Answers.Body: <p>The numbers in chroma subsampling notation are the ratio of the sampling rates of the <a href="https://en.wikipedia.org/wiki/Luma_(video)" rel="nofollow noreferrer">luminance</a>, <a href="https://en.wikipedia.org/wiki/Chrominance" rel="nofollow noreferrer">chroma difference</a>, and <a href="https://en.wikipedia.org/wiki/Alpha_compositing" rel="nofollow noreferrer">alpha channel</a>, if present (<a href="http://rads.stackoverflow.com/amzn/click/0071411801" rel="nofollow noreferrer">Whitaker, 2003</a>).</p>
  
  <p>For example:</p>
  
  <ul>
  <li><strong>4:4:4:4</strong> The color difference (and alpha) channels are sampled at the same frequency as the luminance channel.</li>
  <li><strong>4:2:2</strong> The color difference channels are sampled at half the rate of the luminance channel. This yields a 2/3 compression ratio.</li>
  <li><strong>4:1:1</strong> and <strong>4:2:0</strong> The color difference channels are sampled at one quarter the rate of the luminance channel. The difference is the pattern of the subsamples.</li>
  </ul>
  
  <p>Less technically, the numbers can be looked at as number of horizontal (<em>y</em>) and vertical (<em>z</em>) chroma subsamples for every <em>x</em> horizontal luminance samples (<a href="http://rads.stackoverflow.com/amzn/click/B01LYHORQZ" rel="nofollow noreferrer">Pizzi &amp; Jones, 2014</a>).</p>
  
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Answers.CreationDate: 2017-03-16T23:55:26.797Z
Answers.LastActivityDate: 2017-03-17T05:17:36.593Z
Answers.LastEditDate: 2017-03-17T05:17:36.593Z
Answers.UserDisplayName: Michael Liebman
Answers.Body: <p>Yes, there are.</p>
  
  <p>Let <code>x:y:z</code> is a chroma subsampling. Then</p>
  
  <ol>
  <li><code>x = 4</code><br />
  So the begin of the notation is <code>4:</code>.</li>
  <li><code>y|x</code> (<code>y</code> is a divisor of <code>x</code>)<br />
  So there are 3 possibilities for the first two numbers: <code>4:1:</code> or <code>4:2:</code> or <code>4:4:</code>.</li>
  <li><code>z = 0</code> or <code>z = y</code><br />
  So there are 6 possibilities: <code>4:1:0</code>, <code>4:1:1</code>, <code>4:2:0</code> <code>4:2:2</code>, <code>4:4:1</code>, or <code>4:4:4</code>.</li>
  <li><code>y + z</code> determines the resulting color quality (higher is better).<br />
  So <code>4:4:4</code> is <em>the best</em> (as 4 + 4 = 8) while <code>4:1:0</code> is <em>the worst</em> (as 1 + 0 = 1).</li>
  </ol>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-03-17T16:12:25.280Z
Answers.LastActivityDate: 2017-03-17T16:12:25.280Z
Answers.UserDisplayName: MarianD
Body: <p>Are there some <em>simple arithmetical relations</em> (rules, properties) between numbers in <code>x:y:z</code> chroma subsampling notation?</p>
  
Tags: <compression><technical>
Title: Chroma subsampling notation - rules
UserDisplayName: MarianD
ThreadText: # Chroma subsampling notation - rules
  
  (Asked by: username_0 on 2017-03-16)
  
  Are there some *simple arithmetical relations* (rules, properties) between numbers in `x:y:z` chroma subsampling notation?
  
  **Tags:** compression, technical
  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_1 on 2017-03-16. Score: 1 | Accepted answer
  
  The numbers in chroma subsampling notation are the ratio of the sampling rates of the [luminance](https://en.wikipedia.org/wiki/Luma_(video)), [chroma difference](https://en.wikipedia.org/wiki/Chrominance), and [alpha channel](https://en.wikipedia.org/wiki/Alpha_compositing), if present ([Whitaker, 2003](http://rads.stackoverflow.com/amzn/click/0071411801)).
  
  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](http://rads.stackoverflow.com/amzn/click/B01LYHORQZ)).
  
  
  ---
  
  ### Answer by username_0 on 2017-03-17. Score: 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).
  
  
  ---
  
  