SpringerLink
Log in

Local Directional Fractal Signature Method for Surface Texture Analysis

  • Original Paper
  • Published:
Tribology Letters Aims and scope Submit manuscript

Abstract

The detection of changes in surface texture characteristics is an important issue in manufacturing, contact mechanics, control of interactions between surfaces, machine failure analysis, and others. These changes can be detected early on when surface texture is quantified locally at each point. To this end, a new method called local directional fractal signature has recently been developed that calculates local fractal dimensions (FD = 3 − slope) at individual scales and directions. In this method, texture parameters are derived from the slopes of lines fitted to log–log plots of local surface profiles against scales, and FDs to measure local surface roughness and directionality. First, the method is tested on computer-generated isotropic fractal surfaces with the objective to evaluate its ability to differentiate between surfaces exhibiting an increasing local roughness. This follows the method application to detect the anisotropy changes in computer-generated surfaces with increasing roughness in two directions. Finally, the method’s detection ability in finding differences between surfaces is evaluated. Microscopic range-images of sandblasted and abraded titanium alloy plates are used in the evaluation. This work is a further contribution to the advancement in the characterization of surface textures, the numerical tools development for the design of tribological components and the diagnosis of worn and damaged surfaces. Practical applications of the method (e.g., classification of wear images, characterization of coated and uncoated surfaces) would be reported later in the future.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data Availability

Not applicable.

Code Availability

Not applicable.

References

  1. ASME B46.1 Surface Texture, Surface Roughness, Waviness and Lay. Place (2002)

  2. ISO 4287 Geometrical Product Specifications (GPS) -Surface Texture: Profile Method Terms, Definitions and Surface Texture Parameters (1997)

  3. 25178–2 Geometrical product specifications (gps) Surface texture: areal part 2: Terms, definitions and surface texture parameters. International Organization for Standardization, Place International Organization for Standardization (2012)

  4. Articus, K., Brown, A.C., Wilhelm, W.P.: Scale-sensitive fractal analysis using the patchwork method for the assessment of skin roughness. Skin. Res. Technol. 7, 164–167 (2008)

    Article  Google Scholar 

  5. Articus, K., Brown, A.C., Wilhelm, W.P.: Effect of food surface roughness on oil uptake by deep-fat fried products. J. Food. Eng. 101, 179–186 (2010)

    Article  Google Scholar 

  6. Hasegawa, A., Itoh, K., Ichioka, Y.: Detection of cell membranes in human corneal endothelial micrograms using mathematical morphology. Jpn. J. App. Phys. 31, 798 (1992)

    Article  Google Scholar 

  7. Talu, S., Stach, S., Zaharieva, J., Milanova, K., Todorovsky, D., Giovanzana, S.: Surface roughness characterization of poly(methylmethacrylate) films with immobilized Eu(III) B-Diketonates by fractal analysis. Int. J. Polym. Anal. Charact. 19, 404–421 (2014)

    Article  CAS  Google Scholar 

  8. Dallaeva, D., Talu, S., Stach, S., Skarvada, P., Tomanek, P., Grmela, L.: AFM imaging and fractal analysis of surface roughness of AlN epilayers on sapphire substrates. Appl. Surf. Sci. 312, 81–86 (2014)

    Article  CAS  Google Scholar 

  9. Qin, W., **, X., Kirk, A., Shipway, P., Sun, W.: Effects of surface roughness on local friction and temperature distributions in a steel-on-steel fretting contact. Tribol. Int. 120, 350–357 (2018)

    Article  Google Scholar 

  10. Sigvant, M., Pilthammar, J., Hol, J., Wiebenga, J., Chezan, T., Carleer, B., et al.: Friction in sheet metal forming: influence of surface roughness and strain rate on sheet metal forming simulation results. Procedia. Manuf. 29, 512–519 (2019)

    Article  Google Scholar 

  11. Puleo, D.A., Nanci, A.: Understanding and controlling the bone–implant interface. Biomaterials 20, 2311–2321 (1999)

    Article  CAS  Google Scholar 

  12. Wen, C., Mudawar, I.: Modeling the effects of surface roughness on the emissivity of aluminum alloys. Int. J. Heat Mass Transf. 49, 4279–4289 (2006)

    Article  CAS  Google Scholar 

  13. Podsiadlo, P., Wolski, M., Stachowiak, G.W.: Directional signatures of surface texture. Tribol. Lett. 67, 109 (2019)

    Article  Google Scholar 

  14. Pentland, A.: Fractal-based description of natural scenes. IEEE Trans. Pattern Anal. Mach. Intell. 6, 661–674 (1984)

    Article  CAS  Google Scholar 

  15. Novianto, S., Suzuki, Y., Maeda, J.: Near optimum estimation of local fractal dimension for image segmentation. Pattern Recognit. Lett. 24, 365–374 (2003)

    Article  Google Scholar 

  16. Wenxue, J., Lam, N.S.N.: An improved algorithm for computing local fractal dimension using the triangular prism method. Comput. Geosci. 35, 1224–1233 (2009)

    Article  Google Scholar 

  17. Bryan, J.B.: The Abbe principle revisit: an updated interpretation. Precis. Eng. 1, 129–132 (1979)

    Article  Google Scholar 

  18. Whitehouse, D.J.: Handbook of Surface and Nanometrology. CRC Press, Boca Raton (2010)

    Book  Google Scholar 

  19. Stein, M.L.: Fast and exact simulation of fractional Brownian surfaces. J. Comput. Graph. Stat. 11, 587–599 (2002)

    Article  Google Scholar 

  20. Russ, J.C.: Fractal Surfaces. Plenum Press, New York (1994)

    Book  Google Scholar 

  21. Backes, A., Gonçalves, W., Martinez, A., Bruno, O.: Texture analysis and classification using deterministic tourist walk. Pattern Recognit. 43, 685–694 (2010)

  22. Gonçalves, W., Bruno, O.: Combining fractal and deterministic walkers for texture analysis and classification. Pattern Recognit. 46, 2953–2968 (2013)

    Article  Google Scholar 

  23. de Rooij, M., Schipper, D.: A wear measurement method based on the comparison of local surface heights. Wear 217, 182–189 (1998)

    Article  Google Scholar 

  24. Wolski, M., Woloszynski, T., Stachowiak, G.W., Podsiadlo, P.: Towards the automated classification system of worn surfaces. Proc. IMechE Part J 208–210, 1–10 (2019)

    Google Scholar 

  25. Wolski, M., Woloszynski, T., Podsladlo, P., Stachowiak, G.W.: En route to the automated wear surface classification system: differentiating between adhesive, abrasive, and corrosive wear under different load conditions. Tribol. Lett. 8, 87 (2020)

    Article  Google Scholar 

  26. Wolski, M., Podsiadlo, P., Stachowiak, G., Holmberg, K., Laukkanen, A., Ronkainen, H., et al.: Multiscale characterisation of 3D surface topography of DLC coated and uncoated surfaces by directional blanket covering (DBC) method. Wear 388–389, 47–56 (2017)

    Article  Google Scholar 

  27. Wolski, M., Podsiadlo, P., Stachowiak, G., Holmberg, K., Laukkanen, A., Ronkainen, H.: Characterization of DLC-coated and uncoated surfaces by new directional blanket curvature covering (DBCC) method. Tribol. Lett. 66, 153 (2018)

    Article  Google Scholar 

  28. Laukkanen, A., Holmberg, K., Ronkainen, H., Stachowiak, G., Podsiadlo, P., Wolski, M., et al.: Topographical orientation effects on surface stresses influencing on wear in sliding DLC contacts, Part 2: Modelling and simulations. Wear 388–389, 18–28 (2017)

    Article  Google Scholar 

  29. Xu, J., Zeng, W., Zhao, Y., Jia, Z.: Effect of microstructure evolution of the lamellar alpha on impact toughness in a two-phase titanium alloy. Mater. Sci. Eng. A 676, 434–440 (2016)

    Article  CAS  Google Scholar 

  30. Crostack, H., Nellesen, J., Fischer, G., Weber, U., Schmauder, S., Beckmann, F.: 3D Analysis of MMC microstructure and deformation by mu CT and FE simulations. Proc. SPIE 7078, 70781I-70781–70711 (2008)

  31. Stachowiak, G., Wolski, M., Woloszynski, T., Podsiadlo, P.: Detection and prediction of osteoarthritis in knee and hand joints based on the X-ray image analysis. Biosurf. Biotribol. 2, 162–172 (2016)

    Article  Google Scholar 

  32. Podsiadlo, P., Nevitt, M.C., Wolski, M., Stachowiak, G.W., Lynch, J.A., Tolstykh, I., et al.: Baseline trabecular bone and its relation to incident radiographic knee osteoarthritis and increase in joint space narrowing score: directional fractal signature analysis in the MOST study. Osteoarthr. Cartil. 24, 1736–1744 (2016)

    Article  CAS  Google Scholar 

  33. Wolski, M., Podsiadlo, P., Stachowiak, G.W.: Directional fractal signature analysis of trabecular bone: evaluation of different methods to detect early osteoarthritis in knee radiographs. Proc. Inst. Mech. Eng. H 223, 211–236 (2009)

    Article  CAS  Google Scholar 

  34. Wolski, M., Podsiadlo, P., Stachowiak, G.W.: Analysis of AFM images of self-structured surface textures by directional fractal signature method. Tribol. Lett. 49, 465–480 (2013)

    Article  Google Scholar 

  35. Wolski, M., Podsiadlo, P., Stachowiak, G.W.: Characterization of surface topography from small images. Tribol. Lett. 61, 2 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported under Australian Research Council’s Discovery Project funding scheme (Project No. DP180100700). The authors wish to thank the Curtin University and the School of Civil and Mechanical Engineering for their support during preparation of the manuscript.

Funding

Australian Research Council’s Discovery Project funding scheme (Project No. DP180100700).

Author information

Authors and Affiliations

  1. Tribology Laboratory, School of Civil and Mechanical Engineering, Curtin University, GPO Box U1987, Perth, WA, 6845, Australia

    Marcin Wolski, Tomasz Woloszynski, Pawel Podsiadlo & Gwidon W. Stachowiak

Authors
  1. Marcin Wolski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tomasz Woloszynski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pawel Podsiadlo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gwidon W. Stachowiak
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Individual authors contributed to the tasks of materials selection, methods, data collection and analysis. The first draft of the manuscript was written by Marcin Wolski. All the authors corrected and commented on subsequent versions of the manuscript. All authors read and approved the final version of the manuscript.

Corresponding author

Correspondence to Marcin Wolski.

Ethics declarations

Conflict of interest

The authors have no conflict of interest for this manuscript.

Ethical Approval

The study does not involve human participants nor biological material.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wolski, M., Woloszynski, T., Podsiadlo, P. et al. Local Directional Fractal Signature Method for Surface Texture Analysis. Tribol Lett 70, 15 (2022). https://doi.org/10.1007/s11249-021-01547-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11249-021-01547-2

Keywords

Search

Navigation