摘要
按照Ｄａｕｂｅｃｈｉｅｓ的理论，对于规范正交小波基，它的正则性阶数是随其支集宽度线性增长的，本文的结果表明，如果放松正交性要求，则母小波可以同时具备局部支撑性和无限光滑性．文中给出了一类小波，它不像一般的正交小波基局部性和正则性是冲突的，相反，它既是局部支撑的，又是无限光滑的，其二维形式由某个径向函数的一阶或二阶导数构成，与目前常见的张量积高维小波不同，它是不可分的．同时也证明了此类小波是二进小波．因此，任意一个平方可积函数都可以由其二进小波变换来重构，且重构是稳定的．该二维二进小波对图像的小波变换及其相关的计算只依赖于几个整数点上的小波函数值，作为应用，给出了一类快速边缘检测算法，对于Ｎ×Ｎ图像，其计算复杂度为Ｏ（Ｎ２），优于Ｍａｌａｔ快速小波算法的Ｏ（Ｎ２ｌｏｇＮ）量阶．此外，实验结果也是令人满意的．该小波变换极易实现快速计算，故可用于计算机视觉及实时处理等领域，如快速边缘检测、特征提取及纹理分析等．
According to I.Daubechies' theory,the regularity of orthonormal wavelet bases with compact support increases linearly with the support width.By relaxing the orthogonality,much more freedom on the choice of wavelet function is gained.In this paper,an infinitely differentiable wavelet with a local support is proposed.Its properties are different from those of orthonormal wavelet bases.The wavelet is derived from the first or second order derivatives of a radial function.It is then proven that the wavelet is a two dimensional dyadic one.Consequently,an arbitrary square integrable function can be reconstructed from its dyadic wavelet transformation,and the reconstruction is stable.Different from tensor product multidimensional wavelets,this wavelet is inseparable.As an example of application,an algorithm is developed for detecting edges in image by finding the local maxima of its wavelet transform modulus.The computation of the wavelet transform in image processing depends only on the wavelet functional values at a few integer points. For a N×N image,the computational complexity of the detection scheme is O(N 2) ,which is significantly better than the order O(N 2 log N ) by using Mallat's fast wavelet algorithm. Numerical experiments indicate that the wavelet transform given here can be used in computer vision and real time processing, such as edge detection, feature extraction, and texture analysis.
出处
《计算机学报》
EI
CSCD
北大核心
1999年第3期269-274,共6页
Chinese Journal of Computers
基金
国家自然科学基金
国家杰出青年科学基金
西安交通大学研究生院博士学位论文基金
关键词
小波变换
边缘检测
图像处理
计算机视觉
Wavelets,fast wavelet transform,edge detection,image processing,computer vision.
