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