| 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: |
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| distortion0 + lambda*rate0 |
| |
| and |
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| distortion1 + lambda*rate1 |
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| I.e, the 2 problems can be solved independently. |
| |
| Author: Michael Niedermayer |
| Copyright: LGPL |