16 | | There are a lot of clear filamentary structure that Amira is missing. |
| 10 | || Max || 2 || |
| 11 | || Saddle point || 1 || |
| 12 | || Min || 0 || |
| 13 | |
| 14 | After it does this, it considers pairs of critical points that only differ by 1 in the critical index (i.e. saddle points + max, or saddle points + min). These pairs are termed 'persistence pairs'. |
| 15 | |
| 16 | Now the persistence threshold is the difference between 2 points in a persistence pair. So if the points measure density, say, the threshold would say -- is the difference in density at the 2 critical points in the pair > or < the persistence threshold? If it is less than, that pair is thrown out. If it is greater than, it is kept. |
| 17 | |
| 18 | The idea is that pairs with lower 'persistence' (i.e. below the persistence threshold) are topologically weak structures -- meaning that they would not persist above some noise added to the data set. Even weak noise would disrupt the extrema in the pair such that they may no longer be extrema and thus the pair would be destroyed. Filtering the data using persistence is a way of keeping topologically relevant structures in the data set. Now, using the 'mean density' as a persistence threshold essentially gets rid of all data point pairs that are below the mean density (density is strictly positive). |
| 19 | |
| 20 | Now between all persistence pairs that survive, arcs are drawn that connect saddle points to the 2 extrema which connect to them (each saddle point is connected to exactly 2 extrema). Arcs are tangent lines to the gradient field in the data set. ''Filaments are, by default, arcs that connect a saddle point with 2 maximum''. |
| 21 | |
| 22 | = 11/6/15 - Using Amira with the mean density to create filaments = |
41 | | |
| 48 | = 10/5/15 = |
| 49 | |
| 50 | The "auto" skeletonization method appears to take a threshold as an input. This threshold seems to 'mask' (or 'segment') the data so to only look at voxels with values above this threshold. It then does a 'centerline' analysis, a 'distance map' analysis, and finally a 'thinning' of the skeleton so that it is only 1 voxel across. To see the paper on this algorithm, it is attached to this page. It is also possible to do these 3 steps on your own in Amira, and thus gain more control over the skeletonization process. |
| 51 | |
| 52 | Here are some results testing different thresholds in auto skeletonization mode, and comparing them to Federrath's figure (the paper that contains this figure is attached to this page). |
| 53 | |
| 54 | [[Image(compare5.png, 50%)]] |
| 55 | |
| 56 | [[Image(compare2.png, 50%)]] |
| 57 | |
| 58 | [[Image(compare1.png, 50%)]] |
| 59 | |
| 60 | [[Image(comparept01.png, 50%)]] |
| 61 | |
| 62 | |
| 63 | There are a lot of clear filamentary structure that Amira is missing. |