As we can see in the figures, as the circle becomes small, more airy disc appear in the Fourier space. Also, this result is similar to the analytic Fourier transform of a circle which is an equation of the airy disc.
The next image used was a letter A as shown above (left figure). The Fourier transform (center) has an X and a vertical line. The X line corresponds to the orientation of the legs of A while the vertical line corresponds to the general orientation of the letter (i.e. if the letter is rotated 90 degrees, the Fourier transform would have a horizontal line instead of vertical). The last image (right) is the fft of the fft of the image. It is inverted because a forward fft was used instead of the inverse fft.The next activity was to get the convolution of an image with a circle. We used the word VIP as the image and I used the circles I used above.
Since convolution is like mixing the images together, we can see that the larger the aperture (circle) the clearer the object. This happens because the Fourier transform of a small aperture produces more airy disc therefore contributing more to the final image.
To find identical patterns, we used correlation. This was done by multiplying element wise the conjugate of the Fourier transform of the text image (left) with the Fourier transform of the pattern that we wanted to find, in this case the letter A (middle figure). The resulting image (right) have a maximum (white) where the letter A appears in the text.The concept used in correlation was modified to find edges in images. I used a horizontal, vertical, and spot pattern.
The detected edges mostly follows the pattern used. For the horizontal pattern (left) the convolve image has mostly horizontal edges, the vertical has mostly vertical edges, and the spot pattern detects both horizontal and vertical edges.For this activity, I give myself a grade of 10 because I did the activity properly and independently.
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