Okay, so I could no longer keep my restless fingers under control... 
here it is, dithered output directly from POV-Ray.

To showcase the effect, I chose a bit depth of 5 bit (the lowest you can 
get with PNG), but the algorithm works perfectly fine with other bit 
depths as well.

First image shows the original in 8 bit (no dithering applied; if you 
look /very/ closely, you may still see some banding in the sky). All 
other images use 5 bits per colour channel:

(off) 5 bit image without dithering (I guess I don't need to mention the 
banding).

(b2) Bayes dithering using a 2x2 pattern

(b4) Bayes dithering using a 4x4 pattern

(d1) 1-dimensional error diffusion dithering (propagating all the error 
to the next pixel to the right)

(d2) 2-dimensional error diffusion dithering (propagating half of the 
error to the next pixel to the right, and a quarter, respectively, to 
the pixels below and below right)

(fs) the famous Floyd-Steinberg dithering (another error diffusion 
dithering)

I didn't bother to implement random dithering, as I don't think it gives 
real added value at the bit depths typically used. (b2), (b4) and (d1) 
have the advantage of using (almost) no additional memory (I implemented 
(d2) and (fs) using an additional 2-pixel-row buffer to avoid messing 
with the original data), while (fs) probably gives the best results. 
I'll probably drop (d2) as it doesn't seem to add much value either.

A point I'd like to emphasize is that I implemented the diffusion 
dithering methods to propagate the error /before/ gamma 
encoding/pre-correction. (One reason why dithered black-and-white images 
typically lose quite some "depth" is that they are implemented without 
attention to gamma.) Not that it will probably matter much with the 
typical bit depths, but you know - I just had to do this right ;-)

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Download 'dither_off_8bit.png' (129 KB) Download 'dither_off.png' (80 KB) Download 'dither_b2.png' (113 KB) Download 'dither_b4.png' (132 KB) Download 'dither_d1.png' (299 KB) Download 'dither_d2.png' (326 KB) Download 'dither_fs.png' (331 KB)

Preview of image 'dither_off_8bit.png'

Preview of image 'dither_off.png'

Preview of image 'dither_b2.png'

Preview of image 'dither_b4.png'

Preview of image 'dither_d1.png'

Preview of image 'dither_d2.png'

Preview of image 'dither_fs.png'