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IMAGE PYRAMIDS FOR CALCULATION OF THE BOX COUNTING DIMENSION

H. AHAMMER

Institute of Biophysics, Medical University of Graz, Harrachgasse 21, A-8010 Graz, Austria

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and

M. MAYRHOFER-REINHARTSHUBER

Institute of Biophysics, Medical University of Graz, Harrachgasse 21, A-8010 Graz, Austria

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https://doi.org/10.1142/S0218348X12500260Cited by:8 (Source: Crossref)

Abstract

The fractal dimensions of real world objects are commonly investigated using digital images. Unfortunately, these images are unable to represent an infinitesimal range of scales. In addition, a proper evaluation of the applied methods that encompass the image processing techniques is often missing. Several mathematical well-defined fractals with theoretically known fractal dimensions, represented by digital images, were investigated in this work. The very popular Box counting method was compared to a new image pyramid approach as well as to the Minkowski dilation method. Effects from noise and altered aspect ratios were also considered. The new Pyramid method is quite identical to the Box counting method, but it is easier to implement. Additionally, the calculation times are much shorter and memory requirements are almost comparable.

Keywords:

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