Pat's Applied Physics 186 Blog.: AP 186 Activity 6: Familiarization with Discreet FFT

The Fourier tranform has ubiquitous applications, and in this activity we apply it to image processing. In any typical tansformation, the FT is in the frequency domain. According to wiki, the domain of the new function is typically called the frequency domain, and the new function itself is called the frequency domain representation of the original function. A more preferred method of FT is the fast Fourier Transform (FFT).

To familiarize with FFT, we observe its effect on a centered circle. Going clockwise, the topmost left is the original circle, then applied fft2 then shifted, then taken the inverse fft.

For the image of the text A, the same procedure was done. Notice that the last image (topmost right) is inverse of the original image (topmost left). The FT has rendered its matrices shifted, resulting to an inverted image.

Next we consider the FT in terms of viewing an object. Let circles of different sizes be the apertures, and the image of the text 'VIP' be the object. As can be expected, the larger the aperture size, the sharper the image.

Another feature of the FT is the ability to compare a template and an image. In this example, a text image was correlated with the text image of a single letter 'A'. This will be to determine which letters in the text image check out with the 'A' template.

The bright spots in the transformed image (right) are the points where A is present in the text image, note that the transformed image is flipped though.

Lastly, the FT was used for edge detection.