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05/01/2008

Fractal Boundary Dimension Measurement Tool

This tool measures the boundary fractal dimension of objects.  The blob tool also has this capability - see list of blob statistics.


Coordinate Averaging Method - Step Lengths

Boundary fractal dimension, Db, is measured vs. the step length, sl, within logarithmic step length ranges.  Method by Adler.

Step Length Label
1
2
3
4
5
6
7
Log (step length)
0 - .5
.5 - 1
1 1.5
1.5 - 2
2 2.5
2.5 3
3.0 3.5
Step Length in pixels
1-3
3-10
10-30
30-100
100-300
300-1000
1000-3000

(Note: Lispix uses rounded pixel ranges. Actually, 10 ^ .5 =  3.1622777..., not 3, etc.)


Minkowski Sausage Method.

This method seems to be less reliable than the Alder method for images of particles. 

The fractal dimension is the local slope of the Richardson plot of perimeter vs step length.

Perimeter and step length are obtained from the Minkowski sausage, which is obtained from the histogram of the Euclidian distance map (EDM).

(see 'Help / references / fractal' for bibliography)