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 : [email protected]
%% Faulty of Engineering, Electrical&Computer Department,Tehran
%% University,Iran,June 2004
function [G,gabout] = gaborfilter1(I,Sx,Sy,f,theta)
if isa(I,'double')~=1
I = double(I);
end
for 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);
end
end
Imgabout = 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 : [email protected]
%% Faulty of Engineering, Electrical&Computer Department,Tehran
%% University,Iran,June 2004
function [G,gabout] = gaborfilter(I,Sx,Sy,U,V);
if isa(I,'double')~=1
I = double(I);
end
for 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));
end
end
Imgabout = 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：
3. 方式三
%%%%%%%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 : [email protected]
%% Faulty of Engineering, Electrical&Computer Department,Tehran
%% University,Iran,June 2004
function [G1,G2,gabout1,gabout2] = gaborfilter2(I,Sx,Sy,f,theta)
if isa(I,'double')~=1
I = double(I);
end
for 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;
end
end
Imgabout1 = 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：