Enhancement in the Frequency Dom

Part 1:(FFT of 2D sine function)

Increasing the frequency of the 2D sine function increases the separation of the peak frequency in the FFT space and by rotating the sine function by some angle also rotates the peak frequency in the FFT space.
Multiplication of two sine function create a four peaks in the FFT space. The spacing of the peaks depends on the frequency of the of each sine. If the two sine functions have different frequencies, the peaks will not form a perfect square.

Part 2: (Finger Print)
Source code for finger print improvement:
a = imread("E:\AP 186\activity 7\finger ko.bmp");//image read
b = im2gray(a);
IM=fft(b,-1);
h1=mkfftfilter(b,'butterworth1',5);
h2=mkfftfilter(b,'butterworth2',30);
h=(h1-h2)*255;//Create filter
c = fft2(b);
apergrayshift = fftshift(h);
FR = apergrayshift.*(c);
IRA = (fft2(FR));
scf(1)
imshow(abs(fft2(fft2(IRA))),[]);
scf(2)
imshow(b,[]);
Part 3: (Space image improvement)

There is a given a image having vertical lines with uniform spacing, we can eliminate these vertical lines by taking the 2D Fourier Transform. By creating a filter which blocks the cross line on the Fourier Space of the original image, we can eliminate the vertical line present on the image. The FFT, the filter and the resulting image is shown below:

Collaborators:
Rafael Jaculbia, Elizabeth Anne Prieto

In this activity,I will give myself myself a grade of 7 because I believe that I did not obtain the right result for the second part.