An efficient and uniformly behaving streamline-based \(\mu\)CT fibre tracking algorithm using volume-wise structure tensor and signal processing techniques. (English) Zbl 07526216

Summary: A method for reconstructing polygonal paths of fibres in reinforced composites imaged using micro-computed tomography is formally described, implemented and tested. The algorithm has been crafted to be explicable, require no training data and behave uniformly in all axes or orientations. It consists of four phases: (1) segmenting fibre regions using a scale-dependent Iterative Difference of Gaussians approach, (2) extracting directionality using the structure tensor minimum eigenvector, (3) automatically placing the seeds near a set of user-defined restricting surfaces, and (4) tracking fibres using a streamline-based integration method. The algorithm cost grows in relation to the target fibre diameter and is proportional to the number of voxels in the input volume. Its behaviour, ability to process very curved fibres, and error have been assessed using both synthetic and real datasets. The C++ implementation is performant and parallelizable, and produces helpful visualisations to gain insight of the intermediate and final results.


74G75 Inverse problems in equilibrium solid mechanics
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
Full Text: DOI


[1] Kruth, J.; Bartscher, M.; Carmignato, S.; Schmitt, R.; De Chiffre, L.; Weckenmann, A., Computed tomography for dimensional metrology, CIRP Ann., 60, 2, 821-842 (2011), URL https://www.sciencedirect.com/science/article/pii/S0007850611002083
[2] Garcea, S.; Wang, Y.; Withers, P., X-ray computed tomography of polymer composites, Compos. Sci. Technol., 156, 305-319 (2018), URL https://www.sciencedirect.com/science/article/pii/S0266353817312460
[3] Mori, S.; Crain, B.; Chacko, V.; van zijl, P., Three dimensional tracking of axonal projections in the brain by magnetic resonance imaging, Ann. Neurol., 45, 265-269 (1999)
[4] Mori, S.; van Zijl, P. C.M., Fiber tracking: principles and strategies – a technical review, NMR Biomed., 15, 7-8, 468-480 (2002), arXiv:https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/pdf/10.1002/nbm.781, URL https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/abs/10.1002/nbm.781
[5] Basser, P. J.; Pajevic, S.; Pierpaoli, C.; Duda, J.; Aldroubi, A., In vivo fiber tractography using DT-MRI data, Magn. Reson. Med., 44, 4, 625-632 (2000), arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/1522-2594
[6] Bhattacharya, A.; Heinzl, C.; Amirkhanov, A.; Kastner, J.; Wenger, R., MetaTracts - A method for robust extraction and visualization of carbon fiber bundles in fiber reinforced composites, (2015 IEEE Pacific Visualization Symposium, PacificVis (2015)), 191-198
[7] Creveling, P. J.; Whitacre, W. W.; Czabaj, M. W., A fiber-segmentation algorithm for composites imaged using X-ray microtomography: Development and validation, Composites A, 126, Article 105606 pp. (2019), URL https://www.sciencedirect.com/science/article/pii/S1359835X19303550
[8] Blanc, R.; Germain, C.; Costa, J. D.; Baylou, P.; Cataldi, M., Fiber orientation measurements in composite materials, Composites A, 37, 2, 197-206 (2006), CompTest 2004, https://doi.org/10.1016/j.compositesa.2005.04.021, URL https://www.sciencedirect.com/science/article/pii/S1359835X05002472
[9] Kronenberger, M.; Schladitz, K.; Hamann, B.; Hagen, H., Fiber segmentation in crack regions of steel fiber reinforced concrete using principal curvature, Image Anal. Stereol., 37, 2, 127-137 (2018), URL https://www.ias-iss.org/ojs/IAS/article/view/1914 · Zbl 1443.94019
[10] Schöttl, L.; Dörr, D.; Pinter, P.; Weidenmann, K. A.; Elsner, P.; Kärger, L., A novel approach for segmenting and mapping of local fiber orientation of continuous fiber-reinforced composite laminates based on volumetric images, NDT & E Int., 110, Article 102194 pp. (2020), URL https://www.sciencedirect.com/science/article/pii/S0963869519303743
[11] Sencu, R.; Yang, Z.; Wang, Y.; Withers, P.; Rau, C.; Parson, A.; Soutis, C., Generation of micro-scale finite element models from synchrotron X-ray CT images for multidirectional carbon fibre reinforced composites, Composites A, 91, 85-95 (2016), URL https://www.sciencedirect.com/science/article/pii/S1359835X16303049
[12] Dahl, V. A.; Emerson, M. J.; Trinderup, C. H.; Dahl, A. B., Content-based propagation of user markings for interactive segmentation of patterned images, (2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, CVPRW (2020)), 4280-4288
[13] Emerson, M. J.; Jespersen, K. M.; Dahl, A. B.; Conradsen, K.; Mikkelsen, L. P., Individual fibre segmentation from 3D X-ray computed tomography for characterising the fibre orientation in unidirectional composite materials, Composites A, 97, 83-92 (2017), URL https://www.sciencedirect.com/science/article/pii/S1359835X16304560
[14] Amjad, K.; Christian, W.; Dvurecenska, K.; Chapman, M.; Uchic, M.; Przybyla, C.; Patterson, E., Computationally efficient method of tracking fibres in composite materials using digital image correlation, Composites A, 129, Article 105683 pp. (2020), URL https://www.sciencedirect.com/science/article/pii/S1359835X19304324
[15] Gaiselmann, G.; Manke, I.; Lehnert, W.; Schmidt, V., Extraction of curved fibers from 3D data, Image Anal. Stereol., 32, 1, 57-63 (2013), URL https://www.ias-iss.org/ojs/IAS/article/view/979
[16] Fritz, L.; Hadwiger, M.; Geier, G.; Pittino, G.; Groller, M. E., A visual approach to efficient analysis and quantification of ductile iron and reinforced sprayed concrete, IEEE Trans. Vis. Comput. Graphics, 15, 6, 1343-1350 (2009)
[17] Bhattacharya, A.; Weissenböck, J.; Wenger, R.; Amirkhanov, A.; Kastner, J.; Heinzl, C., Interactive exploration and visualization using MetaTracts extracted from carbon fiber reinforced composites, IEEE Trans. Vis. Comput. Graphics, 23, 8, 1988-2002 (2017)
[18] Heinzl, C.; Stappen, S., Star: Visual computing in materials science, Comput. Graph. Forum, 36, 3, 647-666 (2017), arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.13214, URL https://onlinelibrary.wiley.com/doi/abs/10.1111/cgf.13214
[19] Weissenböck, J.; Amirkhanov, A.; Gröller, E.; Kastner, J.; Heinzl, C., PorosityAnalyzer: Visual analysis and evaluation of segmentation pipelines to determine the porosity in fiber-reinforced polymers, 101-110 (2016)
[20] Fröhler, B.; Elberfeld, T.; Möller, T.; Hege, H.; Weissenböck, J.; De Beenhouwer, J.; Sijbers, J.; Kastner, J.; Heinzl, C., A visual tool for the analysis of algorithms for tomographic fiber reconstruction in materials science, Comput. Graph. Forum, 38, 3, 273-283 (2019), arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.13688, URL https://onlinelibrary.wiley.com/doi/abs/10.1111/cgf.13688
[21] Fröhler, B.; Elberfeld, T.; Möller, T.; Hege, H.-C.; Beenhouwer, J. D.; Sijbers, J.; Kastner, J.; Heinzl, C., Analysis and comparison of algorithms for the tomographic reconstruction of curved fibres, Nondestruct. Test. Eval., 35, 3, 328-341 (2020)
[22] Math2Market GmbH, B., GeoDict (2021), [Internet] URL https://www.geodict.com/Solutions/aboutGD.php
[23] Volume Graphics, B., VGSTUDIO MAX (2021), [Internet] URL https://www.volumegraphics.com/en/products/vgsm.html
[24] Thermo Fisher Scientific Inc., B., Avizo software (2021), [Internet] URL https://www.thermofisher.com/es/es/home/electron-microscopy/products/software-em-3d-vis/avizo-software.html
[25] de Pascalis, F.; Nacucchi, M., Relationship between the anisotropy tensor calculated through global and object measurements in high-resolution X-ray tomography on cellular and composite materials, J. Microsc., 273, 1, 65-80 (2019), arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/jmi.12762, URL https://onlinelibrary.wiley.com/doi/abs/10.1111/jmi.12762
[26] Mehdikhani, M.; Breite, C.; Swolfs, Y.; Wevers, M.; Lomov, S. V.; Gorbatikh, L., Combining digital image correlation with X-ray computed tomography for characterization of fiber orientation in unidirectional composites, Composites A, 142, Article 106234 pp. (2021), URL https://www.sciencedirect.com/science/article/pii/S1359835X2030470X
[27] Krause, M.; Hausherr, J.; Burgeth, B.; Herrmann, C.; Krenkel, W., Determination of the fibre orientation in composites using the structure tensor and local X-ray transform, J. Mater. Sci., 45, 888-896 (2010)
[28] Straumit, I.; Lomov, S. V.; Wevers, M., Quantification of the internal structure and automatic generation of voxel models of textile composites from X-ray computed tomography data, Composites A, 69, 150-158 (2015), URL https://www.sciencedirect.com/science/article/pii/S1359835X14003625
[29] Otsu, N., A threshold selection method from gray-level histograms, IEEE Trans. Syst. Man Cybern., 9, 1, 62-66 (1979)
[30] Huang, D.-Y.; Wang, C.-H., Optimal multi-level thresholding using a two-stage otsu optimization approach, Pattern Recognit. Lett., 30, 3, 275-284 (2009), URL https://www.sciencedirect.com/science/article/pii/S0167865508002985
[31] Frangi, A. F.; Niessen, W. J.; Vincken, K. L.; Viergever, M. A., Multiscale vessel enhancement filtering, (Wells, W. M.; Colchester, A.; Delp, S., Medical Image Computing and Computer-Assisted Intervention — MICCAI’98 (1998), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg), 130-137
[32] G.M.P.V. Kempen, N. van den Brink, L.J. van Vliet, M.V. Ginkel, P.W. Verbeek, H. Blonk, The application of a Local Dimensionality Estimator to the analysis of 3-D microscopic network structures, in: SCIA’99, Proceedings of the 11th Scandinavian Conference on Image Analysis (Kangerlussuaq 1999), 1999, pp. 447-455.
[33] Robb, K.; Wirjadi, O.; Schladitz, K., Fiber orientation estimation from 3D image data: Practical algorithms, visualization, and interpretation, (7th International Conference on Hybrid Intelligent Systems, HIS 2007 (2007)), 320-325
[34] Budde, M. D.; Frank, J. A., Examining brain microstructure using structure tensor analysis of histological sections, Neuroimage, 63, 1, 1-10 (2012), URL https://www.sciencedirect.com/science/article/pii/S105381191200657X
[35] Pinter, P.; Dietrich, S.; Bertram, B.; Kehrer, L.; Elsner, P.; Weidenmann, K., Comparison and error estimation of 3D fibre orientation analysis of computed tomography image data for fibre reinforced composites, NDT & E Int., 95, 26-35 (2018), URL https://www.sciencedirect.com/science/article/pii/S0963869517303821
[36] Karamov, R.; Martulli, L. M.; Kerschbaum, M.; Sergeichev, I.; Swolfs, Y.; Lomov, S. V., Micro-CT based structure tensor analysis of fibre orientation in random fibre composites versus high-fidelity fibre identification methods, Compos. Struct., 235, Article 111818 pp. (2020), URL https://www.sciencedirect.com/science/article/pii/S0263822319322986
[37] Scharr, H., Optimale Operatoren in der Digitalen Bildverarbeitung, 145-156 (2000), Naturwissenschaftlich-Mathematischen Gesamtfakultät, URL http://www.ub.uni-heidelberg.de/archiv/962
[38] Golub, G. H.; van der Vorst, H. A., Eigenvalue computation in the 20th century, J. Comput. Appl. Math., 123, 1, 35-65 (2000), Numerical Analysis 2000. Vol. III: Linear Algebra, https://doi.org/10.1016/S0377-0427(00)00413-1, URL https://www.sciencedirect.com/science/article/pii/S0377042700004131 · Zbl 0965.65057
[39] Jacobi, C., Über ein leichtes Verfahren die in der Theorie der Säcularstörungen vorkommenden Gleichungen numerisch aufzulösen*, 1846, 30, 51-94 (1846)
[40] Westin, C.-F.; Maier, S.; Mamata, H.; Nabavi, A.; Jolesz, F.; Kikinis, R., Processing and visualization for diffusion tensor MRI, Med. Image Anal., 6, 2, 93-108 (2002), URL https://www.sciencedirect.com/science/article/pii/S1361841502000531
[41] Mori, S., Introduction to Diffusion Tensor Imaging (2007), Elsevier Science B.V.: Elsevier Science B.V. Amsterdam, URL https://www.sciencedirect.com/book/9780444528285
[42] Press, W.; Flannery, B.; Teukolsky, S.; Vetterling, W., Numerical Recipes in FORTRAN 77: Volume 1, Volume 1 of Fortran Numerical Recipes: The Art of Scientific Computing (1992), Cambridge University Press, URL https://books.google.es/books?id=LRO0zAEACAAJ · Zbl 0778.65002
[43] Cash, J. R.; Karp, A. H., A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides, ACM Trans. Math. Software, 16, 3, 201-222 (1990) · Zbl 0900.65234
[44] Ruiz, M.; Julià, A.; Boada, I., Starviewer and its comparison with other open-source DICOM viewers using a novel hierarchical evaluation framework, Int. J. Med. Inform., 137, Article 104098 pp. (2020), URL https://www.sciencedirect.com/science/article/pii/S1386505619301108
[45] Qt Group Oyj, M., Qt libraries (2021), [Internet] URL https://www.qt.io
[46] Kitware Inc., M., The visualization ToolKit (2021), [Internet] URL https://www.vtk.org
[47] Mehdikhani, M.; Breite, C.; Swolfs, Y.; Wevers, M.; Lomov, S. V.; Gorbatikh, L., A dataset of micro-scale tomograms of unidirectional glass fiber/epoxy and carbon fiber/epoxy composites acquired via synchrotron computed tomography during in-situ tensile loading, Data in Brief, 34, Article 106672 pp. (2021), URL https://www.sciencedirect.com/science/article/pii/S2352340920315511
[48] Lindeberg, T., Scale-space for discrete signals, IEEE Trans. Pattern Anal. Mach. Intell., 12, 3, 234-254 (1990)
[49] Lindeberg, T., (Scale-Space Theory in Computer Vision. Scale-Space Theory in Computer Vision, The Springer International Series in Engineering and Computer Science (1994), Royal Institute of Technology, Stockholm, Sweden: Royal Institute of Technology, Stockholm, Sweden Springer), XII, 424 · Zbl 0812.68040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.