二维图象中二阶导数滤波器边缘定位误差的理论分析

本文从理论上讨论了低通滤波后二维图象中弯曲边缘的定位误差问题.边缘位置通常由二阶导数算子的零交叉点定义.研究表明:梯度方向上的二阶导数算子(secondderivativein gradient direction SDGD)产生向心的、可预测的边缘偏移;而线性拉普拉斯算子(Laplacian Operator)产生相反方向(离心)的可预测位置偏移.由此可推断:两者之和——称之为PLUS,将产生比其组成成份(SDGD 和 Laplace)更为精确的边缘定位算子.文章讨论了常用的低通滤波器(如 Gaussian 滤波器及 Tepee 滤波器)对边缘定位精度的影响.

THEORETICAL ANALYSIS OF THE ERROR OF EDGE LOCALIZATION IN 2-D IMAGE BY SECOND DERIVATIVE FILTERS

In this paper,the location error of curved edges in two dimensional images after low-pass filtering is studied theoretically.A commonly used definition of edge location is the zero crossing of a second derivative operator.It is shown that a second derivative in gradient direction (SDGD) gives a predictable bias in edge location towards the center of the curvature while a linear Laplace filter produces a shift in opposite direction.So we can deduce that the sum of above two high-pass filters, which is called PLUS (PLUS=Laplace+SDGD),results in an edge detector that finds curved edges more accurate than its constituents.The influence of commonly used low-pass filters,such as Gaussian filter and Tepee filter,is studied.