| |
| Tuesday, July 08, 2008 |
| Activity 6: Fourier Transform of Image Formation |
For this activity we were given 4 parts, each related with Fourier transform of images.
Familiarization with the discrete FFT
We were tasked to create a 128x128 image of a circle in MS Paint and to perform the Fast Fourier Transform (FFT) on the image. Below are the results I obtained, the color was from the jetcolormap function of Scilab.
The intensity image shows the circle transposed at the four corners, that is when it is shifted we will observe the correct transform of the circle: an Airy disk.
An Airy disk is a bright spot with concentric rings (like halos) surrounding it. Performing the FFT twice on the circle produced the same image. Or did it?
Performing the same method but this time with the image of the letter A we see that performing FFT twice inverts the original image.
Simulation of an imaging device
With the FFT we can actually simulate a camera. That is, with an image acting as an "aperture" we can actually see the resulting image of the object the camera is aiming at (that is, the other image. In this case an image with the acronym: VIP)
As with an actual camera, when the aperture is small (hence few light rays enter to expose the negative of what the image really is) the image is blurred. The bigger the aperture opening, the clearer the image is, and the greater its resemblance with the original.
Template matching using correlation
Template matching is a pattern recognition technique which looks for the pattern you wish to locate in an image. In this activity, we look for the pattern given by "A" (which we actually saw in the first activity) in a sentence. As we can see we have 5 bright dots indicating where "A" is. The "A"s can be seen where an inversion of the words: "rain", "spain", "stays", "mainly", and "plain" are supposed to be.
Edge detection using the convolution integral
Edge detection is simply finding out the edges of a particular orientation. Depending on what kind of pattern an image is convolved with, it shows the edges sharing the same orientation. For example when the pattern is horizontal, the horizontal edges shine brightly (similar with what we observed earlier in template matching).
I give myself 9/10 neutrinos for this activity since honestly I think I need more time to fully grasp these concepts all in one sitting.
Oh, and I want to thank Dr. Soriano for providing the codes. Thanks ma'am! |
posted by poy @ 10:40 PM  |
|
|
|
|
|
|
