Part 1.2: Hybrid Images

Image set 1 - Derek and Nutmeg

For this set, I used a sigma of 10 for the Gaussian filter.
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Image set 2 - Lincoln and Washington

For this set, I first converted Washington to black-and-white. I used a sigma of 23 for the Gaussian filter.
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Image set 3 - Pen and Eraser

For this set I used a sigma of 5 for the Gaussian filter. I consider this image a failure, since the effect is not very convincing. This is because there is no way to align the pen and eraser together properly, since their shapes are too different.
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Fourier analysis of Lincoln and Washington

Through the Fourier analysis, it's clear that the high-frequency components are being removed from the Lincoln image, and the low-frequency components are being removed from the Washington image.
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Original image, Fourier transform of image, Fourier transform of filtered image
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Original image, Fourier transform of image, Fourier transform of filtered image
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Hybrid image, Fourier transform of hybrid image

Bells and Whistles: Adding color

The color in the foreground is not very prominent, so the first and third images are very similar. I prefer both layers to be colored, but the answer is a matter of personal preference.
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Colored background
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Colored foreground
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Both colored