This Article 
 Bibliographic References 
 Add to: 
Use of the Two-Dimensional Radon Transform to Generate a Taxonomy of Shape for the Characterization of Abrasive Powder Particles
December 2000 (vol. 22 no. 12)
pp. 1411-1423

Abstract—A novel image processing technique for the extraction of parameters characteristic of the shape and angularity of abrasive powder particles is proposed. The image data are not analyzed directly. Information concerning angularity and shape is extracted from the parametric transformation of the 2D binarized edge map. The transformation process used, the Radon Transform, is one to many, that is, each image point generates in transform space the parameters of all the possible curves on which it may lie and the resulting distribution is an accumulation of that evidence. Once the image data are segmented, the technique has the potential to deliver a comprehensive numerical description of the shape and angularity of the particles under investigation without the need for further interaction by the operator. The parameters obtained are arranged into a Taxonomy according to their usefulness in categorizing the shapes under inspection. The technique is novel in that it offers an analytical definition of a corner and its apex and it automatically selects only those protrusions coincident with the convex hull of the shape and, hence, those most likely to contribute to the process of abrasion. The advantages and potential pitfalls of using the technique are illustrated and discussed using real image data.

[1] M.A. Verspui, P. Van der Velden, and P.J. Slikkerveer, “Angularity Determination of Abrasive Particles,” Wear, vol. 199, pp. 122-126, 1996.
[2] T.B. Kirk, R.V. Anamalay, and Z.L. Xu, “Computer Image Analysis of Wear Debri for Machine Conditioning Monitoring and Fault Diagnosis,” Wear, vol. 181, pp. 717-722, 1995.
[3] T. Allen, Particle Size Measurement. Chapman and Hall, 1997.
[4] A.E. Hawkins, The Shape of Powder-Particle Outlines. New York: John Wiley, 1993.
[5] B.H. Kaye, The Direct Characterization of Fineparticles. New York: John Wiley, 1981.
[6] B.H. Kaye, G.G. Clark, and Y. Liu, “Characterizing the Structure of Abrasive Fine Particles,” Particle and Particle Systems Characterization, vol. 9, pp. 1-8, 1992.
[7] G.W. Stachowiak, “Numerical Characterization of Wear Particle Morphology and Angularity of Particles and Surfaces,” Tribology, vol. 31, pp. 139-157, 1998.
[8] G.L. Turin, “An Introduction to Matched Filters,” IRE Trans. Information Theory, vol. 6, 1960.
[9] P.V.C. Hough, “Method and Means for Recognizing Complex Patterns,” US Patent 3069654, 1962.
[10] G.C. Stockman and A.K. Agrawala, “Equivalence of Hough Curve Detection to Template Matching,” Comm. ACM, vol. 20, 1977.
[11] D. Casasent and R. Krishnapuram, “Curved Object Location by Hough Transformations and Inversions, Pattern Recognition, vol. 20, no. 2, pp. 181-188, 1987.
[12] D.H. Ballard, “Generalizing the Hough Transform to Detect Arbitrary Shapes,” Pattern Recognition, vol. 13, pp. 111-122, 1981.
[13] V.F. Leavers, "Survey: Which Hough transform?," CVGIP: Image Understanding, vol. 58, no. 2, pp. 250-264, Sept. 1993.
[14] J. Radon, “Uber die Bestimmung von Funktionen durch ihre Integralwerte langs gewisser Mannigfaltigkeiten,” Berichte Sachsische Akademie der Wissenschaften Leipzig, vol. 69, pp. 262-267, 1917.
[15] I.M. Gel'fand, M.I. Graev, and N.Y. Vilenkin, Generalized Functions, vol. 5.New York: Academic Press, 1966.
[16] S.R. Deans, “Hough Transform from the Radon Transform,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 3, Mar. 1981.
[17] S.R. Deans, Applications of the Radon Transform. New York: Wiley Interscience Publications, 1983.
[18] V.F. Leavers, U.K. Patent Application No. 9908152.3, Apr. 1999.
[19] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active Contour Models,” Int'l J. Computer Vision, pp. 321-331, 1988.
[20] N. Kiryati and A.M. Bruckstein, “Antialiasing the Hough Transform,” CVGIP Graphical Models and Image Processing, vol. 53, no. 3, pp. 213-222, May 1991.
[21] A.G. Flook, “Fourier Analysis of Particle Shape,” Particle Size Analysis, 1981.
[22] W.E. Full and R. Ehrlich, “Some Approaches for Location of Centroids of Quartz Grain Outlines to Increase Homology between Fourier Amplitude Spectra,” Mathmatical Geology, vol. 14, pp. 43-55, 1982.
[23] A. Latto, D. Mumford, and J. Shah, “The Representation of Shape,” Proc. IEEE Workshop Computer Vision, 1984.

Index Terms:
Radon Transform, shape characterization, powder particle technology, wear particles.
Violet F. Leavers, "Use of the Two-Dimensional Radon Transform to Generate a Taxonomy of Shape for the Characterization of Abrasive Powder Particles," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 12, pp. 1411-1423, Dec. 2000, doi:10.1109/34.895975
Usage of this product signifies your acceptance of the Terms of Use.