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excellent first pass at a description; now it's time for the Ministry of 

English Composition to tear it apart and rebuild it, stronger than before

Originally committed as revision 17801 to svn://svn.ffmpeg.org/ffmpeg/trunk
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Mike Melanson 2009-03-04 05:24:59 +00:00
parent 87574416f7
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doc/rate_distortion.txt
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A quick description of Rate distortion theory. A Quick Description Of Rate Distortion Theory.
We want to encode a video, picture or music optimally. We want to encode a video, picture or piece of music optimally. What does
What does optimally mean? "optimally" really mean? It means that we want to get the best quality at a
It means that we want to get the best quality at a given given filesize OR we want to get the smallest filesize at a given quality
filesize OR (which is almost the same actually) We want to get the (in practice, these 2 goals are usually the same).
smallest filesize at a given quality.
Solving this directly isnt practical, try all byte sequences Solving this directly is not practical; trying all byte sequences 1
1MB long and pick the best looking, yeah 256^1000000 cases to try ;) megabyte in length and selecting the "best looking" sequence will yield
256^1000000 cases to try.
But first a word about Quality also called distortion, this can But first, a word about quality, which is also called distortion.
really be almost any quality meassurement one wants. Commonly the Distortion can be quantified by almost any quality measurement one chooses.
sum of squared differenes is used but more complex things that Commonly, the sum of squared differences is used but more complex methods
consider psychivisual effects can be used as well, it makes no differnce that consider psychovisual effects can be used as well. It makes no
to us here. difference in this discussion.
First step, that RD factor called lambda ... First step: that rate distortion factor called lambda...
Lets consider the problem of minimizing Let's consider the problem of minimizing:
distortion + lambda*rate distortion + lambda*rate
for a fixed lambda, rate here would be the filesize, distortion the quality For a fixed lambda, rate would represent the filesize, while distortion is
Is this equivalent to finding the best quality for a given max filesize? the quality. Is this equivalent to finding the best quality for a given max
The awnser is yes, for each filesize limit there is some lambda factor for filesize? The answer is yes. For each filesize limit there is some lambda
which minimizing above will get you the best quality (in your provided quality factor for which minimizing above will get you the best quality (using your
meassurement) at that (or a lower) filesize chosen quality measurement) at the desired (or lower) filesize.
Second step, spliting the problem. Second step: splitting the problem.
Directly spliting the problem of finding the best quality at a given filesize Directly splitting the problem of finding the best quality at a given
is hard because we dont know how much filesize to assign to each of the filesize is hard because we do not know how many bits from the total
subproblems optimally. filesize should be allocated to each of the subproblems. But the formula
But distortion + lambda*rate can trivially be split from above:
just consider
(distortion0 + distortion1) + lambda*(rate0 +rate1) distortion + lambda*rate
a problem made of 2 independant subproblems, the subproblems might be 2
16x16 macroblocks in a frame of 32x16 size. can be trivially split. Consider:
to minimize
(distortion0 + distortion1) + lambda*(rate0 +rate1) (distortion0 + distortion1) + lambda*(rate0 + rate1)
one just have to minimize
distortion0 + lambda*rate0 This creates a problem made of 2 independent subproblems. The subproblems
might be 2 16x16 macroblocks in a frame of 32x16 size. To minimize:
(distortion0 + distortion1) + lambda*(rate0 + rate1)
we just have to minimize:
distortion0 + lambda*rate0
and and
distortion1 + lambda*rate1
aka the 2 problems can be solved independantly distortion1 + lambda*rate1
I.e, the 2 problems can be solved independently.
Author: Michael Niedermayer Author: Michael Niedermayer
Copyright: LGPL Copyright: LGPL