Abstract
Abstract 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 filamentarityF 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.
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