3 ms·

Another way to think of dither (that may only make sense to people with a signals background) is that it linearizes the error introduced by the quantization ste

Another way to think of dither (that may only make sense to people with a signals background) is that it linearizes the error introduced by the quantization step (which is a non-linear process). This has a bunch of conceptual implications (like elimination of error harmonics being natural consequence) but maybe most importantly allows you to continue using linear analysis tools and techniques in systems with a quantization filter.

nullc 6y ago
This thesis on noise shaping and dither http://uwspace.uwaterloo.ca/bitstream/10012/3867/1/thesis.pdf http://uwspace.uwaterloo.ca/bitstream/10012/3867/1/thesis.pd... is an excellent mathematical treatment of the subject.
- CyberRabbi 6y ago
  Very cool paper. Something that bothers me is that the Floyd-steinberg error diffusion without dithering looks superior than the version with the dithering. I think this demonstrates that perceptible patterns in the error (non-linear) don’t always look so bad.
  - nullc 6y ago
    One thing I've found (admittedly with audio) is that you can usually get away with less dither power than is needed to completely linearize the error, at the cost of some harmonics for pathological signals which still ends up being less noticeable than the higher power dither noise. I expect something similar to apply to images.
    - CyberRabbi 6y ago
      Right, I think that’s what’s going on in my image example. I think this is a key lesson to people who apply these types of mathematical techniques to the lossy compression of data meant to be experienced by humans. Random noise is not always preferable to non-linear error, i.e. reducing non-linear error is not necessarily the equivalent of improving the perceived quality of the data in question. It can be but the function that determines what “looks good” or what “sounds good” to humans is probably a bit more complex. This is something I’ve run into with image compression techniques but it applies here too (quantization being a form of compression). E.g. JPEG compresses images in 8x8 blocks because doing the whole image at once would look horrible. Figuring out the redundant information that can be thrown away with the least impact to image quality is still fundamentally an art.

nullc 6y ago

This thesis on noise shaping and dither http://uwspace.uwaterloo.ca/bitstream/10012/3867/1/thesis.pdf http://uwspace.uwaterloo.ca/bitstream/10012/3867/1/thesis.pd... is an excellent mathematical treatment of the subject.

CyberRabbi 6y ago
Very cool paper. Something that bothers me is that the Floyd-steinberg error diffusion without dithering looks superior than the version with the dithering. I think this demonstrates that perceptible patterns in the error (non-linear) don’t always look so bad.
- nullc 6y ago
  One thing I've found (admittedly with audio) is that you can usually get away with less dither power than is needed to completely linearize the error, at the cost of some harmonics for pathological signals which still ends up being less noticeable than the higher power dither noise. I expect something similar to apply to images.
  - CyberRabbi 6y ago
    Right, I think that’s what’s going on in my image example. I think this is a key lesson to people who apply these types of mathematical techniques to the lossy compression of data meant to be experienced by humans. Random noise is not always preferable to non-linear error, i.e. reducing non-linear error is not necessarily the equivalent of improving the perceived quality of the data in question. It can be but the function that determines what “looks good” or what “sounds good” to humans is probably a bit more complex. This is something I’ve run into with image compression techniques but it applies here too (quantization being a form of compression). E.g. JPEG compresses images in 8x8 blocks because doing the whole image at once would look horrible. Figuring out the redundant information that can be thrown away with the least impact to image quality is still fundamentally an art.