Shape Statistics for Random Domains and Particles

  • Dietrich Stoyan
  • Ashot Davtyan
  • Daulet Turetayev
Part of the Lecture Notes in Physics book series (LNP, volume 600)


This paper surveys ideas of statistical analysis of planar images of particles such as powder particles or sand grains, domains such as monolayer domains on water or water droplets on planar surfaces and biological cells or vesicles. For a simple and fast discrimination between collectives of particles, shape ratios or indices such as ‘area:perimeter’ ratio are powerful tools. A more detailed description is possible by means of various functions such as radius-vector function, tangent-angle function and erosion function. A deeper understanding of particle shape and size is possible by studying the relevant physical processes which generate them, such as fracture, abrasion and growth by aggregation.

The second part of the paper discusses a particular stochastic model, called Gibbs pixelparticle. It produces two-dimensional connected lattice figures, often called lattice animals, the distribution of which depends on an energy function which is controled by particle area and boundary length and roughness. These pixel-particles vary in a broad spectrum of possible shapes and sizes.


Diagonal Direction Total Projection Shape Ratio Erosion Function Minkowski Functional 
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-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Dietrich Stoyan
    • 1
  • Ashot Davtyan
    • 1
  • Daulet Turetayev
    • 1
  1. 1.Institut für StochastikTU Bergakademie FreibergFreiberg

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