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51 lines
1.8 KiB
Plaintext
51 lines
1.8 KiB
Plaintext
A quick description of Rate distortion theory.
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We want to encode a video, picture or music optimally.
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What does optimally mean?
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It means that we want to get the best quality at a given
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filesize OR (which is almost the same actually) We want to get the
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smallest filesize at a given quality.
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Solving this directly isnt practical, try all byte sequences
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1MB long and pick the best looking, yeah 256^1000000 cases to try ;)
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But first a word about Quality also called distortion, this can
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really be almost any quality meassurement one wants. Commonly the
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sum of squared differenes is used but more complex things that
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consider psychivisual effects can be used as well, it makes no differnce
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to us here.
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First step, that RD factor called lambda ...
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Lets consider the problem of minimizing
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distortion + lambda*rate
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for a fixed lambda, rate here would be the filesize, distortion the quality
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Is this equivalent to finding the best quality for a given max filesize?
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The awnser is yes, for each filesize limit there is some lambda factor for
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which minimizing above will get you the best quality (in your provided quality
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meassurement) at that (or a lower) filesize
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Second step, spliting the problem.
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Directly spliting the problem of finding the best quality at a given filesize
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is hard because we dont know how much filesize to assign to each of the
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subproblems optimally.
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But distortion + lambda*rate can trivially be split
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just consider
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(distortion0 + distortion1) + lambda*(rate0 +rate1)
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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.
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to minimize
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(distortion0 + distortion1) + lambda*(rate0 +rate1)
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one just have to minimize
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distortion0 + lambda*rate0
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and
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distortion1 + lambda*rate1
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aka the 2 problems can be solved independantly
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Author: Michael Niedermayer
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Copyright: LGPL
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