Super-Resolution via Neural-Network-Based Image Analogies
This is where we begin, with a 128 X 128 pixel picture of Beka (a home-made test image with all the right properties for experimentation, pretty much in place of the notorious Lena image). Images on the left below are generated using a simple image-analogies-based Java tool developed in support of this project proposal. On the right are images generated using Genuine Fractals PrintPro (a leading "fractal-based" image compression and super-resolution software on the market).
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We now make Beka larger — she is now 256 X 256 pixels. Twice the width of the original. This is what Genuine Fractals is designed for, and so, unsurprisingly, it has produced a much more pleasing result at this scale.
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We crop a bit of Beka and enlarge that to 256 X 256 pixels — the whole Beka would now be 512 pixels wide.
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We now crop a bit of that bit of Beka and enlarge it to 256 X 256 pixels — the whole Beka would now be 1024 pixels wide (try to find the part of the previous image that was enlarged).
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And again... the whole Beka would now be 2048 pixels wide.
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And again... the whole Beka would now be 4096 pixels wide.
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And again... the whole Beka would now be 8192 pixels wide.
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And again... the whole Beka would now be 16384 pixels wide.
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And again... the whole Beka would now be 32768 pixels wide.
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And again... the whole Beka would now be 65536 pixels wide.
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And again... the whole Beka would now be 131072 pixels wide. Evidently, images on the right are inexorably converging to a monochrome grey. We shall continue with the left column only from this point on.
And again... the whole Beka would now be 262144 pixels wide.
And again... the whole Beka would now be 524288 pixels wide.
And again... the whole Beka would now be 1048576 pixels wide.
And again... the whole Beka would now be 2097152 pixels wide.
And again... the whole Beka would now be 4194304 pixels wide.
And again... the whole Beka would now be 8388608 pixels wide.
And again... the whole Beka would now be 16777216 pixels wide.
And again... the whole Beka would now be 33554432 pixels wide.
And again... the whole Beka would now be 67108864 pixels wide.
And again... the whole Beka would now be 134217728 pixels wide.
And again... the whole Beka would now be 268435456 pixels wide.
By now, we have enlarged Beka's width 2,097,152 times and her surface area 4,398,046,511,104 times. This means that the final image represents a 0.000000003725-th bit of the whole Beka and it would take around 23,000,000,000 computer screens to see the whole Beka of this size. In other words, the final image, relative to the size of Beka's real head, is more than a million times smaller than a millimetre — that is about ten thousand times smaller than a single Beka's cell (typically 10 micrometers) and about a half the width of the DNA helix.
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