Skip to main content
SpringerLink
Log in

Estimation of Minkowski Dimension Using Neighborhood Operations

  • Published:
Mathematical Geology Aims and scope Submit manuscript

Abstract

A method to estimate the Minkowski dimension using neighborhood operations is described. Its implementation using a software package IMAGER-2 on a square grid with eight connectivity is presented. It is observed that a range of successive pairs of dilations helps in arriving at the best estimate. The methodology is applied to find the Minkowski dimension of the skeleton of a stress corrosion crack.

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

  • Bhattacharya, D. K., and Raj, B., 1990, Analysis of failure in AISI 304 L SS dished end: IGCAR/DPEND/FA/90/1, 20 p.

  • Falconer, K., 1985, The Geometry of fractal sets: Cambridge University Press, New York, 288 p.

    Google Scholar 

  • Feder, J., 1988, Fractals: Plenum Press, New York, 283 p.

    Google Scholar 

  • Flook, A., 1978, Use of dilation logic on the Quantimet to achieve fractal dimension characterisation of surface and structural profiles: Powder Technology, v. 21, p. 295–298.

    Google Scholar 

  • Kanmani, S., Babu Rao, C., and Raj, B., 1992, On the computation of the Minkowski dimension using morphological operations: J. Microsc. v. 170, p. 81–85.

    Google Scholar 

  • Kanmani, S., Babu Rao, C., Bhattacharya, D. K., and Raj, B., 1992, Multifractal analysis of stress corrosion cracks: Acta Stereo v. 11, p. 349–354.

    Google Scholar 

  • Mandelbrot, B. B., 1982, The fractal geometry of nature: Freeman, San Francisco, 468 p.

    Google Scholar 

  • Rigaut, J. P., 1982, Automated image segmentation by mathematical morphology and fractal geometry: J. Microsc, v. 150, p. 21–30.

    Google Scholar 

  • Russ, J. C., 1999, Image processing handbook: CRC Press, Boca Raton, 771 p.

    Google Scholar 

  • Serra, J., 1982, Image analysis and mathematical morphology: Academic Press, London, p. 147–148.

    Google Scholar 

  • Soille, P., and Rivest, J. F., 1996, On the validity of fractal dimension measurements in image analysis: J. Visual Comm. Image Representation, v. 7, no. 3, p. 217–229.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603 102, India

    C. Babu Rao & Baldev Raj

  2. Division for PIE & NDT Development, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603 102, India

    C. Babu Rao

Authors
  1. C. Babu Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Baldev Raj
    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

Rao, C.B., Raj, B. Estimation of Minkowski Dimension Using Neighborhood Operations. Mathematical Geology 33, 369–376 (2001). https://doi.org/10.1023/A:1007642424442

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007642424442

Search

Navigation