ISP Matab Gabor濾波器

1. 方式一

 

Sx,Sy在公式裏分別表示Guass函數沿着x,y軸的標準差，相當於其他的gabor函數中的 sigma. 同時也用Sx,Sy指定了gabor濾波器的大小。（濾波器矩陣的大小）

這裏沒有考慮到相位偏移.

 

%%%%%%%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);

這個gaobor函數生成的gabor濾波器的圖像如圖：

不同的參數也會導致不同的結果。

 

2. 方式二

 

這個gabor濾波器的實現增加了尺度和方向變換，其他的參數以及意義都和上面的一樣。

 

%%%%%%%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));

調用代碼：

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));

 

濾波器圖片：

 

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);

 

調用代碼：

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)));

 

生成的濾波器圖片：