title: What is the "Law of the Eight"?
body: <p>While studying this document on the <a href="http://jpegclub.org/temp/Evolution_of_JPEG.doc" rel="nofollow noreferrer">Evolution of JPEG</a>, i came across "<strong>The law of the eight</strong>" in Section 7.3 of the above document.</p>
  
  <blockquote>
    <p>Despite the introduction of other block sizes from 1 to 16 with the SmartScale extension, beyond the fixed size 8 in the original JPEG standard, the fact remains that the block size of 8 will still be the default value, and that all other-size DCTs are scaled in reference to the standard 8x8 DCT.</p>
    
    <p>The “<strong>Law of the Eight</strong>” explains, why the size 8 is the right default and reference value for the DCT size.</p>
  </blockquote>
  
  <p>My question is  </p>
  
  <h2>What exactly is this <em>"law of the eight"</em> ?</h2>
  
  <ul>
  <li><p>Historically, was a study performed that evaluated numerous images from a sample to arrive at the conclusion that <strong>8x8</strong> image block contains enough redundant data to support compression techniques using DCT? With very large image sizes like 8M(4Kx4K) fast becoming the norm in most digital images/videos, is this assumption still valid?</p></li>
  <li><p>Another historic reason to limit the macro-block to 8x8 would have been the computationally prohibitive image-data size for larger macro-blocks. With modern super-scalar architectures (eg. CUDA) that restriction no longer applies.</p></li>
  </ul>
  
  <p>Earlier similar questions exist - <a href="https://stackoverflow.com/questions/74892/is-there-a-quality-file-size-or-other-benefit-to-jpeg-sizes-being-multiples-of"><strong>1</strong></a>, <a href="https://stackoverflow.com/questions/11147666/why-do-image-compression-algorithms-process-the-image-by-sub-blocks"><strong>2</strong></a> and <a href="https://stackoverflow.com/questions/10780425/why-jpeg-compression-processes-image-by-8x8-blocks"><strong>3</strong></a>. But none of them bother about any details/links/references to this mysterious fundamental "<strong>law of the eight</strong>".</p>
  
  <hr>
  
  <p><sub>
  1. References/excerpts/details of the original study will be highly appreciated as i would like to repeat it with a modern data-set with very large sized images to test the validity of 8x8 macro blocks being optimal. 
  </sub></p>
  
  <p><sub>
  2. In case a similar study has been recently carried-out, references to it are welcome too.
  </sub></p>
  
  <p><sub>
  3. I <strong>do</strong> understand that <a href="http://en.wikipedia.org/wiki/Libjpeg#libjpeg-turbo" rel="nofollow noreferrer"><strong>SmartScale</strong></a> is <a href="http://hardwarebug.org/2010/02/01/ijg-swings-again-and-misses/" rel="nofollow noreferrer">controversial</a>. Without any clear potential benefits <sup><a href="http://www.libjpeg-turbo.org/About/SmartScale-Lossy" rel="nofollow noreferrer">1</a></sup>, at best it is comparable with other backward-compliant extensions of the jpeg standard <sup><a href="http://www.libjpeg-turbo.org/About/SmartScale-Lossless" rel="nofollow noreferrer">2</a></sup>. My goal is to understand whether the original reasons behind choosing 8x8 as the DCT block-size (in jpeg image compression standard) are still relevant, hence i need to know what the <strong>law of the eight</strong> is.
  </sub></p>