Fractal dimension

Fractal Dimension: Reports the fractal dimension of the object’s outline.

 

this is the definition Image Analysis Pro gives in the index, but I'm interested to know in details how it works (how can I reproduce what the software do?)

Answers

  • IPP implements a variation on the hand and divider method, using measurements of the perimeter using 'strides' (minimum step lengths) of various sizes. We calculate the fractal dimension as 1 minus the slope of the regression line obtained when plotting the log of the perimeter (for various strides) against the log of the stride length.

    IPP accounts for variations in the perimeter measurement as a result of different starting points along the outline (i.e. depending on the where you first put the ruler to start measuring the outline, the perimeter is going to vary slightly even if the ruler stays the same). The original method doesn't compensate, which is one of its main drawbacks.
  • Does anyone know the details of how Image Pro Plus (7.0) calculates the fractal dimension?

    I think that it uses a method based on Box Counting, however, the calculation function in Image Pro plus does not allow to establish "box sizes" while ImageJ (1.52) allows it (e.g. 2,4,8,16, 64).

    Thank you.

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