References

The Minkowski tensor algorithms implemented in the morphometer are described in the following publications:

  • [DOI] G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, F. M. Schaller, B. Breidenbach, D. Hug, and K. Mecke, “Minkowski tensors of anisotropic spatial structure,” New journal of physics, vol. 15, iss. 8, p. 83028, 2013.
  • [DOI] G. E. Schröder-Turk, W. Mickel, S. C. Kapfer, M. A. Klatt, F. M. Schaller, M. J. F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, and K. Mecke, “Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures,” Adv. mater., vol. 23, iss. 22-23, p. 2535–2553, 2011.
Statistical physics and condensed matter:
  • [DOI] M. E. Evans, G. E. Schröder-Turk, and A. M. Kraynik, “A geometric exploration of stress in deformed liquid foams,” Journal of physics: condensed matter, vol. 29, iss. 12, p. 124004, 2017.
  • M. A. Klatt, “Morphometry of random spatial structures in physics,” PhD Thesis, Erlangen, 2016.
  • [DOI] F. M. Schaller, S. C. Kapfer, J. E. Hilton, P. W. Cleary, K. Mecke, C. D. Michele, T. Schilling, M. Saadatfar, M. Schröter, G. W. Delaney, and G. E. Schröder-Turk, “Non-universal Voronoi cell shapes in amorphous ellipsoid packs,” Epl (europhysics letters), vol. 111, iss. 2, p. 24002, 2015.
  • [DOI] C. Scholz, F. Wirner, M. A. Klatt, D. Hirneise, G. E. Schröder-Turk, K. Mecke, and C. Bechinger, “Direct relations between morphology and transport in Boolean models,” Physical review e, vol. 92, iss. 4, p. 43023, 2015.
  • [DOI] M. A. Klatt and S. Torquato, “Characterization of maximally random jammed sphere packings: Voronoi correlation functions,” Physical review e, vol. 90, iss. 5, p. 52120, 2014.
  • [DOI] M. E. Evans, A. M. Kraynik, D. A. Reinelt, K. Mecke, and G. E. Schröder-Turk, “Networklike propagation of cell-level stress in sheared random foams,” Phys. rev. lett., vol. 111, p. 138301, 2013.
  • S. Kapfer, “Morphometry and Physics of Particulate and Porous Media, Morphometrie und Physik Korpuskularer und Poröser Medien,” PhD Thesis, Erlangen, 2011.
  • [DOI] G. E. Schröder-Turk, W. Mickel, M. Schröter, G. W. Delaney, M. Saadatfar, T. J. Senden, K. Mecke, and T. Aste, “Disordered spherical bead packs are anisotropic,” Epl (europhysics letters), vol. 90, iss. 3, p. 34001, 2010.
  • [DOI] S. C. Kapfer, W. Mickel, F. M. Schaller, M. Spanner, C. Goll, T. Nogawa, N. Ito, K. Mecke, and G. E. Schröder-Turk, “Local anisotropy of fluids using Minkowski tensors,” Journal of statistical mechanics: theory and experiment, vol. 2010, iss. 11, p. P11010, 2010.
  • Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation, K. R. Mecke and D. Stoyan, Eds., Berlin Heidelberg: Springer-Verlag, 2000.
  • [DOI] K. R. Mecke and H. Wagner, “Euler characteristic and related measures for random geometric sets,” Journal of statistical physics, vol. 64, iss. 3-4, p. 843–850, 1991.
Mathematical models of physical systems:
  • [DOI] M. A. Klatt, G. Last, K. Mecke, C. Redenbach, F. M. Schaller, and G. E. Schröder-Turk, “Cell Shape Analysis of Random Tessellations Based on Minkowski Tensors,” in Tensor Valuations and Their Applications in Stochastic Geometry and Imaging, Springer, Cham, 2017, p. 385–421.
  • [DOI] M. A. Klatt, G. E. Schröder-Turk, and K. Mecke, “Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals,” J. stat. mech. theor. exp., vol. 2017, iss. 2, p. 23302, 2017.
  • [DOI] D. Hug, G. Last, and M. Schulte, “Second-order properties and central limit theorems for geometric functionals of Boolean models,” The annals of applied probability, vol. 26, iss. 1, p. 73–135, 2016.
  • [DOI] J. Hörrmann, D. Hug, M. A. Klatt, and K. Mecke, “Minkowski tensor density formulas for Boolean models,” Advances in applied mathematics, vol. 55, p. 48–85, 2014.
Nuclear physics:
  • [DOI] B. Schuetrumpf, M. A. Klatt, K. Iida, G. E. Schröder-Turk, J. A. Maruhn, K. Mecke, and P. -G. Reinhard, “Appearance of the single gyroid network phase in “nuclear pasta” matter,” Physical review c, vol. 91, iss. 2, 2015.
  • [DOI] B. Schuetrumpf, M. A. Klatt, K. Iida, J. A. Maruhn, K. Mecke, and P. -G. Reinhard, “Time-dependent Hartree-Fock approach to nuclear “pasta” at finite temperature,” Physical review c, vol. 87, iss. 5, 2013.
  • [DOI] H. Sonoda, G. Watanabe, K. Sato, K. Yasuoka, and T. Ebisuzaki, “Phase diagram of nuclear “pasta” and its uncertainties in supernova cores,” Physical review c, vol. 77, iss. 3, p. 35806, 2008.
  • [DOI] G. Watanabe, K. Sato, K. Yasuoka, and T. Ebisuzaki, “Phases of hot nuclear matter at subnuclear densities,” Physical review c, vol. 69, iss. 5, p. 55805, 2004.
  • [DOI] G. Watanabe, K. Sato, K. Yasuoka, and T. Ebisuzaki, “Structure of cold nuclear matter at subnuclear densities by quantum molecular dynamics,” Physical review c, vol. 68, iss. 3, p. 35806, 2003.
Astronomy and cosmology:
  • D. Göring, M. Klatt, C. Stegmann, and K. Mecke, “Morphometric analysis in gamma-ray astronomy using Minkowski functionals – source detection via structure quantification,” Astronomy & astrophysics, vol. 555, p. A38, 2013.
  • [DOI] M. Kerscher, K. Mecke, J. Schmalzing, C. Beisbart, T. Buchert, and H. Wagner, “Morphological fluctuations of large-scale structure: The PSCz survey,” Astronomy & astrophysics, vol. 373, iss. 1, p. 1–11, 2001.
  • [DOI] M. Kerscher, K. Mecke, P. Schuecker, H. Böhringer, L. Guzzo, C. A. Collins, S. Schindler, D. S. Grandi, and R. Cruddace, “Non-Gaussian morphology on large scales: Minkowski functionals of the REFLEX cluster catalogue,” Astronomy & astrophysics, vol. 377, iss. 1, p. 1–16, 2001.
Biology and medicine:
  • [DOI] B. D. Wilts, B. A. Zubiri, M. A. Klatt, B. Butz, M. G. Fischer, S. T. Kelly, E. Spiecker, U. Steiner, and G. E. Schröder-Turk, “Butterfly gyroid nanostructures as a time-frozen glimpse of intracellular membrane development,” Science advances, vol. 3, iss. 4, p. e1603119, 2017.
  • [DOI] M. A. Klatt, G. E. Schröder-Turk, and K. Mecke, “Mean-intercept anisotropy analysis of porous media. II. conceptual shortcomings of the MIL tensor definition and Minkowski tensors as an alternative,” Medical physics, vol. 44, iss. 7, pp. 3663-3675.
  • [DOI] M. Barbosa, R. Natoli, K. Valter, J. Provis, and T. Maddess, “Integral-geometry characterization of photobiomodulation effects on retinal vessel morphology,” Biomedical optics express, vol. 5, iss. 7, p. 2317–2332, 2014.
  • [DOI] C. Beisbart, M. S. Barbosa, H. Wagner, and L. F. da Costa, “Extended morphometric analysis of neuronal cells with Minkowski valuations,” The european physical journal b – condensed matter and complex systems, vol. 52, iss. 4, p. 531–546, 2006.
Pattern analysis:
  • [DOI] C. Scholz, G. E. Schröder-Turk, and K. Mecke, “Pattern-fluid interpretation of chemical turbulence,” Physical review e, vol. 91, iss. 4, p. 42907, 2015.
  • [DOI] H. Mantz, K. Jacobs, and K. Mecke, “Utilizing Minkowski functionals for image analysis: a marching square algorithm,” Journal of statistical mechanics: theory and experiment, vol. 2008, iss. 12, p. P12015, 2008.
  • [DOI] J. Becker, G. Grün, R. Seemann, H. Mantz, K. Jacobs, K. R. Mecke, and R. Blossey, “Complex dewetting scenarios captured by thin-film models,” Nature materials, vol. 2, iss. 1, p. 59–63, 2003.
  • [DOI] K. R. Mecke, “Morphological characterization of patterns in reaction-diffusion systems,” Physical review e, vol. 53, iss. 5, p. 4794–4800, 1996.
Statistics and stereology:
  • B. Ebner, N. Henze, M. A. Klatt, and K. Mecke, “Goodness-of-fit tests for complete spatial randomness based on Minkowski functionals of binary images,” Arxiv:1710.02333 [math, stat], 2017.
  • [DOI] A. Kousholt, M. Kiderlen, and D. Hug, “Surface tensor estimation from linear sections,” Mathematische nachrichten, vol. 288, iss. 14-15, p. 1647–1672, 2015.
  • A. Baddeley and E. V. B. Jensen, Stereology for statisticians, CRC Press, 2004.
Integral geometry:
  • [DOI] D. Hug and J. A. Weis, “Kinematic formulae for tensorial curvature measures,” Annali di matematica pura ed applicata (1923-), vol. 197, iss. 5, p. 1349–1384, 2018.
  • [DOI] D. Hug and J. A. Weis, “Crofton formulae for tensorial curvature measures: the general case,” in Analytic aspects of convexity, Springer, 2018, p. 39–60.
  • [DOI] A. Bernig and D. Hug, “Integral geometry and algebraic structures for tensor valuations,” in Tensor valuations and their applications in stochastic geometry and imaging, Springer, 2017, p. 79–109.
  • D. Hug and J. A. Weis, “Integral geometric formulae for minkowski tensors,” Arxiv preprint arxiv:1712.09699, 2017.
  • [DOI] D. Hug and R. Schneider, “Tensor valuations and their local versions,” in Tensor valuations and their applications in stochastic geometry and imaging, Springer, 2017, p. 27–65.
  • [DOI] D. Hug and R. Schneider, “Local tensor valuations,” Geometric and functional analysis, vol. 24, iss. 5, p. 1516–1564, 2014.
Digital image analysis:
  • [DOI] D. Hug, M. Kiderlen, and A. M. Svane, “Voronoi-based estimation of minkowski tensors from finite point samples,” Discrete & computational geometry, vol. 57, iss. 3, p. 545–570, 2017.