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English Composition to tear it apart and rebuild it, stronger than before Originally committed as revision 17801 to svn://svn.ffmpeg.org/ffmpeg/trunkrelease/0.6
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A quick description of Rate distortion theory. |
A Quick Description Of Rate Distortion Theory. |
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We want to encode a video, picture or music optimally. |
We want to encode a video, picture or piece of music optimally. What does |
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What does optimally mean? |
"optimally" really mean? It means that we want to get the best quality at a |
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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 |
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filesize OR (which is almost the same actually) We want to get the |
(in practice, these 2 goals are usually the same). |
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smallest filesize at a given quality. |
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Solving this directly is not practical; trying all byte sequences 1 |
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Solving this directly isnt practical, try all byte sequences |
megabyte in length and selecting the "best looking" sequence will yield |
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1MB long and pick the best looking, yeah 256^1000000 cases to try ;) |
256^1000000 cases to try. |
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But first a word about Quality also called distortion, this can |
But first, a word about quality, which is also called distortion. |
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really be almost any quality meassurement one wants. Commonly the |
Distortion can be quantified by almost any quality measurement one chooses. |
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sum of squared differenes is used but more complex things that |
Commonly, the sum of squared differences is used but more complex methods |
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consider psychivisual effects can be used as well, it makes no differnce |
that consider psychovisual effects can be used as well. It makes no |
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to us here. |
difference in this discussion. |
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First step, that RD factor called lambda ... |
First step: that rate distortion factor called lambda... |
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Lets consider the problem of minimizing |
Let's consider the problem of minimizing: |
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distortion + lambda*rate |
distortion + lambda*rate |
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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 |
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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 |
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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 |
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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 |
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meassurement) at that (or a lower) filesize |
chosen quality measurement) at the desired (or lower) filesize. |
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Second step, spliting the problem. |
Second step: splitting the problem. |
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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 |
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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 |
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subproblems optimally. |
filesize should be allocated to each of the subproblems. But the formula |
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But distortion + lambda*rate can trivially be split |
from above: |
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just consider |
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(distortion0 + distortion1) + lambda*(rate0 +rate1) |
distortion + lambda*rate |
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a problem made of 2 independant subproblems, the subproblems might be 2 |
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16x16 macroblocks in a frame of 32x16 size. |
can be trivially split. Consider: |
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to minimize |
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(distortion0 + distortion1) + lambda*(rate0 +rate1) |
(distortion0 + distortion1) + lambda*(rate0 + rate1) |
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one just have to minimize |
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distortion0 + lambda*rate0 |
This creates a problem made of 2 independent subproblems. The subproblems |
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might be 2 16x16 macroblocks in a frame of 32x16 size. To minimize: |
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(distortion0 + distortion1) + lambda*(rate0 + rate1) |
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we just have to minimize: |
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distortion0 + lambda*rate0 |
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and |
and |
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distortion1 + lambda*rate1 |
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aka the 2 problems can be solved independantly |
distortion1 + lambda*rate1 |
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I.e, the 2 problems can be solved independently. |
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Author: Michael Niedermayer |
Author: Michael Niedermayer |
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Copyright: LGPL |
Copyright: LGPL |
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