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A Quick Description Of Rate Distortion Theory.
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We want to encode a video, picture or piece of music optimally. What does
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"optimally" really mean? It means that we want to get the best quality at a
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given filesize OR we want to get the smallest filesize at a given quality
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(in practice, these 2 goals are usually the same).
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Solving this directly is not practical; trying all byte sequences 1
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megabyte in length and selecting the "best looking" sequence will yield
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256^1000000 cases to try.
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But first, a word about quality, which is also called distortion.
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Distortion can be quantified by almost any quality measurement one chooses.
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Commonly, the sum of squared differences is used but more complex methods
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that consider psychovisual effects can be used as well. It makes no
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difference in this discussion.
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First step: that rate distortion factor called lambda...
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Let's consider the problem of minimizing:
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  distortion + lambda*rate
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rate is the filesize
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distortion is the quality
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lambda is a fixed value choosen as a tradeoff between quality and filesize
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Is this equivalent to finding the best quality for a given max
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filesize? The answer is yes. For each filesize limit there is some lambda
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factor for which minimizing above will get you the best quality (using your
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chosen quality measurement) at the desired (or lower) filesize.
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Second step: splitting the problem.
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Directly splitting the problem of finding the best quality at a given
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filesize is hard because we do not know how many bits from the total
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filesize should be allocated to each of the subproblems. But the formula
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from above:
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  distortion + lambda*rate
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can be trivially split. Consider:
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  (distortion0 + distortion1) + lambda*(rate0 + rate1)
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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
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  distortion1 + lambda*rate1
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I.e, the 2 problems can be solved independently.
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Author: Michael Niedermayer
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Copyright: LGPL