基于样条修匀公式的图像边缘检测

Edge Detection Based on a B Spline Smoothing Formula

本文给出了一类基于Ｂ样条修匀公式的图像边缘检测算子，其过程是先利用等距Ｂ样条函数对图像｛ｆ（ｉ，ｊ）｝Ｎ－１ｉ，ｊ＝０做一个全息光滑曲面公式，进一步利用Ｂ样条函数的局部支撑性质导出，该曲面公式可以严格地局限于每点的某变邻域内计算，即Ｓ（ｘ，ｙ）＝∑（ｉ，ｊ）∈Ｎｋ，ｌ（ｘ，ｙ）ｆ（ｉ，ｊ）Ωｋ（ｘ－ｉ）Ωｌ（ｙ－ｊ）该曲面既有足够的光滑性，又有良好的保凸性；然后，基于这个光滑曲面Ｓ（ｘ，ｙ），再通过求｜Ｓ｜的局部极大值点或求２Ｓ的零交叉来检测边缘．数值实验表明，这是一类十分成功的边缘检测算法，它简捷、可靠，便于实时处理，如可用于计算机视觉系统中的特征提取、图像分割、纹理分析等．

In this paper,an edge detector based on a B spline smoothing formula of image is proposed.Firstly,a smoothing surface with perfect information of the digital image is presented by using the uniform B spline function.Since the B spline is a locally supported function,the smoothing formula can be strictly limited in some neighborhood of a point,i.e., S(x,y)=∑(i,j)∈N k,l (x,y)f(i,j)Ω k(x-i)Ω l(y-j) The surface is smooth,and it has the same convexity as that of the original image.secondly,the edge point is detected by either computing the local extreme of the directional derivative or computing zero crossing of the second order directional derivative of the smoothing surface.Finally,and example of the detector performance is given.The numerical experiment suggests that our detection scheme may be used in computer vision,such as feature extraction,segmentation of image,and texture synthesis.