Reconstructing cell complexes from cross-sections

Abstract

Many interesting segmentations take the form of cell complexes. We present a method to infer a 3D cell complex from of a series of 2D cross-sections. We restrict our attention to the class of complexes whose duals resemble triangulations. This class includes microstructures of polycrystalline materials, as well as other cellular structures found in nature. Given a prescribed matching of 2D cells in adjacent cross-sections we produce a 3D complex spanning these sections such that matched 2-cells are contained in the interior of the same 3-cell. The reconstruction method considers only the topological structure of the input. After an initial 3D complex is recovered, the structure is altered to accommodate geometric properties of the dataset. We evaluate the method using ideal, synthetic datasets as well as serial-sectioned micrographs from a sample of tantalum metal.