【vfp开源代码栏目提醒】:网学会员为广大网友收集整理了,加窗傅立叶变换 - 讲义教程,希望对大家有所帮助!
Gabor 变换属于加窗傅立叶变换,Gabor 函数可以在频域不同尺度、不同方向上提取相关的特征。
另外 Gabor 函数与人眼的生物作用相仿,所以经常用作纹理识别上,并取得了较好的效果。
傅立叶变换---》加窗傅立叶变换(处理信号的局部特性)Gabor 是所有加窗傅立叶变换中能使时频分辨率的乘积最大的形式是 Gauss 函数的形式【 在 xiaoxiaozhu 的大作中提到: 】:: Gabor 变换是一种时频分析工具,早先人们意识到传统的傅立叶分析,: 提供了非常准确的频域特性,频域的分辨率无穷,但是没有时域分辨率,: 也就是说,傅立叶分析,要使用信号时域所有的值,来得到精确的信号频谱;:: 后来人们需要一种既能提供频域分辨率又能提供时域分辨率的分析方法,它: 可以给出“一段”时域信号的频谱信息,: 这样首先产生了傅立叶分析的变种 gabor 变换,它是一种加窗的傅立叶变换,: 它用分析窗提取要分析的一段信号,然后作傅立叶变换,得到这段我们感兴趣: 信号的频谱特性!:: gabor 变换有两大缺点:: 1) 由于其核函数的限制,无论如何离散化,都得不到一组正交基。
: 2) 变换窗的时宽和频宽都固定,不能跟随信号变化的特性。
:: 而后来的小波变换,则克服了以上两个缺点,: 提供了时频分辨率都可随信号特性变化的分析方法。
matlab 下 gabor 滤波算法可以提取图象纹理特征VERSION 1The Gabor filter is basically a Gaussian with variances sx and sy along x and y-axesrespectivelymodulated by a complex sinusoid with centre frequencies U and V along x and y-axesrespectivelydescribed by the following equation 1 -1 x y Gxy ---------- exp -------- 2---- 22piiUxVy 2pisxsy 2 sx sy Describtion : I : Input image Sx amp Sy : Variances along x and y-axes respectively U amp V : Centre frequencies along x and y-axes respectively G : The output filter as described above gabout : The output filtered image Author : Ahmad poursaberi e-mail : a.poursaberiece.ut.ac.ir Faulty of Engineering ElectricalampComputer DepartmentTehran UniversityIranJune 2004function Ggabout gaborfilterISxSyUVif isaIdouble1I doubleIendfor x -fixSx:fixSxfor y -fixSy:fixSyGfixSxx1fixSyy1 1/2piSxSyexp-.5x/Sx2y/Sy22piiUxVyendendImgabout conv2IdoubleimagGsameRegabout conv2IdoublerealGsamegabout uint8sqrtImgabout.Imgabout Regabout.RegaboutVERSION 2ANOTHER DESCRIBTION OF GABOR FILTERThe Gabor filter is basically a Gaussian with variances sx and sy along x and y-axesrespectivelymodulated by a complex sinusoid with centre frequencies U and V along x and y-axesrespectivelydescribed by the following equation -1 x y Gxythetaf exp -------- 2---- 2cos2pifx 2 sx sy x xcosthetaysintheta y ycostheta-xsintheta Describtion : I : Input image Sx amp Sy : Variances along x and y-axes respectively f : The frequency of the sinusoidal function theta : The orientation of Gabor filter G : The output filter as described above gabout : The output filtered image Author : Ahmad poursaberi e-mail : a.poursaberiece.ut.ac.ir Faulty of Engineering ElectricalampComputer DepartmentTehran UniversityIranJune 2004function Ggabout gaborfilterISxSyfthetaif isaIdouble1I doubleIendfor x -fixSx:fixSxfor y -fixSy:fixSyxPrime x costheta y sinthetayPrime y costheta - x sinthetaGfixSxx1fixSyy1 exp-.5xPrime/Sx2yPrime/Sy2cos2pifxPrimeendendImgabout conv2IdoubleimagGsameRegabout conv2IdoublerealGsamegabout sqrtImgabout.Imgabout Regabout.RegaboutVERSION 3ANOTHER DESCRIBTION OF GABOR FILTERThe Gabor filter is basically a Gaussian with variances sx and sy along x and y-axesrespectivelymodulated by a complex sinusoid with centre frequencies U and V along x and y-axesrespectivelydescribed by the following equation 1 -1 x y Gixy ---------- exp -------- 2---- 2Mixyf 2pisxsy 2 sx sy i 12 M1xyf cos2pifsqrtx2y2 M2xyf cos2pifxcostheta ysintheta Describtion : I : Input image Sx amp Sy : Variances along x and y-axes respectively f : The frequency of the sinusoidal function theta : The orientation of Gabor filter G1 amp G2 : The output filters as described above gabout1 amp gabout2 : The outpu