QMT Features: October 2017
Comparing methods for fiber orientation analysis
Rémi Blanc* and Peter Westenberger* look at different approaches to give an insight into fiber orientation

Computed Tomography (CT) is on its way to become the de facto standard in the field of materials science and material development especially when it comes to the analysis of fibrous materials. The current question is mostly about the compromise between image resolution and volume of data being analyzed, to extract accurate information allowing for the characterization of the fibrous material. Among those statistics, we focus here particularly on the distribution of fiber orientations within the material. We will highlight three different approaches that may operate at different resolutions to provide insights about the fiber orientations.

The described procedures are then applied to a real dataset, as well as to an artificial dataset generated with user-defined properties, which provides us with a goldstandard reference against which the result methods can be evaluated. For both datasets, we further investigate the behavior of the proposed approaches with respect to the scanning resolution, and draw conclusions on their respective merits.

Estimation methods
The first estimation method considered (FFT) is based on the principal component analysis of the Fourier Spectrum, inspired from [1]. The second approach (GRAD) relies on the analysis of the local gradients [2]. Both rely on the texture of the image to characterize the local orientation, and are expected to provide results even in the case of low resolution images where individual fibers cannot be distinguished. The third method (XFIBER) consists in extracting the centerline of each individual fiber using a template matching and centerline tracing algorithms described in [3,4], which gives immediate access to all statistics regarding orientations of the fibers, but also their length, diameter or even tortuosity. All three methods are implemented in Avizo 3D software for scientific and industrial data developed by Thermo Fisher Scientific (formerly FEI).

All methods can generate a tensor representing the local distribution of orientations in each considered subvolume. The eigenvalue decomposition of the tensor provides insights about the major orientations, and the dispersion of orientations. In the XFIBER approach, the orientation tensor is clearly interpretable [5].
In contrast, the FFT and GRAD derive their tensors from image texture descriptors, making their interpretation less straightforward, and direct comparisons challenging. Therefore, we perform our comparisons based on the statistical relationship between the estimated tensors, and on the estimated major orientation.

Sources for data
Generation of synthetic data: A synthetic distribution of non-overlapping fibers (straight cylinders) following a skin-core structure has been generated, using a force-biased algorithm inspired from [6]. A fiber volume fraction around 10% was obtained. The volume was discretized and turned into a grayscale image of 512x512x512 voxels, illustrated in Figure 1 including moderate gaussian noise and blurring, such that the average fiber diameter corresponds to 5 voxels.

Glass fiber composite: We also consider an actual µCT acquisition of a Glass Fiber Reinforced Polymer (GFRP), shown in Figure 2, made of standard, 10µm diameter, short fibers. The considered volume of interest is roughly 2x2x2mm³, with 1.5µm voxel size, and the estimated volume fraction is around 17%.

The volumes are subdivided in cubic regions following a regular lattice, to perform local orientation analyses. Both datasets follow a similar skin-core structure with orthogonal fiber orientations. The subdivision of both volumes is made such that most slabs contain homogeneous regions in terms of fiber orientation with one clear major orientation (either X or Z), while other slabs contain a mixture of fibers oriented mostly along X, and along Z.

For both datasets, the local orientation was measured on the full resolution data, but also after downsampling by a factor 4, and 8, using Lanczos interpolation, to evaluate the robustness of the estimates with respect to imaging resolution.
Synthetic data: Considering the whole volume, the different approaches show strong statistical relationships with the reference tensors (Figure 3). The coefficient of determination R² appears to be very strong overall. This tendency is fairly well maintained when decreasing the image resolution, as shown in Figure 3(d). Interestingly, although the actual accuracy of the fiber detection of the XFIBER approach considerably drops at lower resolution, the results of the tracing still show high value in terms of orientation measurements.

Examining the results slab by slab, It appears that in homogeneous regions (all slabs except 3 and 6), the average angular error (angle between the true major orientation, and the estimated orientation) was very low for all 3 methods.
On the other hand, in inhomogeneous regions (slabs 3 and 6), the estimation of the major orientation proved to be much more precise with the fiber tracing approach compared to texture-based methods. Further, as can be seen on Figure 4(b), the XFIBER estimation is significantly more robust to degraded resolution.

Glass fiber composite: A similar experiment was carried out on the GFRP sample. Since no ground truth orientation measurements are available in this case, we use the results generated by the XFIBER method at full resolution as a reference. The results are presented in Figure 5.

As with the synthetic dataset, the different methods appear to be very strongly correlated overall (Figure 5(b)), and the major orientation estimation remains within 5 degrees of error at full resolution, (12 degrees after downsampling by a factor 8), in homogeneous regions.However, when considering inhomogeneous slabs 4 and 7, the estimations from the different methods vary significantly, although the XFIBER approach provides estimated orientation that are relatively consistant across scales (<10° for the major and second orientation at resolution factor 4), the other methods show considerably more deviations (>20°).

The results on both synthetic and real data suggest that the fiber local orientation tensor estimations are, overall, quite consistent for the different methods, and relatively robust to a decrease of the image resolution. Interestingly, even if in terms of detection performance, the fiber tracing accuracy drops significantly when the image resolution reaches the fiber diameter, the results it generates are still exploitable, and actually more accurate than texture-based approaches to characterize the orientations in the sample.

The fiber architecture considered in this study allows us to analyse regions with a single population of fibers, all more or less oriented along the same orientation; as well as regions featuring two populations of fibers with two orthogonal preferred orientations. When a single orientation is present, although the fiber tracing approach is slightly more precise especially at finer resolutions, all considered methods behave accurately. However, when a mixture of orientations are present, the texture-based approaches show significantly decreased performances, whereas the fiber tracing approach remains precise, even at relatively coarse image resolution. This is particularly interesting when considering fibrous materials exhibiting complex distributions of orientations, such as woven fibers, moulded composites, or more random distributions.
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