Skeletonization on 3D tree-embedded graphs

Thinning is for extracting unit-width skeletons from original objects. Such unit-width skeletons are useful in analyzing tree-structured objects, such bronchi or blood tubes. A tree-structured object could be segmented as a graph since the tails of different branches of the object may be too close and taken as cycles. One possible approach for extracting a tree structure from an original tree-oriented object is to extract a unit-width skeleton, then extract a tree structure from the unit-width skeleton. One major drawback of this approach is that the information of the thickness of each branch is vanished in the first step where the thickness of a branch is important in deciding which voxel should be reduced and which should not. This paper proposes an approach to obtain unit width tree structures from original tree-embedded objects directly through the thinning process.