Adaptive Morphological Framework for 3D Directional Filtering

Authors

  • Tin Barisin Fraunhofer ITWM University of Kaiserslautern
  • Katja Schladitz Fraunhofer ITWM
  • Claudia Redenbach University of Kaiserslautern
  • Michael Godehardt Fraunhofer ITWM

DOI:

https://doi.org/10.5566/ias.2639

Keywords:

adaptive directional filtering, computed tomography, crack detection, filter banks, local fiber orientation, local surface normal orientation, orientation estimation

Abstract

Engineering materials often feature lower dimensional and directed structures such as cracks, fibers, or closed facets in foams. The characterization of such structures in 3D is of particular interest in various applications in materials science. In image processing, knowledge of the local structure orientation can be used for structure enhancement, directional filtering, segmentation, or separation of interacting structures. The idea of using banks of directed structuring elements or filters parameterized by a discrete subset of the orientation space is proven to be effective for these tasks in 2D. However, this class of methods is prohibitive in 3D due to the high computational burden of filtering on a sufficiently fine discretization of the unit sphere.

This paper introduces a method for 3D pixel-wise orientation estimation and directional filtering inspired by the idea of adaptive refinement in discretized settings. Furthermore, an operator for distinction between isotropic and anisotropic structures is defined based on our method. This operator utilizes orientation information to successfully preserve structures with one or two dominant dimensions. Finally, feasibility and effectiveness of the method are demonstrated on 3D micro-computed tomography images in three use cases: detection of a misaligned region in a fiber-reinforced polymer, segmentation of cracks in concrete, and separation of facets and strut system in partially closed foams.

Author Biographies

Katja Schladitz, Fraunhofer ITWM

Image Processing Department

Claudia Redenbach, University of Kaiserslautern

Department of Mathematics, Statistics Group

Michael Godehardt, Fraunhofer ITWM

Image Processing Department

References

Altendorf H (2011). 3D morphological analysis and modeling of random fiber networks: applied on glass fiber reinforced composites. Ph.D. thesis,

Technische Universitat Kaiserslautern and Mines ¨ ParisTech. http://nbn-resolving.de/urn:nbn:de:hbz:386-kluedo-28323 (accessed 27 July 2021).

Barisin T, Jung C, Musebeck F, Redenbach C, Schladitz K ¨ (2021). Methods for segmenting cracks in 3d images of concrete: A comparison based on semi-synthetic

images. submitted https://arxiv.org/abs/2112.09493.

Bresenham JE (1965). Algorithm for computer control of a digital plotter. IBM Systems Journal 4:25–30. https://doi.org/10.1147/sj.41.0025.

Curic V, Luengo Hendriks C, Borgefors G (2012). Salience adaptive structuring elements. IEEE J Sel Top Signa 6:809–19. https://doi.org/10.1109/JSTSP.2012.2207371.

Debayle J, Pinoli JC (2011). Spatially adaptive morphological image filtering using intrinsic structuring elements. Image Anal Stereol 24:145–58. https://doi.org/10.5566/ias.v24.p145-158.

Dokladal P, Dokladalova E (2008). Grey-scale 1-d dilations with spatially-variant structuring elements in linear time. In: EUSIPCO’08. https://hal-upec-upem.archives-ouvertes.fr/hal-00622464.

Dokladal P, Dokladalova E (2011). Computationally efficient, one-pass algorithm for morphological filters. J Vis Commun Image R 22:411–20. https://doi.org/10.1016/j.jvcir.2011.03.005.

Dokladal P, Dokladalova E (2008). Grey-scale morphology with spatially-variant rectangles in linear time. In: Lect Notes Comput Sc. https://doi.org/10.1007/978-3-540-88458-3_61.

Dresvyanskiy D, Karaseva T, Makogin V, Mitrofanov S, Redenbach C, Spodarev E (2020). Detecting anomalies in fibre systems using 3-dimensional image data. Stat

Comput 30:1–21. https://doi.org/10.1007/s11222-020-09921-1.

Eberly D, Gardner R, Morse B, Pizer S, Scharlach C (1994). Ridges for image analysis. J Math Imaging Vis 4:353–73. https://doi.org/10.1007/BF01262402.

Ehrig K, Goebbels J, Meinel D, Paetsch O, Prohaska S, Zobel V (2011). Comparison of Crack Detection Methods for Analyzing Damage Processes in Concrete with Computed Tomography. In: Int. Symp. Dig. Ind. Radiol. Comp. Tomogr. https://www.ndt.net/article/dir2011/papers/p2.pdf.

Fliege J, Maier U (1999). The distribution of points on the sphere and corresponding cubature formulae. IMA Journal of Numerical Analysis 19:317–34. https://doi.org/10.1093/imanum/19.2.317.

Fohst S, Osterroth S, Arnold F, Redenbach C (2021). Influence of geometry modifications on the permeability of open-cell foams. AIChE Journal https://doi.org/10.1002/aic.17446.

Frangi R, Niessen W, Vincken K, Viergever M (2000). Multiscale vessel enhancement filtering. Med Image Comput Comput Assist Interv 1496:130–7. https://doi.org/10.1007/BFb0056195.

Freeman WT, Adelson EH (1991). The design and use of steerable filters. IEEE T Patter Anal 13:891–906. https://doi.org/10.1109/34.93808.

Heijmans H, Buckley M, Talbot H (2005). Path openings and closings. J Math Imaging Vis 22:107–19. https://doi.org/10.1007/s10851-005-4885-3.

Kampf J, Schlachter AL, Redenbach C, Liebscher A (2015). Segmentation, statistical analysis, and modelling of the wall system in ceramic foams. Mater Charact 99:38–

https://doi.org/10.1016/j.matchar.2014.11.008.

Landstrom A, Thurley MJ (2013). Adaptive morphology using tensor-based elliptical structuring elements. Pattern Recong Lett 34:1416–22. https://doi.org/10.1016/j.patrec.2013.05.003.

Lerallut R, Decenciere ` E, Meyer F (2007). Image filtering using morphological amoebas. Image and Vision Computing 25:395–404. Lect Notes Comput Sc,

https://doi.org/10.1016/j.imavis.2006.04.018.

Luengo Hendriks CL (2010). Constrained and dimensionality-independent path openings. IEEE T Image Process 19:1587–95. https://doi.org/10.1109/TIP.2010.2044959.

Michelet F, Da Costa JP, Baylou P, Germain C (2006). Local orientation estimation in corrupted images. In: Zheng N, Jiang X, Lan X, eds., Lect Notes Comput Sc. Berlin,

Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/11821045_37.

Morard V, Dokladal P, Decenciere E (2014). Parsimonious path openings and closings. IEEE T Image Process 23:1543–55. https://doi.org/10.1109/TIP.2014.2303647.

Perreault S, Hebert P (2007). Median filtering in constant time. IEEE T Image Process 16:2389–94. https://doi.org/10.1109/TIP.2007.902329.

Redenbach C, Giertzsch M, Godehardt M, Schladitz K (2008). Modelling a ceramic foam using locally adaptable morphology. J Microsc Oxford 230:396–404. https://doi.org/10.1111/j.1365-2818.2008.01998.x.

Redenbach C, Wirjadi O, Rief S, Wiegmann A (2011). Modeling of ceramic foams for filtration simulation. Adv Eng Mater 13:171 – 177. https://doi.org/10.1002/adem.201000222.

Robb K, Wirjadi O, Schladitz K (2007). Fiber orientation estimation from 3d image data: Practical algorithms, visualization, and interpretation. In: Proc. 7th Int. Conf.

Hybrid Intelligent Systems. Kaiserslautern, Germany. https://doi.org/10.1109/HIS.2007.26.

Saff E, Kuijlaars A (1997). Distributing many points on a sphere. Mat Intel 19:5–11. https://doi.org/10.1007/BF03024331.

Sandau K, Ohser J (2007). The chord length transform and the segmentation of crossing fibres. J Microsc Oxford 226:43–53. https://doi.org/10.1111/j.1365-2966.2007.01748.x.

Sandberg K, Brega M (2007). Segmentation of thin structures in electron micrographs using orientation fields. J Struct Biol 157:403–15. https://doi.org/10.1016/j.jsb.2006.09.007.

Sazak C, Nelson CJ, Obara B (2019). The multiscale bowler-hat transform for blood vessel enhancement in retinal images. Patter Recogn 88:739–50. https://doi.org/10.1016/j.patcog.2018.10.011.

Schladitz K, Buter A, Godehardt M, Wirjadi O, Fleckenstein J, Gerster T, Hassler U, Jaschek K, Maisl M, Maisl U, Mohr S, Netzelmann U, Potyra T, Steinhauser MO (2017). Non-destructive characterization of fiber orientation in reinforced smc as input

for simulation based design. Compos Struct 160:195–203. https://doi.org/10.1016/

j.compstruct.2016.10.019.

Semeraro F, Ferguson JC, Panerai F, King RJ, Mansour NN (2020). Anisotropic analysis of fibrous and woven materials part 1: Estimation of local orientation. Comp

Mater Sci 178:109631. https://doi.org/10.1016/j.commatsci.2020.109631.

Sliseris J, Andra H, Kabel M, Wirjadi O, Dix B, Plinke B (2015). Estimation of fiber orientation and fiber bundles of MDF. Mater Struct 49. https://doi.org/10.

/s11527-015-0769-1.

Soille P (1999). Morphological Image Analysis: Principles and Applications. Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-662-03939-7.

Soille P, Talbot H (2001). Directional morphological filtering. IEEE T Patter Anal 23:1313–29. https://doi.org/10.1109/34.969120.

Su R, Sun C, Zhang C, Pham TD (2014). A new method for linear feature and junction enhancement in 2d images based on morphological operation, oriented anisotropic gaussian function and hessian information. Pattern Recogn 47:3193–208. https://doi.org/10.1016/j.patcog.2014.04.024.

Tankyevych O, Talbot H, Dokladal P (2008). Curvilinear morpho-hessian filter. In: 2008 I S Biomed Imaging. https://doi.org/10.1109/ISBI.2008.4541170.

Tankyevych O, Talbot H, Dokladal P, Passat N (2009). Direction-adaptive grey-level morphology. Application to 3d vascular brain imaging. In: IEEE Image Proc.

https://doi.org/10.1109/ICIP.2009.5414356.

Weickert J (1999). Coherence-enhancing diffusion filtering. Int J Comput Vis 31:111–27. https://doi.org/10.1023/A:1008009714131.

Wirjadi O (2009). Models and Algorithms for ImageBased Analysis of Microstructures. Ph.D. thesis, Technische Universitat Kaiserslautern. https://kluedo.ub.uni-kl.de/frontdoor/index/index/year/2009/docId/2077 (accessed 27 July 2021).

Wirjadi O, Godehardt M, Schladitz K, Wagner B, Rack A,Gurka M, Nissle S, Noll A (2014). Characterization of multilayer structures in fiber reinforced polymer

employing synchrotron and laboratory X-ray CT. Int J Mater Res 105:645–54. https://doi.org/doi:10.3139/146.111082.

Wirjadi O, Schladitz K, Easwaran P, Ohser J (2016). Estimating fibre direction distributions of reinforced composites from tomographic images. Image Anal

Stereol 35:167–79. https://doi.org/10.5566/ias.1489.

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Published

2022-04-08

How to Cite

Barisin, T., Schladitz, K., Redenbach, C., & Godehardt, M. (2022). Adaptive Morphological Framework for 3D Directional Filtering. Image Analysis and Stereology, 41(1). https://doi.org/10.5566/ias.2639

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