一种小波滤波器的构造与多尺度边缘检测

The Construction of a Wavelet Filter and Multiscale Edge Detection

Marr曾经指出,人的视觉对于影像的描述具有多尺度的特性。论文基于这一思想,从二维平滑函数出发,并根据尺度呈级数变化的特点,导出了一组多尺度小波滤波器。该滤波器低通响应关于原点对称,高通响应关于原点反对称,而且截断误差很小,具有近似的紧支撑性和平滑性。同时给出了9组滤波器响应系数,可以实现由粗到精的特征提取,为影像的多尺度边缘检测提供了有用的工具。另一方面,影像经过该滤波器处理后,利用小波变换系数模的局部极大值来提取图像的边缘特征,不仅能够有效地抑制噪声,而且能够以子象素精度确定边缘的位置。最后,利用该滤波器对建筑物遥感影像进行了边缘检测试验,获得了良好的结果,为遥感影像建筑物边缘的自动提取打下了基础。

Marr has pointed out that describing images in human vision has multiresolution characteristics.According to the peculiarity that the scale exhibit progressional variety,this paper deduces a group of multiscale wavelet filter from two dimensions smooth function.The lowpass impulse response of the filter is symmetric at origin,the hignpass response of the filter is anti -symmetric at origin,and the truncation error is very small.They have the characteristics of approximation compact support and smoothness.Meanwhile nine group of filter response coefficient are given to realize the feature extraction from coarse to fine,and provide a useful tools for multiscale edge detection.On the other hand,Detecting the modulus maximum of the wavelet transformation coefficient to acquire the image edge feature after image processing by using the filter.The method not only effectively reduces noise,but also gets the edge position at sub-pixel precision.Finally,the effectiveness of the method is tested,which provides a fundamental basis for automatic extracting the building on remote sensing image.