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Improved Anisotropic Gaussian Filters

Alex Keilmann, Michael Godehardt, Ali Moghiseh, Claudia Redenbach, Katja Schladitz

TL;DR

A modified algorithm for 2D anisotropic Gaussian filters is proposed and shown to be more accurate and robust to noise and applied to synthetic images of fiber bundles shows that this improves their precision.

Abstract

Elongated anisotropic Gaussian filters are used for the orientation estimation of fibers. In cases where computed tomography images are noisy, roughly resolved, and of low contrast, they are the method of choice even if being efficient only in virtual 2D slices. However, minor inaccuracies in the anisotropic Gaussian filters can carry over to the orientation estimation. Therefore, this paper proposes a modified algorithm for 2D anisotropic Gaussian filters and shows that this improves their precision. Applied to synthetic images of fiber bundles, it is more accurate and robust to noise. Finally, the effectiveness of the approach is shown by applying it to real-world images of sheet molding compounds.

Improved Anisotropic Gaussian Filters

TL;DR

A modified algorithm for 2D anisotropic Gaussian filters is proposed and shown to be more accurate and robust to noise and applied to synthetic images of fiber bundles shows that this improves their precision.

Abstract

Elongated anisotropic Gaussian filters are used for the orientation estimation of fibers. In cases where computed tomography images are noisy, roughly resolved, and of low contrast, they are the method of choice even if being efficient only in virtual 2D slices. However, minor inaccuracies in the anisotropic Gaussian filters can carry over to the orientation estimation. Therefore, this paper proposes a modified algorithm for 2D anisotropic Gaussian filters and shows that this improves their precision. Applied to synthetic images of fiber bundles, it is more accurate and robust to noise. Finally, the effectiveness of the approach is shown by applying it to real-world images of sheet molding compounds.
Paper Structure (21 sections, 10 equations, 7 figures, 2 tables)

This paper contains 21 sections, 10 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. Algorithms for Anisotropic Gaussian Filtering
  4. The Hybrid Algorithm
  5. Theoretical Performance Analysis
  6. Fiber Orientation Estimation
  7. Maximal Response of Anisotropic Gaussian Filters
  8. Structure Tensor
  9. Hessian Matrix
  10. Results
  11. Performance of Anisotropic Gaussian Filters
  12. Accuracy
  13. Throughput
  14. Experimental Validation of the MR Method
  15. Setup
  16. ...and 6 more sections

Figures (7)

  • Figure 1: The Gaussian ellipse, i.e., contour line of the Gaussian function, w.r.t. (a) the principal axes $v_1$ and $v_2$, and (b) the axes $x_1$ and $\nu_\ast$geusebroek03.
  • Figure 2: Visualization of the experimental data set for varying contrast $c$.
  • Figure 3: Mean angle error for 50 noise images overlayed with synthetic fiber images with direction $\theta = 0^\circ, ..., 179^\circ$, and with varying contrast. For each noise image contrast combination, the MAE's maximum over fiber directions was calculated. The mean and standard deviations over 50 noise images are depicted as point symbol with bars for each contrast and algorithm. Note, however, that the standard deviations are small and therefore the bars delimiting the interval are in many cases covered by the symbol for the mean value.
  • Figure 4: Analysis of SMC with glass fibers using the MR method with $\sigma_1 = 20.0$, $\sigma_2 = 0.5$, and binarization.
  • Figure 5: Direction estimation of SMC with carbon fibers. The directions are color-coded, see color wheel at the top-right side.
  • ...and 2 more figures