Machine Vision and Applications

, Volume 26, Issue 6, pp 775–789 | Cite as

Grain-size assessment of fine and coarse aggregates through bipolar area morphology

  • Francesco Bianconi
  • Francesco Di Maria
  • Caterina Micale
  • Antonio Fernández
  • Richard W. Harvey
Original Paper


This paper presents a new methodology for computing grey-scale granulometries and estimating the mean size of fine and coarse aggregates. The proposed approach employs area morphology and combines the information derived from both openings and closings to determine the size distribution. The method, which we refer to as bipolar area morphology (BAM), is general and can operate on particles of different size and shape. The effectiveness of the procedure was validated on a set of 13 classes of aggregates of size ranging from 0.125 to 16 mm and made a comparison with standard, fixed-shape granulometry. In the experiments our model consistently outperformed the standard approach and predicted the correct size class with overall accuracy over 92 %. Tests on three classes from real samples also confirmed the potential of the method for application in real scenarios.


Image analysis Granulometry  Area morphology Aggregates 

List of Symbols



Bipolar area morphology


Primary classes


Random classes


Secondary classes

Greek letters

\(\lambda \)

Sieve scale (pixel)

\(\phi _\mathrm{m}\), \(\phi _\mathrm{M}\), \(\phi \)

Minimum, maximum and expected true grain-size (mm)

\(\hat{\phi }\)

Response of image-based granulometry (pixel)

\(\bar{\phi }\)

Estimated mean grain size (mm)

\(\sigma \)

Standard deviation

Latin letters


Classification accuracy for the pth problem


Average classification accuracy


Number of classes

\(\mathcal {C}\)

Morphological closing


Discrete cumulative size distribution


Discrete pattern spectrum

\(\mathbf {I}\)

Input image

\(\mathcal {O}\)

Morphological opening

\(\mathcal {OC}\)

Combined morphological opening and closing (bipolar morphology)

\(V(\mathbf {I})\)

Volume of the input image (sum of pixels’ values)


Number of subdivisions into train and test set (also referred to as number of problems or number of folds)


Coefficient of determination


Standard error


Number of training samples


Height of the input image


Width of the input image


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Francesco Bianconi
    • 1
  • Francesco Di Maria
    • 1
  • Caterina Micale
    • 1
  • Antonio Fernández
    • 2
  • Richard W. Harvey
    • 3
  1. 1.Department of EngineeringUniversità degli Studi di PerugiaPerugiaItaly
  2. 2.School of Industrial EngineeringUniversidade de VigoVigoSpain
  3. 3.School of Computing SciencesUniversity of East AngliaNorwichUK

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