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Are there some simple arithmetical relations (rules, properties) between numbers in x:y:z chroma subsampling notation?

1

The numbers in chroma subsampling notation are the ratio of the sampling rates of the luminance, chroma difference, and alpha channel, if present (Whitaker, 2003).

For example:

  • 4:4:4:4 The color difference (and alpha) channels are sampled at the same frequency as the luminance channel.
  • 4:2:2 The color difference channels are sampled at half the rate of the luminance channel. This yields a 2/3 compression ratio.
  • 4:1:1 and 4:2:0 The color difference channels are sampled at one quarter the rate of the luminance channel. The difference is the pattern of the subsamples.

Less technically, the numbers can be looked at as number of horizontal (y) and vertical (z) chroma subsamples for every x horizontal luminance samples (Pizzi & Jones, 2014).

2

Yes, there are.

Let x:y:z is a chroma subsampling. Then

  1. x = 4
    So the begin of the notation is 4:.
  2. y|x (y is a divisor of x)
    So there are 3 possibilities for the first two numbers: 4:1: or 4:2: or 4:4:.
  3. z = 0 or z = y
    So there are 6 possibilities: 4:1:0, 4:1:1, 4:2:0 4:2:2, 4:4:1, or 4:4:4.
  4. y + z determines the resulting color quality (higher is better).
    So 4:4:4 is the best (as 4 + 4 = 8) while 4:1:0 is the worst (as 1 + 0 = 1).

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