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I grabbed 4th pair of their demo image [0], the high quality image is about 4.8M, the JpegMini'd version - 1.3M.Then I took the high quality image and started bumping up standard JPEG compression level until I reduced the file size to 1.3M. That mapped to 17/100 setting, with 1 being highest quality, 100 - highest compression).
Then I made an arithmetic per-pixel diff between the original high quality image and two 1.3M versions. Cropped them to 2000 x 2000 and saved as PNGs (cropping is to fit the imgur file size limits). Here they are -
Now, have a look and tell me that JPEGMini hasn't got something exciting going on.
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[0] http://media.jpegmini.com/homepageImages/20121203/hipnshoot....