A quick description of Rate distortion theory.

Originally committed as revision 17774 to svn://svn.ffmpeg.org/ffmpeg/trunk

doc/rate_distortion.txt

+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