Reconstructing Cell Complexes From Cross-sections
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 oftantalum metal.
KeywordsSimplicial Complex Cell Complex Homotopy Equivalent Edge Contraction Vertex Removal
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- 2.T. Dey, H. Edelsbrunner, S. Guha, and D. Nekhayev. Topology preserving edge contraction. Publ. Inst. Math.(Beograd)(NS), 66(80):23–45, 1999.Google Scholar
- 3.S. Dillard, J. Bingert, D. Thoma, and B. Hamann. Construction of Simplified Boundary Surfaces from Serial-sectioned Metal Micrographs. IEEE Transactions on Visualization and Computer Graphics, pages 1528–1535, 2007.Google Scholar
- 4.A. Hatcher. Algebraic Topology. Cambridge University Press, 2002.Google Scholar
- 6.L. Nonato, A. Cuadros-Vargas, R. Minghim, and M. De Oliveira. Beta-connection: Generating a family of models from planar cross sections. ACM Transactions on Graphics (TOG), 24(4):1239–1258, 2005.Google Scholar