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+A quick description of Rate distortion theory.

+

+We want to encode a video, picture or music optimally.

+What does optimally mean?

+It means that we want to get the best quality at a given

+filesize OR (which is almost the same actually) We want to get the

+smallest filesize at a given quality.

+

+Solving this directly isnt practical, try all byte sequences

+1MB long and pick the best looking, yeah 256^1000000 cases to try ;)

+

+But first a word about Quality also called distortion, this can

+really be almost any quality meassurement one wants. Commonly the

+sum of squared differenes is used but more complex things that

+consider psychivisual effects can be used as well, it makes no differnce

+to us here.

+

+

+First step, that RD factor called lambda ...

+Lets consider the problem of minimizing

+

+distortion + lambda*rate

+

+for a fixed lambda, rate here would be the filesize, distortion the quality

+Is this equivalent to finding the best quality for a given max filesize?

+The awnser is yes, for each filesize limit there is some lambda factor for

+which minimizing above will get you the best quality (in your provided quality

+meassurement) at that (or a lower) filesize

+

+

+Second step, spliting the problem.

+Directly spliting the problem of finding the best quality at a given filesize

+is hard because we dont know how much filesize to assign to each of the

+subproblems optimally.

+But distortion + lambda*rate can trivially be split

+just consider

+(distortion0 + distortion1) + lambda*(rate0 +rate1)

+a problem made of 2 independant subproblems, the subproblems might be 2

+16x16 macroblocks in a frame of 32x16 size.

+to minimize

+(distortion0 + distortion1) + lambda*(rate0 +rate1)

+one just have to minimize

+distortion0 + lambda*rate0

+and

+distortion1 + lambda*rate1

+

+aka the 2 problems can be solved independantly

+

+Author: Michael Niedermayer

+Copyright: LGPL