Visualizing Gabor filters using mesh

Now, I have implemented the Gabor filter as : In my_gabor_filter.m, I have the following code :

function psi = my_gabor_filter(x,y,mu,nu,sigma)

    phi = pi*mu/8;
    f = sqrt(2);
    k_max = pi/2;
    k_nu = k_max/(f^nu);

    k_vec = [k_nu*cos(phi),k_nu*sin(phi)]';
    z_vec = [x,y]';

    k_vec_norm = norm(k_vec);
    z_vec_norm = norm(z_vec);

    exp1 = (k_vec_norm/(sigma^2));
    exp2 = (exp(-((k_vec_norm^2)*(z_vec_norm^2)/(2*sigma^2))));
    exp3 = (exp(complex(0,k_vec'*z_vec))-exp(-(sigma^2/2)));
    psi = exp1*exp2*exp3;
end
and, in plot_gabor_filter.m I did the following :

function plot_gabor_filter()

    mu = 0;
    nu = 0;
    sigma = 1;

    [X,Y] = meshgrid(0:1:39,0:1:39);

    Z = my_gabor_filter(X, Y, mu, nu, sigma);
    mesh(X,Y,Z,'EdgeColor','black')

end and when I run plot_gabor_filter.m, I get the following output :

>> plot_gabor_filter
Error using  * 
Inner matrix dimensions must agree.

Error in my_gabor_filter (line 17)
exp3 = (exp(complex(0,k_vec'*z_vec))-exp(-(sigma^2/2)));

Error in plot_gabor_filter (line 16)
Z = my_gabor_filter(X.^1 ,Y.^1,mu,nu,sigma);

So I have come this far. Kindly help me.

Answer 1

[Guru Swaroop]

The problem was, that, I was passing X and Y as matrices, which my_gabor_filter(..) cannot handle correctly, so instead I evaluated my_gabor_filter at each point (x,y) with x in X and y in Y, and so the modified version of my_gabor_filter is as follows :

NOTE : I also adjusted the range for X and Y so that the mesh-grid is clearly seen

function plot_gabor_filter()

mu = 0;
nu = 0;
sigma = 1;

[X,Y] = meshgrid(-2:0.1:2,-2:0.1:2);

Z = zeros(41,41);

for i = 1:1:41
    for j = 1:1:41
        Z(i,j) = imag(my_gabor_filter(X(i,j),Y(i,j),mu,nu,sigma));
    end
end

surf(X,Y,Z,'EdgeColor','black')

xlabel('x axis');
ylabel('y axis');
zlabel('g(x,y)');

end

and, This solves my problem.

Answer 2

[Wayne King]

Unless you have posted the incorrect version of my_gabor_filter.m, I show that it errors on this line actually:

    exp3 = (exp(complex(0,k_vec'*z_vec))-exp(-(sigma^2/2)));

k_vec is 2x1 and z_vec is 80x40 so multiplying k_vec' and z_vec is not going to work.

[Guru Swaroop]

Yaa thats right, because while designing my_gabor_filter() I was assuming that x and y are not matrices, but single valued (or matrices of size 1X1). So I fixed plot_gabor_filter as shown here.