Detecting branching nodes of multiply connected 3D structures

In order to detect and analyze branching nodes in 3D images of micro-structures, the topology preserving thinning algorithm of Couprie and Zrour is jointly used with a constraint set derived from the spherical granulometry image. The branching points in the thus derived skeleton are subsequently merged guided by the local structure thickness as provided by the spherical granulometry. This enables correct merging of nodes and thus a correct calculation of the nodes' valences. The algorithm is validated using two synthetic foam structures with known vertices and valences. Subsequently, the algorithm is applied to micro-computed tomography data of a rigid aluminium foam where the valence is known, to the pore space of polar firn samples, and to corrosion casts of mice livers.