Act 7: Enhancement in the Frequency Domain

In this activity, manipulating the frequency domain is used to enhance the image or mask unwanted or unneeded frequencies.

A. Convolution Theorem
We start with an image of two 1-pixel dots:



Using Fourier transform, we obtain this modulus:



Next, we use circles of various radius instead of dots.



Their corresponding FTs are shown below:



We then use two squares instead of circles:



Their corresponding FTs are shown below:



Lastly, we use pairs of Gaussians of variance 0.1, 0.2 and 0.4:



Their corresponding FTs are as follows:



B. Fingerprints: Ridge Enhancement
This time we are to enhance the quality of a fingerprint image. I make use of the image below:

I crop a portion of the image in order to better process it.

The corresponding image in Fourier space of the above image is shown below

The cover up the unwanted frequencies, we use the following mask:

After applying the mask, the image

While its contrast isn't as good as the original image, the fingermarks became much more evened out, and the blotches become less apparent and the ridges are better defined.

C. Lunar Landing Scanned Pictures: Line Removal
This time we are to remove the vertical lines in an image of a lunar landing. The image was reduced in size for faster processing.

Its FT is shown below:

We make use of this mask to hide the lines:

Using the mask, we render the image below:

It can be easily observed that the horizontal lines have been removed due to the mask removing the unwanted frequencies. Thus, we can say that the mask used was appropriate for this image.

D. Canvas Weaved Modeling and Removal
This time we make use of an image of a painting and apply the appropriate mask in order to eliminate the weaves and enhance the brushstrokes.

Its corresponding FT:

We make use of this mask to remove the weaves:

After applying the mask and ifft, the newly rendered image is shown below:

It can be seen that the weaves seem minimized and the brushstrokes are much more prominent as a result. The ifft of the mask is shown below

It can be seen that the pattern is similar to the canvas weaves, and thus, the mask is fitting for this image.

I will give myself a grade of 10/10 for accomplishing all the steps in this activity completely. I would like to thank Raffy and Earl for their help as well as their ideas regarding this activity.