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Reconstructing Cell Complexes From Cross-sections

  • Scott E. Dillard
  • Dan Thoma
  • Bernd Hamann
Chapter
Part of the Mathematics and Visualization book series (MATHVISUAL)

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 oftantalum metal.

Keywords

Simplicial Complex Cell Complex Homotopy Equivalent Edge Contraction Vertex Removal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2011

Authors and Affiliations

  • Scott E. Dillard
    • 1
    • 2
  • Dan Thoma
    • 1
  • Bernd Hamann
    • 2
  1. 1.Los Alamos National LaboratoryMaterials Design InstituteLos AlamosUSA
  2. 2.Institute for Data Analysis and Visualization, Department of Computer ScienceUniversity of CaliforniaDavisUSA

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