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Part A: Materials Science

Fitting Laguerre tessellation approximations to tomographic image data

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Pages 166-189 | Received 06 Aug 2015, Accepted 23 Nov 2015, Published online: 12 Jan 2016

References

  • K.M. Döbrich, C. Rau, and C.E. Krill III, Quantitative characterization of the three-dimensional microstructure of polycrystalline Al-Sn using X-ray microtomography, Metall. Mater. Trans. A 35A (2004), p. 1953–1961.
  • D.J. Rowenhorst, J.P. Kuang, K. Thornton, and P.W. Voorhees, Three-dimensional analysis of particle coarsening in high volume fraction solid-liquid mixtures, Acta Mater. 54 (2006), p. 2027–2039.
  • N. Limodin, L. Salvo, M. Suéry, and M. DiMichiel, In situ investigation by X-ray tomography of the overall and local microstructural changes occurring during partial remelting of an Al–15.8wt.% Cu alloy, Acta Mater. 55 (2007), p. 3177–3191.
  • M. Groeber, S. Ghosh, M.D. Uchic, and D.M. Dimiduk, A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 1: Statistical characterization, Acta Mater. 56 (2008), p. 1257–1273.
  • W. Ludwig, A. King, P. Reischig, M. Herbig, E.M. Lauridsen, S. Schmidt, H. Proudhon, S. Forest, P. Cloetens, S. Rolland du Roscoat, J.Y. Buffière, T.J. Marrow, and H.F. Poulsen, New opportunities for 3D materials science of polycrystalline materials at the micrometre lengthscale by combined use of X-ray diffraction and X-ray imaging, Mater. Sci. Eng. A 524 (2009), p. 69–76.
  • A. Lyckegaard, E.M. Lauridsen, W. Ludwig, R.W. Fonda, and H.F. Poulsen, On the use of Laguerre tessellations for representations of 3D grain structures, Adv. Eng. Mater. 13 (2011), p. 165–170.
  • T. Werz, M. Baumann, U. Wolfram, and C.E. Krill III, Particle tracking during Ostwald ripening using time-resolved laboratory X-ray microtomography, Mater. Charact. 90 (2014), p. 185–195.
  • A. Spettl, R. Wimmer, T. Werz, M. Heinze, S. Odenbach, C.E. Krill III, and V. Schmidt, Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase, Modell. Simul. Mater. Sci. Eng. 23 (2015), p. 065001.
  • Z. Fan, Y. Wu, X. Zhao, and Y. Lu, Simulation of polycrystalline structure with Voronoi diagram in Laguerre geometry based on random closed packing of spheres, Comput. Mater. Sci. 29 (2004), p. 301–308.
  • M. Beil, S. Eckel, F. Fleischer, H. Schmidt, V. Schmidt, and P. Walther, A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 2: Synthetic structure generation, J. Theor. Biol. 241 (2006), p. 62–72.
  • M. Groeber, S. Ghosh, M.D. Uchic, and D.M. Dimiduk, A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 2: Synthetic structure generation, Acta Mater. 56 (2008), p. 1274–1287.
  • C. Lautensack, Fitting three-dimensional Laguerre tessellations to foam structures, J. Appl. Stat. 35 (2008), p. 985–995.
  • C. Lautensack, H. Ewe, P. Klein, and T. Sych, 3D characterization, modeling and effective thermal conductivity of open aluminium foams, in Aluminium Alloys -- Their Physical and Mechanical Properties, J. Hirsch, B. Skrotski, and G. Gottstein, Wiley-VCH, Weinheim, 2008, p. 1368–1374.
  • V. Schmidt, G. Gaiselmann, and O. Stenzel, Stochastic 3D models for the micro-structure of advanced functional materials, in Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms, V. Schmidt, ed., Springer, Cham, 2015, p. 95–141.
  • C. Redenbach and A. Liebscher, Random tessellations and their application to the modelling of cellular materials, in Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms, V. Schmidt, ed., Springer, Cham, 2015, p. 73–93.
  • D. Westhoff, J.J. van Franeker, T. Brereton, D.P. Kroese, R.A.J. Janssen, and V. Schmidt, Stochastic modeling and predictive simulations for the microstructure of organic semiconductor films processed with different spin coating velocities, Modell. Simul. Mater. Sci. Eng. 23 (2015), p. 045003.
  • S.N. Chiu, D. Stoyan, W.S. Kendall, and J. Mecke, Stochastic Geometry and its Applications, 3rd ed., John Wiley & Sons, Chichester, 2013.
  • A. Okabe, B. Boots, K. Sugihara, and S.N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd ed., Wiley, Chichester, 2000.
  • H. Telley, T.M. Liebling, A. Mocellin, and F. Righetti, Simulating and modelling grain growth as the motion of a weighted Voronoi diagram, Mater. Sci. Forum 94–96 (1992), p. 301–306.
  • H. Telley, T.M. Liebling, and A. Mocellin, The Laguerre model of grain growth in two dimensions: I. Cellular structures viewed as dynamical Laguerre tessellations, Philos. Mag. B 73 (1996), p. 395–408.
  • H. Telley, T.M. Liebling, and A. Mocellin, The Laguerre model of grain growth in two dimensions: II. Examples of coarsening simulations, Philos. Mag. B 73 (1996), p. 409–427.
  • X. Xue, F. Righetti, H. Telley, and T.M. Liebling, The Laguerre model for grain growth in three dimensions, Philos. Mag. B 75 (1997), p. 567–585.
  • C. Lautensack and T. Sych, 3D image analysis of open foams using random tessellations, Image Anal. Stereol. 25 (2006), p. 87–93.
  • A. Liebscher, Stochastic modelling of foams, Ph.D. diss., TU Kaiserslautern, Fachbereich Mathematik, 2014.
  • P.F. Ash and E.D. Bolker, Recognizing Dirichlet tessellations, Geom. Dedic. 19 (1985), p. 175–206.
  • D.G. Evans and S.M. Jones, Detecting Voronoi (area-of-influence) polygons, Math. Geol. 19 (1987), p. 523–537.
  • F. Aurenhammer, Recognising polytopical cell complexes and constructing projection polyhedra, J. Symb. Comput. 3 (1987), p. 249–255.
  • D. Hartvigsen, Recognizing Voronoi diagrams with linear programming, ORSA J. Comput. 4 (1992), p. 369–374.
  • F.P. Schoenberg, T. Ferguson, and C. Li, Inverting Dirichlet tessellations, Comput. J. 46 (2003), p. 76–83.
  • A. Adamatzky, Massively parallel algorithm for inverting Voronoi diagram, Neural Netw. World 5 (1993), p. 385–392.
  • Q. Duan, D.P. Kroese, T. Brereton, A. Spettl, and V. Schmidt, Inverting Laguerre tessellations, Comput. J. 57 (2014), p. 1431–1440.
  • A. Suzuki and M. Iri, Approximation of a tessellation of the plane by a Voronoi diagram, J. Oper. Res. Soc. Jpn. 29 (1986), p. 69–96.
  • A. Liebscher, D. Jeulin, and C. Lantuéjoul, Stereological reconstruction of polycrystalline materials, J. Microsc. 258 (2015), p. 190–199.
  • A. Alpers, A. Brieden, P. Gritzmann, A. Lyckegaard, and H. Poulsen, Generalized balanced power diagrams for 3D representations of polycrystals, Philos. Mag. 95 (2015), p. 1016–1028.
  • A. Liebscher, Laguerre approximation of random foams, Philos. Mag. 95 (2015), p. 2777–2792.
  • R.Y. Rubinstein and D.P. Kroese, The Cross-entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning, Springer, New York, 2004.
  • D.P. Kroese, S. Porotsky, and R.Y. Rubinstein, The cross-entropy method for continuous multi-extremal optimization, Method. Comput. Appl. Probab. 8 (2006), p. 383–407.
  • D.P. Kroese, T. Taimre, and Z.I. Botev, Handbook of Monte Carlo Methods, John Wiley & Sons, Hoboken, 2011.
  • Z.I. Botev, D.P. Kroese, R.Y. Rubinstein, and P. L’Ecuyer, The cross-entropy method for optimization, in Machine Learning: Theory and Applications, V. Govindaraju and C.R. Rao, eds., North-Holland, Oxford, 2013, p. 35–59.
  • F. Aurenhammer, Power diagrams: properties, algorithms and applications, SIAM J. Comput. 16 (1987), p. 78–96.
  • K. Sugihara, Three-dimensional convex hull as a fruitful source of diagrams, Theor. Comput. Sci. 235 (2000), p. 325–337.
  • H. Imai, M. Iri, and K. Murota, Voronoi diagram in the Laguerre geometry and its applications, SIAM J. Comput. 14 (1985), p. 93–105.
  • C. Lautensack, Random Laguerre Tessellations, Verlag Lautensack, Weiler bei Bingen, 2007.
  • F. Aurenhammer, A criterion for the affine equivalence of cell complexes Rd and convex polyhedra in Rd+1, Discrete Comput. Geom. 2 (1987), p. 49–64.
  • J.B.T.M. Roerdink and A. Meijster, The watershed transform: definitions, algorithms, and parallellization strategies, Fund. Inform. 41 (2001), p. 187–228.
  • O. Brunke, S. Odenbach, and F. Beckmann, Quantitative methods for the analysis of synchrotron-µCT datasets of metallic foams, Eur. Phys. J. Appl. Phys. 29 (2005), p. 73–81.
  • S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, Optimization by simulated annealing, Science 220 (1983), p. 671–680.
  • A. Spettl, T. Werz, C.E. Krill III, and V. Schmidt, Parametric representation of 3D grain ensembles in polycrystalline microstructures, J. Stat. Phys. 154 (2014), p. 913–928.
  • P.P.N. de Groen, An introduction to total least squares, Nieuw Archief voor Wiskunde, 4th Series 14 (1996), p. 237–253.
  • J. Illian, A. Penttinen, H. Stoyan, and D. Stoyan, Statistical Analysis and Modelling of Spatial Point Patterns, John Wiley & Sons, Chichester, 2008.
  • H. Altendorf, F. Latourte, D. Jeulin, M. Faessel, and L. Saintoyant, 3D reconstruction of a multiscale microstructure by anisotropic tessellation models, Image Anal. Stereol. 33 (2014), p. 121–130.

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