Computing the fibre orientation from Radon data using local Radon transform

Michael Krause; Jan Marcel Hausherr; Walter Krenkel

doi:10.3934/ipi.2011.5.879

Article Contents

2011, Volume 5, Issue 4: 879-891. Doi: 10.3934/ipi.2011.5.879

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Computing the fibre orientation from Radon data using local Radon transform

1.
Ceramic Materials Engineering, University of Bayreuth, 95440 Bayreuth

Received: February 28, 2010

Revised: May 31, 2011

Published: October 2011

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Abstract

Computed tomography (CT) has become a common analysis method in the materials sciences. It allows the internal visualisation of the complete volume of an object, providing 3D information about the internal structures. One field where CT is applied is the examination of fibre-reinforced composite structures. Fibre-reinforced composites are typically composed of two types of material, mainly of high strength fibres embedded in a surrounding matrix. In this material class, the fibres typically determine the strength of the composite materials, which is largely dependent on the orientation of the fibres. Knowledge of the fibre orientation is therefore essential for the evaluation of maximal loading or for the prediction of failure. The easiest way to determine the fibre orientation is to compute it from the reconstructions received from the tomograph. A different method to determine fibre orientation is to compute it directly from Radon data using the combination of reconstruction and image analysis introduced by Louis [A. K. Louis, Combining Image Reconstruction and Image Analysis with an Application to 2D - Tomography, SIAM J. Imaging Sciences 1 (2008), 188--208]. This can be achieved by adapting the reconstruction process in computed tomography by the use of anisotropic, elongated convolution filters, leading to a set of reconstruction kernels that are dependent on the angle of the projections, thereby reflecting the anisotropy of the filters. In this paper, the two-dimensional case of computing fibre orientation directly from simulated Radon data is presented.

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Mathematics Subject Classification: Primary: 65R32; Secondary: 68U10.

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