Tribology Letters

, 61:2 | Cite as

Characterization of Surface Topography from Small Images

  • Marcin WolskiEmail author
  • Pawel Podsiadlo
  • Gwidon W. Stachowiak
Original Paper


Detailed characterization of 3D engineering surface topographies is still an unresolved problem. The reasons are that the majority of the real surfaces are anisotropic and multi-scale, i.e. their directionality and roughness change with the measurement scales. To solve this problem, a variance orientation transform (VOT) method was developed. It calculates fractal dimensions at individual scales, i.e. it calculates the fractal signature (FS) in all possible directions, addressing, in this way, the problems of surfaces’ multi-scale and anisotropic nature. However, the VOT method is not suited for the analysis of image sizes that are smaller than 48 × 48 pixels (e.g. images of wear particles surfaces, small surface defects, etc.). To redress this problem the VOT method was augmented so that it can calculate FSs for all images including those with small sizes. Previous study showed that the augmented VOT (AVOT) method is accurate in the analysis of hand x-ray images where the bone texture images are small (20 × 20 pixels). However, its usefulness in analysing small images of engineering surfaces has not yet been investigated. In the current study, we use range-images of different sizes (20 × 20 and 30 × 30 pixels) of polished (isotropic) and ground (anisotropic) steel plates. When applied to images of steel surfaces of different topography, the AVOT method has detected minute changes at different scales, undetectable by other commonly used surface characterization methods, between the surfaces. The results show that the method can be a valuable tool in characterization of small images of 3D engineering surfaces.


Surface characterization Fractals Roughness Texture 



Fractal dimension


Fractal signature


Variance orientation transform


Augmented VOT


Region of interest


Recursive multi-directional pixel selection


a, b

Major and minor axes of an ellipse


Confidence interval




Hurst coefficient

Iw, Ih (pixel)

Image width and height


Statistical significance

r1, r2 (pixel)

Inner and outer radii

Ra (μm)

Roughness average

Sa (μm)

Arithmetical mean height


Texture minor axis


Texture aspect ratio


Non-fractal texture aspect ratio

Std (°)

Fractal texture direction

Std (°)

Non-fractal texture direction


Standard deviation


Fractal signature S ta


Texture aspect ratio signature

StdS (°)

Texture direction signature

α (°)


θr (°)

Reference direction



The authors wish to thank the Curtin University, Department of Mechanical Engineering and the School of Civil and Mechanical Engineering for their support during preparation of the manuscript. The study was conducted as part of the Implementing Agreement on Advanced Material for Transportation Applications, Annex IV Integrated Engineered Surface Technology. The Implementing agreement functions within a framework created by the International Energy Agency (IEA). The views, findings, and publications of the AMT IA do not necessarily represent the views or policies of the IEA or of all of its individual member countries.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Marcin Wolski
    • 1
    Email author
  • Pawel Podsiadlo
    • 1
  • Gwidon W. Stachowiak
    • 1
  1. 1.Tribology Laboratory, Department of Mechanical Engineering, School of Civil and Mechanical EngineeringCurtin UniversityPerthAustralia

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