gabor滤波器的几种实现方式
1. 方式一
Sx,Sy在公式里分别表示Guass函数沿着x,y轴的标准差，相当于其他的gabor函数中的 sigma. 同时也用Sx,Sy指定了gabor滤波器的大小。（滤波器矩阵的大小）
这里没有考虑到相位偏移.
%%%%%%%VERSION 2%%ANOTHER DESCRIBTION OF GABOR FILTER%The Gabor filter is basically a Gaussian (with variances sx and sy along x and y-axes respectively)%modulated by a complex sinusoid (with centre frequencies U and V along x and y-axes respectively) %described by the following equation%%% -1 x' ^ y' ^ %%% G(x,y,theta,f) = exp ([----{(----) 2+(----) 2}])*cos(2*pi*f*x');% 2 sx' sy'%%% x' = x*cos(theta)+y*sin(theta);%%% y' = y*cos(theta)-x*sin(theta);%% Describtion :%% I : Input image%% Sx & 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.poursaberi@ece.ut.ac.ir%% Faulty of Engineering, Electrical&Computer Department,Tehran%% University,Iran,June 2004function [G,gabout] = gaborfilter1(I,Sx,Sy,f,theta)if isa(I,'double')~=1 I = double(I);endfor x = -fix(Sx):fix(Sx) for y = -fix(Sy):fix(Sy) xPrime = x * cos(theta) + y * sin(theta); yPrime = y * cos(theta) - x * sin(theta); G(fix(Sx)+x+1,fix(Sy)+y+1) = exp(-.5*((xPrime/Sx)^2+(yPrime/Sy)^2))*cos(2*pi*f*xPrime); endendImgabout = conv2(I,double(imag(G)),'same');Regabout = conv2(I,double(real(G)),'same');gabout = sqrt(Imgabout.*Imgabout + Regabout.*Regabout);
这个gaobor函数生成的gabor滤波器的图像如图：
不同的参数也会导致不同的结果。
2. 方式二
这个gabor滤波器的实现增加了尺度和方向变换，其他的参数以及意义都和上面的一样。
%%%%%%%VERSION 1%The Gabor filter is basically a Gaussian (with variances sx and sy along x and y-axes respectively)%modulated by a complex sinusoid (with centre frequencies U and V along x and y-axes respectively) %described by the following equation%%% 1 -1 x ^ y ^%%% G(x,y) = ---------- * exp ([----{(----) 2+(----) 2}+2*pi*i*(Ux+Vy)])% 2*pi*sx*sy 2 sx sy%% Describtion :%% I : Input image%% Sx & Sy : Variances along x and y-axes respectively%% U & 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.poursaberi@ece.ut.ac.ir%% Faulty of Engineering, Electrical&Computer Department,Tehran%% University,Iran,June 2004function [G,gabout] = gaborfilter(I,Sx,Sy,U,V);if isa(I,'double')~=1 I = double(I);endfor x = -fix(Sx):fix(Sx) for y = -fix(Sy):fix(Sy) G(fix(Sx)+x+1,fix(Sy)+y+1) = (1/(2*pi*Sx*Sy))*exp(-.5*((x/Sx)^2+(y/Sy)^2)+2*pi*i*(U*x+V*y)); endendImgabout = conv2(I,double(imag(G)),'same');Regabout = conv2(I,double(real(G)),'same');gabout = uint8(sqrt(Imgabout.*Imgabout + Regabout.*Regabout));
调用代码：
ori=imread('C:\Users\watkins\Pictures\cartoon.jpg');grayimg=rgb2gray(ori);gim=im2double(grayimg); Sx=32;Sy=32;f=sqrt(8);theta=pi/2;u=4;v=4;%[G,gabout] = gaborfilter1(gim,Sx,Sy,f,theta);[G,gabout] = gaborfilter1(gim,Sx,Sy,u,v);imshow(real(G));%imshow(real(gabout));
滤波器图片：
%%%%%%%VERSION 3%%ANOTHER DESCRIBTION OF GABOR FILTER%The Gabor filter is basically a Gaussian (with variances sx and sy along x and y-axes respectively)%modulated by a complex sinusoid (with centre frequencies U and V along x and y-axes respectively) %described by the following equation%%% 1 -1 x ^ y ^%%% Gi(x,y) = ---------- * exp ([----{(----) 2+(----) 2}])*Mi(x,y,f); % 2*pi*sx*sy 2 sx sy%%% i =1,2%%% M1(x,y,f) = cos[2*pi*f*sqrt(x^2+y^2)];%%% M2(x,y,f) = cos[2*pi*f*(x*cos(theta) + y*sin(theta)];%% Describtion :%% I : Input image%% Sx & Sy : Variances along x and y-axes respectively%% f : The frequency of the sinusoidal function%% theta : The orientation of Gabor filter%% G1 & G2 : The output filters as described above%% gabout1 & gabout2 : The output filtered images%% Author : Ahmad poursaberi e-mail : a.poursaberi@ece.ut.ac.ir%% Faulty of Engineering, Electrical&Computer Department,Tehran%% University,Iran,June 2004function [G1,G2,gabout1,gabout2] = gaborfilter2(I,Sx,Sy,f,theta)if isa(I,'double')~=1 I = double(I);endfor x = -fix(Sx):fix(Sx) for y = -fix(Sy):fix(Sy) M1 = cos(2*pi*f*sqrt(x^2+y^2)); M2 = cos(2*pi*f*(x*cos(theta)+y*sin(theta))); G1(fix(Sx)+x+1,fix(Sy)+y+1) = (1/(2*pi*Sx*Sy)) * exp(-.5*((x/Sx)^2+(y/Sy)^2))*M1; G2(fix(Sx)+x+1,fix(Sy)+y+1) = (1/(2*pi*Sx*Sy)) * exp(-.5*((x/Sx)^2+(y/Sy)^2))*M2; endendImgabout1 = conv2(I,double(imag(G1)),'same');Regabout1 = conv2(I,double(real(G1)),'same');Imgabout2 = conv2(I,double(imag(G2)),'same');Regabout2 = conv2(I,double(real(G2)),'same');gabout1 = sqrt(Imgabout1.*Imgabout1 + Regabout1.*Regabout1);gabout2 = sqrt(Imgabout2.*Imgabout2 + Regabout2.*Regabout2);
调用代码：
ori=imread('C:\Users\watkins\Pictures\cartoon.jpg');grayimg=rgb2gray(ori);gim=im2double(grayimg); Sx=16;Sy=16;f=sqrt(2);theta=pi/2;u=8;v=0;%[G,gabout] = gaborfilter1(gim,Sx,Sy,f,theta);%[G,gabout] = gaborfilter1(gim,Sx,Sy,u,v);[G1,G2,gabout1,gabout2] = gaborfilter2(gim,Sx,Sy,f,theta);R=real(G2);k=127.5/max(max(abs(R)));imshow(uint8(k*R+127.5));%imshow(real(G2));%imshow(abs(real(gabout)));
生成的滤波器图片：
