3D morphology of a random field from its 2D cross-section

TL;DR

This paper presents a method to determine the 3D aspect ratios of randomly oriented ellipsoids from a single 2D cross-section by analyzing the probability distribution of filamentarity, applicable to astrophysical data.

Contribution

The authors introduce a novel approach to infer 3D shape aspect ratios from 2D cross-sections using filamentarity distribution, applicable to various shape recognition problems.

Findings

Aspect ratios of ellipsoids can be recovered from 2D filamentarity distribution.

The method is robust and sensitive to shape parameters.

Applied to interstellar medium data, revealing filamentary gas structures.

Abstract

We show that both 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 distribution of the filamentarity F of the structures seen in the cross-section (F=0 for a circle and F=1 for a line). The probability distribution of F has a robust form with a sharp maximum and truncation that are sensitive to the ellipsoids' aspect ratios. We show that the aspect ratios of triaxial ellipsoids with randomly distributed dimensions can still be recovered from the probability distribution of F. This method is applicable to many shape recognition and classification problems, here illustrated with neutral hydrogen density in the turbulent interstellar medium of the Milky Way. The gas distribution is shown to be filamentary with the mean axis ratio 1:2:20.