained: Firstly the spatial derivatives of each variable are approximated applying the MQ quasi-interpolation; secondly the knots are moved according to the moving knots equation to pull the knots to concentrate in regions with large variations. Thirdly the forward difference methods are applied to approximate the temporal derivative of each variable. The resulting scheme is simple, efficient and easy to implement. Also images with complex boundaries can be simulated more efficiently on the basis of the good properties of the adaptive MQ method. Several examples of applications are shown in the paper.