unfoldr-package: Stereological Unfolding for Spheroidal Particles

Description References


Stereological unfolding as implemented in this package consists of the estimation of the joint size-shape-orientation distribution of spheroidal shaped particles based on the same measured quantities of corresponding vertical section profiles. A single trivariate discretized version of the (stereological) integral equation in the case of prolate and oblate spheroids is solved numerically by a variant of the well-known Expectation Maximization (EM) algorithm. In addition, routines for estimating the empirical diameter distribution of spheres from planar sections (better known as the Wicksell's corpuscle problem [3]) is also implemented. The package also provides functions for the simulation of Poisson germ-grain processes with either spheroids, spherocylinders or spheres as grains including functions for planar and vertical sections and digitization of section profiles.


  1. Bene\check{\textrm{s}}, V. and Rataj, J. Stochastic Geometry: Selected Topics Kluwer Academic Publishers, Boston, 2004

  2. Ohser, J. and Schladitz, K. 3D images of materials structures Wiley-VCH, 2009

  3. Ohser, J. and Muecklich, F. Statistical analysis of microstructures in materials science J. Wiley & Sons, 2000

  4. C. Lantu\acute{\textrm{e}}joul. Geostatistical simulation. Models and algorithms. Springer, Berlin, 2002. Zbl 0990.86007

  5. M\textrm{\"u}ller, A., Weidner, A., and Biermann, H. (2015). Influence of reinforcement geometry on the very high-cycle fatigue behavior of aluminum-matrix-composites. Materials Science Forum, 825/826:150-157

unfoldr documentation built on Sept. 25, 2021, 1:07 a.m.