repositories / deb_ffmpeg.git / blame
| Commit | Line | Data |
|---|---|---|
| 2ba45a60 DM |
1 | A Quick Description Of Rate Distortion Theory. |
| 2 | ||
| 3 | We want to encode a video, picture or piece of music optimally. What does | |
| 4 | "optimally" really mean? It means that we want to get the best quality at a | |
| 5 | given filesize OR we want to get the smallest filesize at a given quality | |
| 6 | (in practice, these 2 goals are usually the same). | |
| 7 | ||
| 8 | Solving this directly is not practical; trying all byte sequences 1 | |
| 9 | megabyte in length and selecting the "best looking" sequence will yield | |
| 10 | 256^1000000 cases to try. | |
| 11 | ||
| 12 | But first, a word about quality, which is also called distortion. | |
| 13 | Distortion can be quantified by almost any quality measurement one chooses. | |
| 14 | Commonly, the sum of squared differences is used but more complex methods | |
| 15 | that consider psychovisual effects can be used as well. It makes no | |
| 16 | difference in this discussion. | |
| 17 | ||
| 18 | ||
| 19 | First step: that rate distortion factor called lambda... | |
| 20 | Let's consider the problem of minimizing: | |
| 21 | ||
| 22 | distortion + lambda*rate | |
| 23 | ||
| 24 | rate is the filesize | |
| 25 | distortion is the quality | |
| 26 | lambda is a fixed value chosen as a tradeoff between quality and filesize | |
| 27 | Is this equivalent to finding the best quality for a given max | |
| 28 | filesize? The answer is yes. For each filesize limit there is some lambda | |
| 29 | factor for which minimizing above will get you the best quality (using your | |
| 30 | chosen quality measurement) at the desired (or lower) filesize. | |
| 31 | ||
| 32 | ||
| 33 | Second step: splitting the problem. | |
| 34 | Directly splitting the problem of finding the best quality at a given | |
| 35 | filesize is hard because we do not know how many bits from the total | |
| 36 | filesize should be allocated to each of the subproblems. But the formula | |
| 37 | from above: | |
| 38 | ||
| 39 | distortion + lambda*rate | |
| 40 | ||
| 41 | can be trivially split. Consider: | |
| 42 | ||
| 43 | (distortion0 + distortion1) + lambda*(rate0 + rate1) | |
| 44 | ||
| 45 | This creates a problem made of 2 independent subproblems. The subproblems | |
| 46 | might be 2 16x16 macroblocks in a frame of 32x16 size. To minimize: | |
| 47 | ||
| 48 | (distortion0 + distortion1) + lambda*(rate0 + rate1) | |
| 49 | ||
| 50 | we just have to minimize: | |
| 51 | ||
| 52 | distortion0 + lambda*rate0 | |
| 53 | ||
| 54 | and | |
| 55 | ||
| 56 | distortion1 + lambda*rate1 | |
| 57 | ||
| 58 | I.e, the 2 problems can be solved independently. | |
| 59 | ||
| 60 | Author: Michael Niedermayer | |
| 61 | Copyright: LGPL |