Stereology: recovering 3D morphology of a random field from a single 2D cross-section

Astronomy Unit Seminars
Prof. Anvar Shukurov (U. Newcastle)
David Tsiklauri
January 16th, 2015 at 14:30
GO Jones Room 610

The two aspect ratios of randomly oriented triaxial ellipsoids (representing isosurfaces of an
isotropic 3D random field) can be determined from a single 2D cross-section of their sample
using the probability density function (PDF) of the filamentarity F of individual structures
seen in cross-section (F = 0 for a circle and F = 1 for a line). The PDF of F has a robust
form with a sharp maximum and truncation at larger F, and the most probable and maximum
values of F are uniquely and simply related to the two aspect ratios of the triaxial ellipsoids.
The parameters of triaxial ellipsoids of randomly distributed sizes can still be recovered from
the PDF of F. This method is applicable to many shape-recognition problems, here illustrated
by the neutral hydrogen density in the turbulent interstellar medium of the Milky Way. The
gas distribution is shown to be filamentary with axis ratios of about 1:2:20.