3d Directional Mathematical Morphology for Analysis of Fiber Orientations

Abstract

In this paper we present algorithms for measuring local characteristics of random fiber systems. The calculation of the local directions and radii is based on directional distance transforms and evaluation of the inertia moments and axes of the resulting extremities of the centralized, directed chords. The method provides continuous results while minimizing the runtime by using few sampled directions. Furthermore several steps of improvement for the computation of orientation and radius information are presented. The algorithms are evaluated using synthetic data and applied to images of real microstructures obtained by computer tomography.

Estimating Fibre Direction Distributions of Reinforced Composites From Tomographic Images

“…The moments of inertia have been used as features for object and pattern recognition for a very long time, see e.g., Hu (1962); Prokop and Reeves (1992), and more recently to analyse and segment images of fibrous materials by Altendorf and Jeulin (2009;2011) and Altendorf et al (2012).…”

“…The basic idea of this method of Altendorf and Jeulin (2009) is essentially the same as the one exploited by the just described method: Locally, a fibre can be approximated by a prolate rotation ellipsoid whose shorter half-axis length corresponds to the fibre radius while the direction of the longer axis is the local fibre direction. Altendorf and Jeulin (2009) derive the ellipsoid of inertia from directed distance transforms.…”

“…This can be avoided by utilising grey-value pseudo-distances as described by Altendorf and Jeulin (2009).…”

“…Altendorf and Jeulin (2009) derive the ellipsoid of inertia from directed distance transforms. The main axis of the ellipsoid then yields the local fibre direction.…”

“…It requires testing a certain number of chord directions, entailing the same problematic dependence between accuracy and runtime as observed for the anisotropic Gaussian filter method. The approach of Altendorf and Jeulin (2009) can be seen as an advanced CLT as it is based on the CLT idea but refines estimation of the local fibre direction by computing it from the main axis of inertia. This latter approach will be summarised and evaluated below.…”