Enhancement in the Frequency Domain

The first part of this activity involves studying the some more properties of the Fourier transform. The images below shows a 2D sinusoidal function and its Fourier transform . As can be seen in the images, the maximum in the frequency domain is perpendicular to the direction of the sinusoid. So, as the sinusoid is rotated, the Fourier transform also rotates.

The second parameter investigated was the frequency of the sinusoid used. From the images below we can see that as the frequency is increased, the separation between the points (which corresponds to the black and white stripes) become larger.
Ridge Enhancement
In this activity, we would try to enhance the ridges in a fingerprint by filtering the frequency domain. I used the fingerprint found in the pdf since the fingerprint I scanned was small and so the results are not noticeable. The Fourier transform of the fingerprint and the filter mask I used is shown below. The filter was designed such that the low frequencies in the image are blocked.
After filtering (images below), the ridges in the fingerprint images were enhanced (upper right) but blotches are still present. However, if we take only the real part of the inverse Fourier transform of the filtered Fourier transform, the blotches are almost gone while still maintaining the same ridge quality.


Line Removal
For this activity, we were given an image of the moon with lots of vertical lines in it. Our task is to remove it using filters in the frequency domain. From our past activity, I learned that vertical lines are seen as horizontal lines in the frequency domain. So, I designed a frequency filter which would block these horizontal lines. The fourier transform of the image is shown in the upper left figure and the filter used is shown in the upper right. The original and line removed images are shown below. (left and right respectively)

I give myself a grade of 8 for this activity since I'm not sure if I did the ridge enhancement properly.