基于广义B样条滤波器的图像边缘检测

Image Edge Detection by Generalized B Spline Filter

为了更准确有效地提取图像边缘,提出一种基于广义B样条数字滤波器的边缘检测算法.首先由线性微分方程推导出广义B样条的一般形式.其后,利用广义B样条函数组建了边缘检测微分算子模板,该模板继承了广义B样条尺度因子α,通过调节α,可以改变边缘算子滤波器的幅值特性和带通特性,进而获得边缘表征的最佳效果.而后,结合变分公式和广义B样条函数构造广义B样条光滑滤波器,该滤波器实现了在光滑滤波意义下的直接样条变换,与边缘检测模板算子配合使用可提高边缘检测的抗噪能力.实验证明:该边缘检测算法能有效地检测出图像边缘,无论是边缘提取效果还是抗干扰能力都优于传统的差分算子.

A new edge detection algorithm based on generalized B spline filter is proposed to extract image edge more effectively.First,generalized B spline is deduced from linear derivative equation.Based on generalized B spline,a difference template operator for edge detection is constructed,which inherits the scale factor of generalized B spline,and achieves different amplitude characteristic and band-pass property with different scale factor.Therefore,best edge result can be obtained by adjusting the scale.Thereafter,by combination with generalized B spline function and variational principle,generalized B spline smoothing filter is constructed,which realizes the direct spline transform in the sense of smoothing filtering,and improves the anti-noise ability of edge detection in conjunction with edge detection template operator.Experiments indicate this algorithm can extract target edge reliably,whether its extraction effect or anti-noise capacity are superior to conventional differential operator.