| |
| Thursday, July 10, 2008 |
| Activity 7: Enhancement in the Frequency Domain |
Anamorphic property of the fourier transform
The Fourier Transform of a signal is its spatial frequency distribution. Basically, any image or signal can be expressed as a superposition of sinusoids. Unique to the 2 dimensional Fourier Transform is the fact that rotation of the sinusoids result to the rotation of their transformations.
In this activity, we were tasked to observe what the Fourier Transformation of a sinusoid looks like and what happens: when its frequency is changed, when it's rotated, and when it's superimposed with another sinusoid. Using Scilab we can create a sinusoid (similar to Activity 5), take its FT, and expect that the rotation of the sinusoid results into the rotation of its Fourier Transformation.
As expected from previous activities, the Fourier Transformation of a sine function is a delta function. The two dots in the figure above for each frequency (f=4,8,12) were the delta functions. And as we can observe, if frequency were to be changed the spaces between the sinusoids will change. From the results we can see that, as frequency increased, the distance between the lines (the sine waves) becomes smaller. In the frequency domain (fourier transform), this will cause the delta function to move away from each other as seen above.
For varying angle of projection we obtain the following results:
The image of two sinusoids that are combined looks like a checkerboard. The Fourier Transform are four points that indicate two delta functions, that are probably from their respective sinusoids.
Fingerprints: Ridge Enhancement
Obtaining my scanned fingerprint, we process this image using Scilab. First of all, we convert the image into grayscale. After that, we remove the Dark Current (DC) by subtracting the mean of the image. To enhance the ridges of the fingerprints, we use the mkfftfilter function of Scilab. With that, we use a high pass filter which is the filter commonly used to increase the magnitude of high frequency components relative to the low frequency components thus producing a sharp contrast between the two. The results show the phenomenon clearly:
Lunar landing scanned pictures: Line removal
To reduce vertical lines in an image, in this case a juxtaposed lunar landscape. To do this reduction, we first subtract the mean of the image. Then we analyze the Fourier Transform and apply a filter that would eliminate the distinct Fourier Transformations of the vertical lines.
Acknowledgements
Thanks to Jeric for the absolutely brilliant method of removing the vertical lines from the lunar image. And thanks to Dr. Soriano for the codes on the first part of the activity. This had been a long activity, but worth the effort. I give myself a 9/10 neutrinos.
 |
posted by poy @ 4:54 PM  |
|
|
|
|
|
|
