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Dithering is a method for converting high pixel depth low resolution into a format suitable for display on high resolution low bit depth devices and formats.
Typically you would use it to convert (for instance) a 72dpi 8 bit per color image for a screen into a 600dpi 1 bit per color image for a printer. The trade off of resolution for bit depth lets you simulate higher bit depth on the printer and look about the same. Dithering the image to a resolution different than the device resolution doesn't really make a lot of sense, and will cause moire banding and doing it at a resolution different than the device resolution is basically wrong and worse than doing nothing.
My assumption is that the original kobo was only black and white, with no grey scale. You can simulate grey scale with dithering.
Also, I assume that pre-dithering the image for a screen that already supports grey scale is probably obsolete. A screen with 4 bit depth (16 shades of grey) is not bad and dithering to black and white will probably make it look worse, although it would be possible to dither 8 bit to 4 bit rather than 8 bit to 1 bit and have it look ok. But then, I would also assume that the device knows its gamut better than a generic dithering algorithm, and letting the device dither to its version of grey scale is probably better.
I would also assume that the 4 bit grey kobo screen is really just black and white dithered to simulate 4 bit depth, and that dithering twice probably isn't that great either.
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