Three-dimensional skeletonizing and topological analysis of bicontinuous network structures

A novel method to measure the topological features of three-dimensional (3D) network structures is presented. It involves skeletonizing 3D structures using a new axis thinning ("skeletonization") algorithm. The 3D structures were imaged by laser scanning confocal microscopy (LSCM), and by transmission electron microscopy (TEM) assisted by computer tomography (CT). Unlike the existing 3D skeletonization techniques, the proposed method provides the rules for skeletonizing at the edge planes of the volume data. The algorithm assures the positions of the junctions. They are useful in the evaluation of the topological quantities of the network, which were neglected in the existing 3D skeletonization algorithms. The 3D skeletonization was thoroughly tested using a model network structure. Gyroid, which is one of the infinite periodic minimal surfaces (IPMS). We confirmed that the method was robust and gave an accurate number of junctions.