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:

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