Characterisation of irregular spatial structures by parallel sets and integral geometric measures

Colloids and Surfaces A: Physicochemical and Engineering Aspects

Volumn 241, Issue 1-3, 2004, Pages 351-372

  Arns, C H ^a   Knackstedt, M A ^a   Mecke, K R ^b,c  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

^c UNIVERSITY OF STUTTGART   (Germany)

Author keywords

02.40. k; 05.40 a; 81.05.Rm; Euler number; Minkowski functional; Morphology; Porous media

Indexed keywords

CHARACTERIZATION; EROSION; MORPHOLOGY; SET THEORY;

DILATION OPERATIONS; RANDOM SYSTEMS;

SURFACE STRUCTURE;

ACCURACY; ANALYTIC METHOD; CONFERENCE PAPER; GEOMETRY; IMAGE ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MEASUREMENT; MORPHOLOGY; PRIORITY JOURNAL; STRUCTURE ANALYSIS;

EID: 4143100566     PISSN: 09277757     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.colsurfa.2004.04.034     Document Type: Conference Paper

References (58)

1. M. Joshi, A class of stochastic models for porous materials, Ph.D. thesis, University of Kansas, Lawrence, 1974.
2. Adler P.M., Jacquin C.G., Quiblier J.A. Flow in simulated porous media. Int. J. Multiphase Flow. 16:1990;691-712
3. Adler P., Jacquin C., Thovert J.-F. The formation factor of reconstructed porous media. Water Resour. Res. 28:1992;1571-1576
4. J. Serra (Ed.), Image Analysis and Mathematical Morphology, vol. 2, Theoretical Advances, Academic Press, New York, 1992.
5. Roberts A.P. Statistical reconstruction of three-dimensional porous media from two-dimensional images. Phys. Rev. E. 56:1997;3203-3212
6. Yeong C.L.Y., Torquato S. Reconstructing random media. Phys. Rev. E. 57:1998;495-506
7. Yeong C.L.Y., Torquato S. Reconstructing random media. II. Three-dimensional media from two-dimensional cuts. Phys. Rev. E. 58:1998;224-233
8. Coker D.A., Torquato S., Dunsmuir J.H. Morphology and physical properties of Fontainebleau sandstone via a tomographic analysis. J. Geophys. Res. 101:1996;17497-17506
9. A. Scheidegger, The Physics of Flow through Porous Media, University of Toronto Press, Toronto, 1974.
10. Manwart C., Torquato S., Hilfer R. Stochastic reconstruction of sandstones. Phys. Rev. E. 62(1):2000;893-899
11. R. Hilfer, Transport and Relaxation Phenomena in Porous Media, Advances in Chemical Physics, vol. XCII, Wiley, New York, 1958, pp. 299-424.
12. A. Rosenfeld, Digital Picture Processing, Academic Press, New York, 1976.
13. L.A. Santaló, Integral Geometry and Geometric Probability, Addison-Wesley, Reading, 1976.
14. Mecke K.R. Integral geometry and statistical physics. Int. J. Modern Phys. B. 12:1998;861-899
15. K.R. Mecke, Additivity, Convexity, and Beyond: Applications of Minkowski Functionals in Statistical Physics, Lecture Notes in Physics, vol. 554, Springer, Berlin, 2000, pp. 111-184.
16. K.R. Mecke, D. Stoyan (Eds.), Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation, Lecture Notes in Physics, vol. 554, Springer, Berlin, 2000.
17. K.R. Mecke, D. Stoyan (Eds.), Morphology of Condensed Matter: Physics and Geometry of Spatially Complex Systems, Lecture Notes in Physics, vol. 600, Springer, Berlin, 2002.
18. Mecke K.R. Morphological characterization of patterns in reaction diffusion systems. Phys. Rev. E. 53:1996;4794-4800
19. Jacobs K., Herminghaus S., Mecke K.R. Thin polymer films rupture via defects. Langmuir. 14:1998;965-969
20. K.R. Mecke, Integralgeometrie in der Statistischen Physik: Perkolation, komplexe Flüssigkeiten und die Struktur des Universums, Harry Deutsch, Frankfurt, 1994, pp. 61-68.
21. Tscheschel A., Stoyan D., Hilfer R. Erosion-dilation analysis for experimental and synthetic microstructures of sedimentary rock. Physica A. 284:2000;46-58
22. H. Hadwiger, Vorlesungenüber Inhalt, Oberfläche und Isoperimetrie, Springer, Berlin, 1957.
23. Miles R.E. Adv. Appl. Prob. 7:1975;818
24. W. Weil, Convexity and its Applications,, Ch. Stereology, Birkhäuser, 1983.
25. Mecke K.R., Wagner H. Euler characteristic and related measures for random geometric sets. J. Stat. Phys. 64:1991;843
26. M. Kerscher, Statistical analysis of large-scale structures in the universe, in: K.R. Mecke, D.Stoyan (Eds.), Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation, Lecture Notes in Physics, vol. 554, Springer, Berlin, 2000, pp. 36-71.
27. C.H. Arns, M.A. Knackstedt, W.V. Pinczewski, K.R. Mecke, Euler-Poincarè characteristics of classes of disordered media, Phys. Rev. E 63 (2001) 031112:1-13.
28. C.H. Arns, M.A. Knackstedt, K. Mecke, Characterising the morphology of disordered materials, Lecture Notes in Physics, vol. 600, Springer, Berlin, 2002, pp. 40-78.
29. Hyde S.T., Barnes I.S., Ninham B.W. Curvature energy of surfactant interfaces confined to the plaquettes of a cubic lattice. Langmuir. 6:1990;1055-1062
30. A.J. Baddeley, B.W. Silverman, A cautionary example on the use of second-order methods for analyzing point patterns, Biometrics 40 (1089-1094).
31. D. Stoyan, W.S. Kendall, J. Mecke, Stochastic Geometry and its Applications, Wiley, Chichester, 1995.
32. M. Kerscher, K. Mecke, P. Schücker, et.al., Non-Gaussian morphology on large scales: Minkowski functionals of the REFLEX cluster catalogue, Astron. Astrophys. 377 (2001) 1-16.
33. M. Kerscher, K. Mecke, J. Schmalzing, C. Beisbart, T. Buchert, H. Wagner, Morphological fluctuations of large-scale structure: the PSCz survey, Astron. Astrophys. 373 (2001) 1-11.
34. Mecke K., Buchert T., Wagner H. Robust morphological measure for large scale structure in the universe. Astron. Astrophys. 288:1994;697-704
35. M. Krüger, K.R. Mecke, Morphometry of spherical point patterns, in preparation for Astron. Astrophys.
36. Herminghaus S., Jacobs K., Mecke K., Bischof J., Frey A., Ibn-Elhaj M., Schlagowski S. Spinodal dewetting in liquid crystal and liquid metal films. Science. 282:1998;916-919
37. Borgefors G. Distance transformations in digital images. Comput. Vis. Graphics Image Process. 34:1986;344-371
38. Saito T., Toriwaki J.-I. New algorithms for Euclidean distance transformation of an n-dimensional digitized picture with applications. Pattern Recognit. 27(11):1994;1551-1565
39. Quiblier J. A new three-dimensional modeling technique for studying porous media. J. Colloid Interface Sci. 98:1984;84-102
40. Teubner M., Strey R. Origin of the scattering peak in microemulsions. J. Chem. Phys. 87:1987;3195-3200
41. Berk N.F. Scattering properties of the leveled-wave model of random morphologies. Phys. Rev. A. 44:1991;5069-5079
42. Marčelja S. Localized random wave description of continuous microemulsions. J. Phys. Chem. 94:1990;7259-7261
43. Roberts A.P., Knackstedt M. Structure-property correlations in model composite materials. Phys. Rev. E. 54:1996;2313-2328
44. Cahn J.W. Phase separation by spinodal decomposition in isotropic systems. J. Chem. Phys. 42:1965;93-99
45. Berk N.F. Scattering properties of a model bicontinuous structure with a well defined length scale. Phys. Rev. Lett. 58:1987;2718-2721
46. L. Gibson, M. Ashby, Cellular Solids: Structure and Properties, Pergamon Press, Oxford, 1988.
47. Mecke K. Morphology of spatial patterns: porous media, spinodal decomposition and dissipative structures. Acta Phys. Polonica B. 28:1997;1747-1781
48. W. Oh, W.B. Lindquist, Image thresholding by indicator kriging, IEEE Trans. Pattern Anal. Mach. Intell. 21 (1999) 590-602.
49. Flannery B.P., Deckman H.W., Roberge W.G., D'Amico K.L. Three-dimensional X-ray microtomography. Science. 237:1987;1439-1444
50. Dunsmuir J.H., Ferguson S.R., D'Amico K.L. Design and operation of an imaging X-ray detector for microtomography. IOP Conf. Ser. 121:1991;257-261
51. Spanne P., Thovert J.F., Jacquin C.J., Lindquist W.B., Jones K.W., Adler P.M. Synchotron computed microtomography of porous media: topology and transports. Phys. Rev. Lett. 73:1994;2001-2004
52. Lindquist W.B., Venkatarangan A. Investigating 3D geometry of porous media from high resolution images. PCEA. 25:1999;593-599
53. W.B. Lindquist, A. Venkatarangan, J. Dunsmuir, T.F. Wong, Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones, J. Geophys. Res. 105B (2000) 21509-21527.
54. C.H. Arns, M.A. Knackstedt, K. Mecke, Reconstructing complex materials via effective grain shapes, Phys. Rev. Lett. 91 (2003) 215506.
55. C.H. Arns, The influence of morphology on physical properties of reservoir rocks, Ph.D. thesis, University of New South Wales, 2002.
56. J.-F. Thovert, F. Yousefian, P. Spanne, C.G. Jacquin, P.M. Adler, Grain reconstruction of porous media: Application to a low-porosity Fontainebleau sandstone, Phys. Rev. E 63 (2001) 061307.
57. Øren P.E., Bakke S. Process based reconstruction of sandstones and prediction of transport properties. Transp. Porous Media. 46(2):2002;311-343
58. Roberts N., Reed M., Nesbitt G. Estimation of the connectivity of a synthetic porous medium. J. Microsc. 187:1997;110-118