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.
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 
13 
310 
1030 
30100 
100300 
3001000 
10003000 
(Note: Lispix uses rounded pixel ranges. Actually, 10 ^ .5 = 3.1622777..., not 3, etc.)
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)