Noise reduction and quantification of fiber orientations in greyscale images

Autoři: Maximilian Witte aff001;  Sören Jaspers aff002;  Horst Wenck aff002;  Michael Rübhausen aff001;  Frank Fischer aff002
Působiště autorů: Center for Free-Electron Laser Science (CFEL), University of Hamburg, Hamburg, Germany aff001;  Beiersdorf AG, Hamburg, Germany aff002
Vyšlo v časopise: PLoS ONE 15(1)
Kategorie: Research Article


Quantification of the angular orientation distribution of fibrous tissue structures in scientific images benefits from the Fourier image analysis to obtain quantitative information. Measurement uncertainties represent a major challenge and need to be considered by propagating them in order to determine an adaptive anisotropic Fourier filter. Our adaptive filter method (AF) is based on the maximum relative uncertainty δcut of the power spectrum as well as a weighted radial sum with weighting factor α. We use a Monte-Carlo simulation to obtain realistic greyscale images that include defined variations in fiber thickness, length, and angular dispersion as well as variations in noise. From this simulation the best agreement between predefined and derived angular orientation distribution is found for evaluation parameters δcut = 2.1% and α = 1.5. The resulting cumulative orientation distribution was modeled by a sigmoid function to obtain the mean angle and the fiber dispersion. A comparison to a state-of-the-art band-pass method revealed that the AF method is more suitable for the application on greyscale fiber images, since the error of the fiber dispersion significantly decreased from (33.9 ± 26.5)% to (13.2 ± 12.7)%. Both methods were found to accurately quantify the mean fiber orientation with an error of (1.9 ± 1.5)° and (2.3 ± 2.1)° in case of the AF and the band-pass method, respectively. We demonstrate that the AF method is able to accurately quantify the fiber orientation distribution in in vivo second-harmonic generation images of dermal collagen with a mean fiber orientation error of (6.0 ± 4.0)° and a dispersion error of (9.3 ± 12.1)%.

Klíčová slova:

Aspect ratio – Collagens – Fourier analysis – Grayscale – Image processing – Imaging techniques – Monte Carlo method – Signal filtering


1. Ní Annaidh A, Bruyère K, Destrade M, Gilchrist MD, Otténio M. Characterization of the anisotropic mechanical properties of excised human skin. J Mech Behav Biomed Mater. 2012;5(1):139–148. doi: 10.1016/j.jmbbm.2011.08.016 22100088

2. Bancelin S, Lynch B, Bonod-Bidaud C, Ducourthial G, Psilodimitrakopoulos S, Dokládal P, et al. Ex vivo multiscale quantitation of skin biomechanics in wild-type and genetically-modified mice using multiphoton microscopy. Sci Rep. 2015;5(December):1–14.

3. Chen X, Nadiarynkh O, Plotnikov S, Campagnola PJ. Second harmonic generation microscopy for quantitative analysis of collagen fibrillar structure. Nat Protoc. 2012;7(4):654–669. doi: 10.1038/nprot.2012.009 22402635

4. Frisch KE, Duenwald-Kuehl SE, Kobayashi H, Chamberlain CS, Lakes RS, Vanderby R. Quantification of collagen organization using fractal dimensions and Fourier transforms. Acta Histochem. 2012;114(2):140–144. doi: 10.1016/j.acthis.2011.03.010 21529898

5. Levillain A, Orhant M, Turquier F, Hoc T. Contribution of collagen and elastin fibers to the mechanical behavior of an abdominal connective tissue. J Mech Behav Biomed Mater. 2016;61:308–317. doi: 10.1016/j.jmbbm.2016.04.006 27100469

6. Marquez JP. Fourier analysis and automated measurement of cell and fiber angular orientation distributions. Int J Solids Struct. 2006;43(21):6413–6423. doi: 10.1016/j.ijsolstr.2005.11.003

7. Mega Y, Robitaille M, Zareian R, McLean J, Ruberti J, DiMarzio C. Quantification of lamellar orientation in corneal collagen using second harmonic generation images. Opt Lett. 2012;37(16):3312–4. doi: 10.1364/OL.37.003312 23381241

8. Mercatelli R, Ratto F, Rossi F, Tatini F, Menabuoni L, Malandrini A, et al. Three-dimensional mapping of the orientation of collagen corneal lamellae in healthy and keratoconic human corneas using SHG microscopy. J Biophotonics. 2017;10(1):75–83. doi: 10.1002/jbio.201600122 27472438

9. Nesbitt S, Scott W, Macione J, Kotha S. Collagen Fibrils in Skin Orient in the Direction of Applied Uniaxial Load in Proportion to Stress while Exhibiting Differential Strains around Hair Follicles. Materials (Basel). 2015;8(4):1841–1857. doi: 10.3390/ma8041841

10. Rezakhaniha R, Agianniotis A, Schrauwen JTC, Griffa A, Sage D, Bouten CVC, et al. Experimental investigation of collagen waviness and orientation in the arterial adventitia using confocal laser scanning microscopy. Biomech Model Mechanobiol. 2012;11(3-4):461–473. doi: 10.1007/s10237-011-0325-z 21744269

11. Ribeiro JF, dos Anjos EHM, Mello MLS, de Campos Vidal B. Skin Collagen Fiber Molecular Order: A Pattern of Distributional Fiber Orientation as Assessed by Optical Anisotropy and Image Analysis. PLoS One. 2013;8(1):5–7. doi: 10.1371/journal.pone.0054724

12. Schriefl AJ, Reinisch AJ, Sankaran S, Pierce DM, Holzapfel GA. Quantitative assessment of collagen fibre orientations from two-dimensional images of soft biological tissues. J R Soc Interface. 2012;9(76):3081–3093. doi: 10.1098/rsif.2012.0339 22764133

13. Stender CJ, Rust E, Martin PT, Neumann EE, Brown RJ, Lujan TJ. Modeling the effect of collagen fibril alignment on ligament mechanical behavior. Biomech Model Mechanobiol. 2018;17(2):543–557. doi: 10.1007/s10237-017-0977-4 29177933

14. Van Zuijlen PPM, Ruurda JJB, Van Veen HA, Van Marle J, Van Trier AJM, Groenevelt F, et al. Collagen morphology in human skin and scar tissue: No adaptations in response to mechanical loading at joints. Burns. 2003. doi: 10.1016/s0305-4179(03)00052-4 12880721

15. Wu S, Li H, Yang H, Zhang X, Li Z, Xu S. Quantitative analysis on collagen morphology in aging skin based on multiphoton microscopy. J Biomed Opt. 2011. doi: 10.1117/1.3565439

16. Pourdeyhimi B, Dent R, Davis H. Measuring Fiber Orientation in Nonwovens Part III: Fourier Transform. Text Res J. 1997;67(2):143–151. doi: 10.1177/004051759706700211

17. Ghassemieh E, Acar M, Versteeg H. Microstructural analysis of non-woven fabrics using scanning electron microscopy and image processing. Part 1: Development and verification of the methods. Proc Inst Mech Eng Part L J Mater Des Appl. 2002;216(3):199–207.

18. Ayres CE, Jha BS, Meredith H, Bowman JR, Bowlin GL, Henderson SC, et al. Measuring fiber alignment in electrospun scaffolds: A user’s guide to the 2D fast Fourier transform approach. J Biomater Sci Polym Ed. 2008;19(5):603–621. doi: 10.1163/156856208784089643 18419940

19. D’Amore A, Stella JA, Wagner WR, Sacks MS. Characterization of the complete fiber network topology of planar fibrous tissues and scaffolds. Biomaterials. 2010;31(20):5345–54. doi: 10.1016/j.biomaterials.2010.03.052 20398930

20. Liu C, Zhu C, Li J, Zhou P, Chen M, Yang H, et al. The effect of the fibre orientation of electrospun scaffolds on the matrix production of rabbit annulus fibrosus-derived stem cells. Bone Res. 2015;3(January).

21. Redon C, Chermant L, Chermant JL, Coster M. Assessment of fibre orientation in reinforced concrete using Fourier image transform. J Microsc. 1998;191(3):258–265. doi: 10.1046/j.1365-2818.1998.00393.x 9767490

22. Stender CJ, Rust E, Martin PT, Neumann EE, Brown RJ, Lujan TJ. Modeling the effect of collagen fibril alignment on ligament mechanical behavior. Biomech Model Mechanobiol. 2018;17(2):543–557. doi: 10.1007/s10237-017-0977-4 29177933

23. Gasser TC, Ogden RW, Holzapfel GA. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface. 2006;3(6):15–35. doi: 10.1098/rsif.2005.0073 16849214

24. Fan R, Sacks MS. Simulation of planar soft tissues using a structural constitutive model: Finite element implementation and validation. J Biomech. 2014. doi: 10.1016/j.jbiomech.2014.03.014 24746842

25. Wu H, Fan J, Chu CC, Wu J. Electrospinning of small diameter 3-D nanofibrous tubular scaffolds with controllable nanofiber orientations for vascular grafts. J Mater Sci Mater Med. 2010;21(12):3207–3215. doi: 10.1007/s10856-010-4164-8 20890639

26. Frahs SM, Oxford JT, Neumann EE, Brown RJ, Keller-Peck CR, Pu X, et al. Extracellular Matrix Expression and Production in Fibroblast-Collagen Gels: Towards an In Vitro Model for Ligament Wound Healing. Ann Biomed Eng. 2018;46(11):1882–1895. doi: 10.1007/s10439-018-2064-0 29873012

27. Lau TY, Ambekar R, Toussaint KC. Quantification of collagen fiber organization using three-dimensional Fourier transform-second-harmonic generation imaging. Opt Express. 2012;20(19):21821. doi: 10.1364/OE.20.021821 23037302

28. Lutz V, Sattler M, Gallinat S, Wenck H, Poertner R, Fischer F. Impact of collagen crosslinking on the second harmonic generation signal and the fluorescence lifetime of collagen autofluorescence. Ski Res Technol. 2012;18(2):168–179. doi: 10.1111/j.1600-0846.2011.00549.x

29. Lutz V, Sattler M, Gallinat S, Wenck H, Poertner R, Fischer F. Characterization of fibrillar collagen types using multi-dimensional multiphoton laser scanning microscopy. Int J Cosmet Sci. 2012;34(2):209–215. doi: 10.1111/j.1468-2494.2012.00705.x 22235828

30. Annaidh AN, Karine Bruyère, Destrade M, Gilchrist MD, Maurini C, Otténio M, et al. Automated estimation of collagen fibre dispersion in the dermis and its contribution to the anisotropic behaviour of skin. Ann Biomed Eng. 2012;40(8):1666–1678. doi: 10.1007/s10439-012-0542-3

31. Bredfeldt JS, Liu Y, Pehlke CA, Conklin MW, Szulczewski JM, Inman DR, et al. Computational segmentation of collagen fibers from second-harmonic generation images of breast cancer. J Biomed Opt. 2014;19(1):016007. doi: 10.1117/1.JBO.19.1.016007

32. Kim A, Lakshman N, Petroll WM. Quantitative assessment of local collagen matrix remodeling in 3-D Culture: The role of Rho kinase. Exp Cell Res. 2006. doi: 10.1016/j.yexcr.2006.08.009

33. Sander EA, Barocas VH. Comparison of 2D fiber network orientation measurement methods. J Biomed Mater Res—Part A. 2009;88(2):322–331. doi: 10.1002/jbm.a.31847

34. Morrill EE, Tulepbergenov AN, Stender CJ, Lamichhane R, Brown RJ, Lujan TJ. A validated software application to measure fiber organization in soft tissue. Biomech Model Mechanobiol. 2016;15(6):1467–1478. doi: 10.1007/s10237-016-0776-3 26946162

35. Yang W, Sherman VR, Gludovatz B, Schaible E, Stewart P, Ritchie RO, et al. On the tear resistance of skin. Nat Commun. 2015;6:6649. doi: 10.1038/ncomms7649 25812485

36. Polzer S, Gasser TC, Forsell C, Druckmüllerova H, Tichy M, Staffa R, et al. Automatic identification and validation of planar collagen organization in the aorta wall with application to abdominal aortic aneurysm. Microsc Microanal. 2013;19(6):1395–1404. doi: 10.1017/S1431927613013251 24016340

37. Schriefl AJ, Wolinski H, Regitnig P, Kohlwein SD, Holzapfel GA. An automated approach for three-dimensional quantification of fibrillar structures in optically cleared soft biological tissues. J R Soc Interface. 2012.

38. Puschmann S, Rahn CD, Wenck H, Gallinat S, Fischer F. In vivo quantification of human dermal skin aging using SHG and autofluorescence. Multimodal Biomed Imaging VII. 2012;8216:821608. doi: 10.1117/12.906460

39. MATLAB. version (R2018a). The MathWorks Inc.; 2018.

40. MATLAB. Image Processing Toolbox (version 10.2). The MathWorks Inc.; 2018.

41. MATLAB. Curve Fitting Toolbox (version 3.5.7). The MathWorks Inc.; 2018.

42. Paul H, Jex I, Paul H, Jex I. Photon statistics. Introd to Quantum Opt. 2010; p. 127–154.

43. Becker RI, Morrison N. The errors in FFT estimation. IEEE Trans Signal Process. 2002;44(8):133–135.

44. Withayachumnankul W, Fischer BM, Lin H, Abbott D. Uncertainty in terahertz time-domain spectroscopy measurement. J Opt Soc Am B. 2008;25(6):1059. doi: 10.1364/JOSAB.25.001059

45. Moisan L. Periodic plus smooth image decomposition. J Math Imaging Vis. 2011;39(2):161–179. doi: 10.1007/s10851-010-0227-1

46. University of Wisconsin. Public-Domain Test Images for Homeworks and Projects;. Available from:

47. Lagarias C J, Reeds A J, Wright H M, Wright E P. Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions. SIAM J Optim. 1998;9(1):112–147. doi: 10.1137/S1052623496303470

48. Koenig K, Riemann I. High-resolution multiphoton tomography of human skin with subcellular spatial resolution and picosecond time resolution. J Biomed Opt. 2003;8(3):432. doi: 10.1117/1.1577349

49. Rahn CD, Meine H, Gallinat S, Wenck H, Wittern KP, Fischer F. Fully automated data acquisition and fast data interpretation in a customized multimodal multiphoton microscope. In: Three-Dimensional Multidimens. Microsc. Image Acquis. Process. XVII; 2010.

50. Schwarz M, Riemann I, Stracke F, Huck V, Gorzelanny C, Schneider SW, et al. A comparative study of different instrumental concepts for spectrally and lifetime-resolved multiphoton intravital tomography (5D-IVT) in dermatological applications. In: Imaging, Manip. Anal. Biomol. Cells, Tissues VIII; 2010.

Článek vyšel v časopise


2020 Číslo 1
Nejčtenější tento týden