Skip to main content
SpringerLink
Log in

Quantitative shape analysis: A review

  • Published:
Journal of the International Association for Mathematical Geology Aims and scope Submit manuscript

Abstract

Sedimentologists, among others, have been accustomed to the analysis of the shape of sedimentary particles. Recently such shapes have been subjected to more quantitative analysis, almost completely removing the subjective element so long inherent in the various indices. However, these quantitative analyses themselves are not free from qualitative bias, partly displayed in the choice of appropriate technique, and to some extent in the intermediate steps of the data collection and analysis. Various numerical methods are introduced within the framework of a typology based on whether the analysis is performed on the grain considered as an outline, or as a planar surface. Nine desirable properties are suggested, as a yardstick against which to evaluate the descriptors. In all these techniques the object is to examine a discrete approximation of single items, in two dimensions only. Some of the methods are nevertheless applicable to three dimensions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alt, F. L., 1962, Digital pattern recognition by moments: Jour. Assoc. Comp. Mach., v. 9, p. 240–258.

    Google Scholar 

  • Anstey, R. L., and Delmet, D. A., 1973, Fourier analysis of zooecial shapes of fossil bryozoans: Bull. Geol. Soc. Amer., v. 84, p. 1753–1764.

    Google Scholar 

  • Armstrong, A. C., 1980, A novel system for digitizing trace records: Area, v. 12, p. 123–127.

    Google Scholar 

  • Barrett, P. J., 1980, The shape of rock particles: a critical review: Sedimentology, v. 27, p. 291–303.

    Google Scholar 

  • Beddow, J. K. and Philip, G., 1975, On the use of a Fourier analysis technique for describing the shape of individual particles: Planseeber. Pulvermet., v. 23, p. 3–14.

    Google Scholar 

  • Benson, R. H., 1967, Muscle scar patterns in Pleistocene (Kansan) ostracodes,in Teichart, Curt and Yochelson (eds.), Essays in paleontology and stratigraphy: Kansas University Press, Lawrence, Kansas, p. 211–241.

    Google Scholar 

  • Bloore, F. J., 1977, The shape of pebbles: Jour. Math. Geol., v. 9, p. 113–122.

    Google Scholar 

  • Brill, E. L., 1972, Character recognition via Fourier descriptors: WESCON Tech. Papers, session 25, p. 1–10.

    Google Scholar 

  • Cosgriff, R. L., 1960, Identification of shape: Ohio State University Research Foundation Report 820-11, AF33(616)-5590, 13 p.

  • Cheng, D. C.-H. and Sutton, H. M. 1971, Absolute determination of particle size and shape: Nature Phys. Sci., v. 232, p. 192–3.

    Google Scholar 

  • Clark, M. W. and Clark, I., 1976, A sedimentological pattern recognition problem,in D. F. Merriam (ed.), Quantitative techniques for the analysis of sediments: Pergamon, Oxford, p. 121–141.

    Google Scholar 

  • Czarnecka, E. and Gillott, J. E., 1977, A modified Fourier method of shape and surface texture analysis of planar sections of particles: Jour. Test Evaluation ASTM, v. 5, p. 292–298.

    Google Scholar 

  • Czarnecka, E. and Gillott, J. E., 1980, Roughness of limestone and quartzite pebbles by the modified Fourier method: Jour. Sedim. Petrol., v. 50, p. 857–868.

    Google Scholar 

  • Davies, K. W. and Hawkins, A. E., 1979, Harmonic description of particle shape: their role in discrimination (abs): second European Symposium on Particle Characterisation, Nurnberg.

  • Davies R., 1975, A simple feature space representation of particle shape: Powder Tech., v. 12, p. 111–124.

    Google Scholar 

  • Davis, P. F. and Dexter, A. R., 1972, Two methods for quantitative description of soil particle shape: J. Soil Sci., v. 23, p. 448–455.

    Google Scholar 

  • Duda, R. O. and Hart, P. E., 1973, Pattern classification and scene analysis: John Wiley & Sons, New York.

    Google Scholar 

  • Ehrlich, R., Brown, P. J., Yarus, J. M., and Przygocki, R. S., 1980, The origin of shape frequency distributions and the relationship between size and shape: J. Sedim. Petrol., v. 50, p. 475–484.

    Google Scholar 

  • Ehrlich, R. and Weinberg, B., 1970, An exact method for characterization of grain shape: J. Sedim. Petrol., v. 40, p. 205–212.

    Google Scholar 

  • Fabbri, A. G., 1980, Giapp: geological image-analysis program package for estimating geometrical probabilities: Comp. Geosci., v. 6, p. 153–162.

    Google Scholar 

  • Firey, W. J., 1974, Shapes of worn stones: Mathematika, v. 21, p. 1–11.

    Google Scholar 

  • Freeman, H., 1961, On the encoding of arbitrary geometric configurations: IEEE Trans. Elec. Comp., EC-10, p. 260–268.

    Google Scholar 

  • Freeman, H., 1962, On the digital computer classification of geometric line patterns: Proc. Natl. Electr. Conf., p. 312–324.

  • Freeman, H. and Glass, J. M., 1969, On the quantization of line drawing data: IEEE Trans. Sys. Sci. Cyber. SSC-5, p. 70–79.

    Google Scholar 

  • Fong, S. T., Beddow, J. K., and Vetter, A. F., 1979, A refined method of particle shape representation: Powder Tech., v. 22, p. 17–21.

    Google Scholar 

  • Fritzche, D. L., 1961, A systematic method for character recognition: Ohio State University Research Foundation Report, 1222-4 ASTIA AD254 792, 56 pp.

  • Gotoh, K. and Finney, J. L., 1975, Representation of the size and shape of a single particle: Powder Tech., v. 12, p. 125–130.

    Google Scholar 

  • Granlund, G. H., 1972, Fourier preprocessing for hand print character recognition: IEEE Trans. Comp. C21, p. 195–201.

  • Griffiths, J. C., 1967, Scientific method in the analysis of sediments: McGraw-Hill, New York, 508 p.

    Google Scholar 

  • Hu, M-K., 1962, Visual pattern recognition by moment invariants: IEEE Trans. Inf. Theory IT8, p. 179–187.

  • Haralick, R. M. and Shanmugan, K., 1973, Computer classification of reservoir sandstones. IEEE Trans. Geosci. Electronics GE11, p. 171–177.

  • Jarvis, R. S., 1976, Classification of nested tributary basins in analysis of drainage basin shape: Water Res. Res., v. 12, p. 1151–1164.

    Google Scholar 

  • Klein, J. C. and Serra, J., 1972, The texture analyser: Jour. Microscopy, v. 95, p. 349–356.

    Google Scholar 

  • Levine, M. D., 1969, Feature extraction—a survey: Proc. IEEE, v. 57, p. 1391–1407.

    Google Scholar 

  • Matheron, G., 1975, Random sets and integral geometry: Wiley, New York.

    Google Scholar 

  • Medalia, A. I., 1970, Dynamic shape factors of particles: Powder Tech., v. 4, p. 117–138.

    Google Scholar 

  • Meloy, T. P., 1977a, A hypothesis for morphological characterisation of particle shape and physiochemical properties: Power Tech., v. 16, p. 233–253.

    Google Scholar 

  • Meloy, T. P., 1977b, Fast Fourier transform applied to shape analysis of particle silhouettes to obtain morphological data: Powder Tech., v. 17, p. 27–35.

    Google Scholar 

  • Metzler, B., Searle, N. H., and Brown, R., 1967, Numerical specification of biological form: Nature, v. 216, p. 32–36.

    Google Scholar 

  • Nahin, P. J., 1972, A parallel machine for describing and classifying silhouettes: (PhD Thesis) Univ. Calif. (Irvine), 184 pp.

  • Nahin, P. J., 1974, The theory and measurement of a silhouette descriptor for image preprocessing and recognition: Pattern Recog., v. 6, p. 85–95.

    Google Scholar 

  • Persoon, E. and Fu, K. S., 1974, Shape discrimination using Fourier descriptors. Second International Joint Conference on Pattern Recognition, Copenhagen, p. 126–130.

  • Piper, D. J. W., 1970, The use of the D-Mac pencil follower in routine determinations of sedimentary parameters,in J. T. Cutbill (ed.), Data processing in biology and geology, 97–103.

  • Powers, M. C., 1953, A new roundness scale for sedimentary particles: J. Sedim. Petrol., v. 23, p. 117–119.

    Google Scholar 

  • Richard, C. W. and Hemami, H., 1974, Identification of three-dimensional objects using Fourier descriptors of the boundary curve: IEEE Trans. Sys. Man Cyber. SMC4, p. 371–378.

  • Schwarcz, H. P. and Shane, K. C., 1969, Measurement of particle shape by Fourier analysis: Sedimentology, v. 13, p. 213–231.

    Google Scholar 

  • Sebestyn, G. S., 1959, On pattern recognition with application to silhouettes: (PhD Thesis) MIT 113 pp.

  • Sklansky, J. and Davison, G. A., 1971, Recognizing three dimensional objects by their silhouettes: Jour. Soc. Photo-Opt. Instrum. Eng., v. 10, p. 10–17.

    Google Scholar 

  • Sklansky, J. and Nahin, P. J., 1972, A parallel mechanism for describing silhouettes: IEEE Trans. Comp. C21, v. 11, p. 1233–1239.

    Google Scholar 

  • Szadeczsky-Kardross, E., 1933, Die Bestimmung des Abrollungsgrades: Zentralb. Mineral. Geol. Paleontol. B, p. 389–401.

  • Tucker, N. D. and Evans, F. C., 1974, A two stage strategy for character recognition using geometrical moments.: Second International Joint Conference on Pattern Recognition, Copenhagen, 223–225.

  • Watson, G. S. 1975, Texture analysis: Geol. Soc. Amer. Mem., v. 142, p. 367–391.

    Google Scholar 

  • Weichert, R. and Huller, D., 1979, Measurement of volume shape of particles by threedimensional image analysis (abs)., Second European Symposium on Particle Characterisation, Nurnberg.

  • Zahn, C. T. and Roskies, R. Z., 1972, Fourier descriptors for plane closed curves: IEEE Trans. Comp. C21, p. 269–281.

Download references

Author information

Authors and Affiliations

  1. Imperial College Computer Centre, SW7 2BX, London, England

    Malcolm W. Clark

Authors
  1. Malcolm W. Clark
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Clark, M.W. Quantitative shape analysis: A review. Mathematical Geology 13, 303–320 (1981). https://doi.org/10.1007/BF01031516

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01031516

Key words

Search

Navigation