in this activity we try to determine how the output would look like if one applies a Fourier Transform on an image. the Fast Fourier Transform is a powerful algorithm that basically recasts a signal into another complex plane showing the image’s spatial frequency.
in the first slideshow, input images (1) were applied with an FFT using fft2(), and the resulting pattern was applied with abs() to get it’s intensity values (2). fftshift() was then applied to show more clearly the intensity plot (3). then from (2) another fft2() was applied to revert back to its original (albeit inverted) form. (to avoid this, one can use ifft().)
in the second set of figures, i used convolution to simulate the effect of changing the size of the aperture to the quality of the image. convolution is a method used to combine two signals such that the resulting signal would look similar to both input signals. the primary image used was “VIP”, and the apertures used were of radii from 0.1, 0.2, … , 1.0. the final output reveals that the smaller the aperture, the lesser the quality of the output. higher quality outputs were generated with bigger apertures.
in these set of figures, i used correlation to determine the similarity of a given pattern and the whole image. the pattern is “rolled” across the main image and the amount of correlation is determined. using this technique one could determine more of less the positions of the letter A’s through correlation and thresholding.
the final figure illustrates edge detection using convolution. three sets of patterns were used (left), and these patterns were convolved around the image (previously used in the correlation part). the results show that the edges that were being detected would depend on the pattern used. a horizontal pattern would yield horizontal edges, vertical patterns would lead to vertical edges, and dot patterns would detect all possible edges and corners.
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