## ffmpeg / doc / viterbi.txt @ 22b6a24c

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1 | dc7d978a | Michael Niedermayer | This is a quick description of the viterbi aka dynamic programing |
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2 | algorthm. |
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3 | |||

4 | Its reason for existence is that wikipedia has become very poor on |
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5 | describing algorithms in a way that makes it useable for understanding |
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6 | them or anything else actually. It tends now to describe the very same |
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7 | algorithm under 50 different names and pages with few understandable |
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8 | by even people who fully understand the algorithm and the theory behind. |
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9 | |||

10 | Problem description: (that is what it can solve) |
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11 | assume we have a 2d table, or you could call it a graph or matrix if you |
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12 | prefer |
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13 | |||

14 | O O O O O O O |
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15 | |||

16 | O O O O O O O |
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17 | |||

18 | O O O O O O O |
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19 | |||

20 | O O O O O O O |
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21 | |||

22 | |||

23 | That table has edges connecting points from each column to the next column |
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24 | and each edge has a score like: (only some edge and scores shown to keep it |
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25 | readable) |
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26 | |||

27 | |||

28 | O--5--O-----O-----O-----O-----O |
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29 | 2 / 7 / \ / \ / \ / |
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30 | \ / \ / \ / \ / \ / |
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31 | O7-/--O--/--O--/--O--/--O--/--O |
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32 | \/ \/ 1/ \/ \/ \/ \/ \/ \/ \/ |
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33 | /\ /\ 2\ /\ /\ /\ /\ /\ /\ /\ |
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34 | O3-/--O--/--O--/--O--/--O--/--O |
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35 | / \ / \ / \ / \ / \ |
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36 | 1 \ 9 \ / \ / \ / \ |
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37 | O--2--O--1--O--5--O--3--O--8--O |
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38 | |||

39 | |||

40 | |||

41 | Our goal is to find a path from left to right through it which |
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42 | minimizes the sum of the score of all edges. |
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43 | (and of course left/right is just a convention here it could be top down too) |
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44 | Similarly the minimum could be the maximum by just fliping the sign, |
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45 | Example of a path with scores: |
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46 | |||

47 | O O O O O O O |
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48 | |||

49 | >---O. O O .O-2-O O O |
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50 | 5. .7 . |
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51 | O O-1-O O O 8 O O |
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52 | . |
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53 | O O O O O O-1-O---> (sum here is 24) |
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54 | |||

55 | |||

56 | The viterbi algorthm now solves this simply column by column |
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57 | For the previous column each point has a best path and a associated |
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58 | score: |
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59 | |||

60 | O-----5 O |
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61 | \ |
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62 | \ |
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63 | O \ 1 O |
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64 | \/ |
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65 | /\ |
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66 | O / 2 O |
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67 | / |
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68 | / |
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69 | O-----2 O |
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70 | |||

71 | |||

72 | To move one column forward we just need to find the best path and associated |
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73 | scores for the next column |
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74 | here are some edges we could choose from: |
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75 | |||

76 | |||

77 | O-----5--3--O |
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78 | \ \8 |
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79 | \ \ |
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80 | O \ 1--9--O |
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81 | \/ \3 |
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82 | /\ \ |
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83 | O / 2--1--O |
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84 | / \2 |
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85 | / \ |
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86 | O-----2--4--O |
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87 | |||

88 | Finding the new best pathes and scores for each point of our new column is |
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89 | trivial given we know the previous column best pathes and scores: |
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90 | |||

91 | O-----0-----8 |
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92 | \ |
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93 | \ |
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94 | O \ 0----10 |
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95 | \/ |
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96 | /\ |
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97 | O / 0-----3 |
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98 | / \ |
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99 | / \ |
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100 | O 0 4 |
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101 | |||

102 | |||

103 | the viterbi algorthm continues exactly like this column for column until the |
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104 | end and then just picks the path with the best score (above that would be the |
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105 | one with score 3) |
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106 | |||

107 | |||

108 | Author: Michael niedermayer |
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109 | Copyright LGPL |