Gabor filter convolution matrix in C

Question

I'm trying to write an algorithm in C that computes a convolution matrix of a gabor filter to be applied to an image. Right now, I just need the convolution matrix.

So, I'm using this equation: http://i.stack.imgur.com/APMC7.png

I mapped it to this little piece of code:

#include <stdio.h>
#include <math.h>
#define PI 3.14159265

int main(){
    int kernelSize = 5;
    float kernel[kernelSize][kernelSize];
    int x, y;
    //gamma = aspect ratio
    //lambda = wavelength
    //theta = orientation
    float xz, yz, theta, sigma, gamma, lambda;
    theta = 0;
    sigma = 1;
    lambda = 1;
    gamma = 1;

    for(x = 0; x < kernelSize; x++){
        for(y = 0; y < kernelSize; y++){
            xz = x * cos(theta) + y * sin(theta);
            yz = -x * sin(theta) + y * cos(theta);
            kernel[x][y] = exp(-(xz*xz + gamma*gamma*yz*yz)/(2*sigma*sigma)) * cos(2*PI*xz/lambda);
        }
    }
    for(x = 0; x < kernelSize; x++){
        for(y = 0; y < kernelSize; y++){
            printf("%.2f ", kernel[x][y]);
        }
        printf("\n)");
    }
    return(0);

}

The output with these parameters are:

1.00 0.61 0.14 0.01 0.00
0.61 0.37 0.08 0.01 0.00 
0.14 0.08 0.02 0.00 0.00 
0.01 0.01 0.00 0.00 0.00 
0.00 0.00 0.00 0.00 0.00

My questions are: 1 - is it a valid convolution matrix for a gabor filter? If I convolute it with an image, will it apply the gabor filter? 2 - Should I sum all matrix values and normalize it? 3 - Is there anything I should fix in it?

Thanks in advance!

Answer 1

I don't know C so I'm not able to comment on your code, but:

1. By definition, a gabor filter should have a real part and an imaginary part - i.e. complex valued.
2. Your kernel doesn't look anything like a gabor kernel. It should look like a sinusoid multiplied by a gaussian - yours looks like a gaussian centred in the top left corner. No need to normalise it.

I would also tweak your parameters so they aren't unitary. Plot your filter and see if it looks like what you get when you search for 'Gabor wavelet' on Google.