Abstract
Standard granulometry methods are used to count the number of disjoint grains in digital images. For the case of overlapping grains, the standard method is not effective. Two alternative methods for counting overlapping grains in digital images are proposed. The methods are based on mathematical morphology and are suitable for grains of circular shape. The standard and overlapping methods were tested with a Monte-Carlo simulation using 32500 synthetic images with various grain sizes and quantities, as well as different levels of noise. The overall average counting error for all images tested with intermediate amount of noise (zero mean Gaussian noise with σ= 0.05) was 6.03% for the standard method, and 4.40% and 3.56% for the overlapping methods. The performance of the proposed methods was found to be much better than the standard method for images with significant overlap between grains.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Matheron, G.: Random sets and integral geometry. Wiley, Chichester (1975)
Prodanov, D., Heeroma, J., Marani, E.: Automatic morphometry of synaptic boutons of cultured cells using granulometric analysis of digital images. Journal of Neuroscience Methods 151, 168–177 (2006)
Serra, J.: Image analysis and mathematical morphology. Academic Press, London (1982)
Theera-Umpon, N., Dougherty, E.R., Gader, P.D.: Non-homothetic granulometric mixing theory with application to blood cell counting. Pattern Recognition 34, 2547–2560 (2001)
Francus, P.: An image-analysis technique to measure grain-size variation in thin sections of soft clastic sediments. Sedimentary Geology 121, 289–298 (1998)
Selmaoui, N., Repetti, B., Laporte-Magoni, C., Allenbach, M.: Coupled strata and granulometry detection on indurated cores by gray-level image analysis. Geo-Mar Lett. 24, 241–251 (2004)
Dougherty, E.R., Cuciurean-Zapan, C.: Optimal reconstructive z-openings for disjoint and statistically modeled nondisjoint grains. Signal Processing 56, 45–58 (1997)
Syngenta. Water-sensitive paper for monitoring spray distributions. CH-4002. Basle, Switzerland, Syngenta Crop Protection AG (2002)
Gonzalez, R.C., Woods, R.E.: Digital Image Processing. Prentice-Hall, Englewood Cliffs (2002)
Gonzalez, R.C., Woods, R.E., Eddins, S.L.: Digital Image Processing using MATLAB. Prentice-Hall, Englewood Cliffs (2004)
Haralick, R.M., Shapiro, L.G.: Computer and Robot Vision, vol. I, pp. 28–48. Addison-Wesley, Reading (1992)
Using Matlab, Version 6.5. The MathWorks, Inc. Natick. MA (2002)
Dougherty, E.R., Sand, F.: Representation of Linear Granulometric Moments for Deterministic and Random Binary Euclidean Images. Journal of Visual Communication and Image Representation 6, 69–79 (1995)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Marçal, A.R.S. (2008). Alternative Methods for Counting Overlapping Grains in Digital Images. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2008. Lecture Notes in Computer Science, vol 5112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69812-8_105
Download citation
DOI: https://doi.org/10.1007/978-3-540-69812-8_105
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69811-1
Online ISBN: 978-3-540-69812-8
eBook Packages: Computer ScienceComputer Science (R0)