Analysis of Spatial Point Patterns in Microscopic and Macroscopic Biological Image Data

  • Frank Fleischer
  • Michael Beil
  • Marian Kazda
  • Volker Schmidt
Part of the Lecture Notes in Statistics book series (LNS, volume 185)


Point process characteristics like for example Ripley’s K-function, the L-function or Baddeley’s J-function are especially useful for cases of data with significant differences with respect to intensities. We will discuss two examples in the fields of cell biology and ecology were these methods can be applied. They have been chosen, because they demonstrate the wide range of applications for the described techniques and because both examples have specific interest- ing properties. While the point patterns regarded in the first application are three dimensional, the second application reveals planar point patterns having a vertically inhomogeneous structure.

Key words

Baddeley’s J-function Centromeric Heterochromatin Structures CSR Planar Sections of Root Systems in Tree Stands Ripley’s K-function 


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  1. [1]
    I. Alcobia, A.S. Quina, H. Neves, N. Clode and L. Parreira. The spatial organization of centromeric heterochromatin during normal human lymphopoiesis: evidence for ontogenically determined spatial patterns. Experimental Cell Research, 290:358–369, 2003.CrossRefGoogle Scholar
  2. [2]
    A.J. Baddeley. Spatial sampling and censoring. In W. S. Kendall, M.N.M. van Lieshout and O.E. Barndorff-Nielsen, editors, Current Trends in Stochastic Geometry and its Applications. Chapman and Hall, 1998.Google Scholar
  3. [3]
    A.J. Baddeley and R.D. Gill. Kaplan-Meier estimators of distance distribution for spatial point processes. The Annals of Statistics, 25(1):263–292, 1997.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    M. Beil, D. Durschmied, S. Paschke, B. Schreiner, U. Nolte, A. Bruel and T. Irinopoulou. Cytometry. Spatial distribution patterns of interphase centromeres during retinoic acid-induced differentiation of promyelocytic leukemia cells, 47:217–225, 2002.Google Scholar
  5. [5]
    M. Beil, F. Fleischer, S. Paschke and V. Schmidt. Statistical analysis of 3d centromeric heterochromatin structure in interphase nuclei. Journal of Microscopy, 217:60–68, 2005.MathSciNetCrossRefGoogle Scholar
  6. [6]
    M.M. Caldwell, J.H. Manwaring and S.L. Durham. Species interaction at the level of fineroots in the field: influence of soil nutrient heterogeneity and plant size. Oecologia, 106:440–447, 1996.CrossRefGoogle Scholar
  7. [7]
    S.N. Chiu and D. Stoyan. Estimators of distance distributions for spatial patterns. Statistica Neerlandica, 52(2):239–246, 1998.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    M. Cremer, K. Kupper, B. Wagler, L. Wizelman, J. von Hase, Y. Weiland, L. Kreja, J. Diebold, M. R. Speicher and T. Cremer. Inheritance of gene density-related higher order chromatin arrangements in normal and tumor cell nuclei. The Journal of Cell Biology, 162:809–820, 2003.CrossRefGoogle Scholar
  9. [9]
    T. Cremer and C. Cremer. Chromosome territories, nuclear architecture and gene regulation in mammalian cells. Nature Reviews Genetics, 2:292–301, 2001.CrossRefGoogle Scholar
  10. [10]
    H. de The, C. Chomienne, M. Lanotte, L. Degos and A. Dejean. The t(15;17) translocation of acute promyelocytic leukaemia fuses the retinoic acid receptor alpha gene to a novel transcribed locus. Nature, 347:558–561, 1990.CrossRefGoogle Scholar
  11. [11]
    P.J. Diggle. Statistical Analysis of Spatial Point Patterns, 2nd ed. Oxford University Press, 2003.Google Scholar
  12. [12]
    P.J. Diggle, J. Mateu and H.E. Clough. A comparison between parametric and non-parametric approaches to the analysis of replicated spatial point patterns. Advances in Applied Probability, 32:331–343, 2000.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    M.C. Drew. Comparison of the effects of a localized supply of phosphate, nitrate, ammonium and potassium on the growth of the seminal root system, and the shoot, of barley. New Phytologist, 75:479–490, 1975.CrossRefGoogle Scholar
  14. [14]
    C. Dussert, G. Rasigni, J. Palmari, M. Rasigni, A. Llebaria and F. Marty. Minimal spanning tree analysis of biological structures. Journal of Theoretical Biology, 125:317–323, 1987.Google Scholar
  15. [15]
    C. Dussert, G. Rasigni, M. Rasigni, J. Palmari and A. Llebaria. Minimal spanning tree: a new approach for studying order and disorder. Physical Revue B, 34:3528–3531, 1986.CrossRefGoogle Scholar
  16. [16]
    P. Fenaux, C. Chomienne and L. Degos. Acute promyelocytic leukemia: biology and treatment. Seminars in Oncology, 24:92–102, 1997.Google Scholar
  17. [17]
    F. Fleischer, S. Eckel, I. Schmid, V. Schmidt and M. Kazda. Statistical analysis of the spatial distribution of tree roots in pure stands of fagus sylvatica and picea abies. Preprint, 2005.Google Scholar
  18. [18]
    T. Haaf and M. Schmid. Chromosome topology in mammalian interphase nuclei. Experimental Cell Research, 192:325–332, 1991.CrossRefGoogle Scholar
  19. [19]
    K.-H. Hanisch. Some remarks on estimators of the distribution function of nearest-neighbor distance in stationary spatial point patterns. Statistics, 15:409–412, 1984.zbMATHMathSciNetGoogle Scholar
  20. [20]
    R.B. Jackson and M.M. Caldwell. Geostatistical patterns of soil heterogeneity around individual perennial plants. Journal of Ecology, 81:683–692, 1993.Google Scholar
  21. [21]
    R.B. Jackson and M.M. Caldwell. Integrating resource heterogeneity and plant plasticity: modeling nitrate and phosphate uptake in a patchy soil environment. Journal of Ecology, 84:891–903, 1996.Google Scholar
  22. [22]
    J. Janevski, P.C. Park and U. De Boni. Organization of centromeric domains in hepatocyte nuclei: rearrangement associated with de novo activation of the vitellogenin gene family in xenopus laevis. Experimental Cell Research, 217:227–239, 1995.CrossRefGoogle Scholar
  23. [23]
    G. Krauss, K. Müller, G. Gärtner, F. Härtel, H. Schanz and H. Blanckmeister. Standortsgemässe durchführung der abkehr von der fichtenwirtschaft im nordwestsächsischen niederland. Tharandter Forstl. Jahrbuch, 90:481–715, 1939.Google Scholar
  24. [24]
    M. Lanotte, V. Martin-Thouvenin, S. Najman, P. Balerini, F. Valensi and R. Berger. Nb4, a maturation inducible cell line with t(15;17) marker isolated from a human acute promyelocytic leukemia (m3). Blood, 77:1080–1086, 1991.Google Scholar
  25. [25]
    J. Lindenmair, E. Matzner, A. Göttlein, A.J. Kuhn and W. H. Schröder. Ion exchange and water uptake of coarse roots of mature norway spruce trees. In W.J. Horst et al., editor, Plant Nutrition — Food Security and Sustainability of Agro-Ecosystems. Kluwer Academic Publishers, 2001.Google Scholar
  26. [26]
    R. Marcelpoil and Y. Usson. Methods for the study of cellular sociology: voronoi diagrams and parametrization of the spatial relationships. Journal of Theoretical Biology, 154:359–369, 1992.Google Scholar
  27. [27]
    J. Mayer. On quality improvement of scientific software: Theory, methods, and application in the GeoStoch development. PhD thesis, University of Ulm, 2003.Google Scholar
  28. [28]
    J. Mayer, V. Schmidt and F. Schweiggert. A unified simulation framework for spatial stochastic models. Simulation Modelling Practice and Theory, 12:307–326, 2004.CrossRefGoogle Scholar
  29. [29]
    E.C. Morris. Effect of localized placement of nutrients on root-thinning in self-thinning populations. Annals of Botany, 78:353–364, 1996.CrossRefGoogle Scholar
  30. [30]
    A. Okabe, B. Boots, K. Sugihara and S.N. Chiu. Spatial Tessellations. John Wiley & Sons, 2000.Google Scholar
  31. [31]
    P.C. Park and U. de Boni. Spatial rearrangement and enhanced clustering of kinetochores in interphase nuclei of dorsal root ganglion neurons in vitro: association with nucleolar fusion. Experimental Cell Research, 203:222–229, 1992.CrossRefGoogle Scholar
  32. [32]
    P.C. Park and U. de Boni. Dynamics of structure-function relationships in interphase nuclei. Life Sciences, 64:1703–1718, 1999.CrossRefGoogle Scholar
  33. [33]
    M.M. Parker and D.H. van Lear. Soil heterogeneity and root distribution of mature loblolly pine stands in piedmont soils. Soil Science Society of America Journal, 60:1920–1925, 1996.CrossRefGoogle Scholar
  34. [34]
    S. Perrod and S.M. Gasser. Long-range silencing and position effects at telomeres and centromeres: parallels and differences. Cellular and Molecular Life Sciences, 60:2303–2318, 2003.CrossRefGoogle Scholar
  35. [35]
    E.J. Richards and S.C.R. Elgin. Epigenetic codes for heterochromatin formation and silencing. Cell, 108:489–500, 2002.CrossRefGoogle Scholar
  36. [36]
    B.D. Ripley. The second-order analysis of stationary point processes. Journal of Applied Probability, 13:255–266, 1976.zbMATHMathSciNetCrossRefGoogle Scholar
  37. [37]
    B.D. Ripley. Spatial Statistics. John Wiley & Sons, 1981.Google Scholar
  38. [38]
    R.J. Ryel, M.M. Caldwell and J.H. Manwaring. Temporal dynamics of soil spatial heterogeneity in sagebrush-wheatgrass steppe during a growing season. Plant Soil, 184:299–309, 1996.CrossRefGoogle Scholar
  39. [39]
    K. Schladitz, A. Särkkä, I. Pavenstädt, O. Haferkamp and T. Mattfeldt. Statistical analysis of intramembranous particles using fracture specimens. Journal of Microscopy, 211:137–153, 2003.MathSciNetCrossRefGoogle Scholar
  40. [40]
    I. Schmid and M. Kazda. Vertical distribution and radial growth of coarse roots in pure and mixed stands of fagus sylvatica and picea abies. Canadian Journal of Forest Research, 31:539–548, 2001.CrossRefGoogle Scholar
  41. [41]
    I. Schmid and M. Kazda. Clustered root distribution in mature stands of fagus sylvatica and picea abies. Oecologia, page (in press), 2005.Google Scholar
  42. [42]
    D. Stoyan, W.S. Kendall and J. Mecke. Stochastic Geometry and its Applications. John Wiley & Sons, 1995.Google Scholar
  43. [43]
    D. Stoyan and H. Stoyan. Fractals, Random Shapes and Point Fields. John Wiley & Sons, 1994.Google Scholar
  44. [44]
    D. Stoyan and H. Stoyan. Improving ratio estimators of second order point process characteristics. Scandinavian Journal of Statistics, 27:641–656, 2000.MathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    D. Stoyan, H. Stoyan, A. Tscheschel and T. Mattfeldt. On the estimation of distance distribution functions for point processes and random sets. Image Analysis and Stereology, 20:65–69, 2001.MathSciNetzbMATHGoogle Scholar
  46. [46]
    M.N.M. van Lieshout and A.J. Baddeley. A nonparametric measure of spatial interaction in point patterns. Statistica Neerlandica, 50:344–361, 1996.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Inc. 2006

Authors and Affiliations

  • Frank Fleischer
    • 1
  • Michael Beil
    • 2
  • Marian Kazda
    • 3
  • Volker Schmidt
    • 4
  1. 1.Department of Applied Information Processing and Department of StochasticsUniversity of UlmUlmGermany
  2. 2.Department of Internal Medicine IUniversity Hospital UlmUlmGermany
  3. 3.Department of Systematic Botany and EcologyUniversity of UlmUlmGermany
  4. 4.Department of StochasticsUniversity of UlmUlmGermany

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