# 2D Gabor Filter(Ver1,2,3)

13 Jun 2004 (Updated )

To design 2D Gabor filter and apply it to image.

gaborfilter(I,Sx,Sy,f,theta);
```%%%%%%%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

%%  Author : Ahmad poursaberi  e-mail : a.poursaberi@ece.ut.ac.ir
%%          Faulty of Engineering, Electrical&Computer Department,Tehran
%%          University,Iran,June 2004

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