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Dear SPM users,I am searching for an image analysis software that allows to determine the fractal dimension (df) of islands of the first few layers in organic thin film growth.The islands are two dimensional objects (the z dimension is fixed by the length of the molecule) and exhibit round to dendritic shapes.So far I have used the coastline fractal dimension analysis exploiting the relationship" perimeter= c* area^ (df/2)" and the gwyddion fractal dimension analysis (cube counting value-1), getting contradictory results aswell between the two measures and already published experiments.In literature people use a box-counting method described in Vicsek's textbook "Fractal growth phenomena" to determine the Hausdorff fractal dimension but do not give any information of how they extract this measure from SPM images.If anybody has software recommendations or other useful tips, please post it or contact me.Thank you in advance and good luck for your research!Andreas Straub-- Andreas Straub,PhD student in PhysicsCNR-ISMN BolognaNanotechnology of Multifunctional Materials Research DivisionVia Gobetti 101I-40129 BolognaItalye-mail: a.straub@bo.ismn.cnr.itweb page: www.bo.ismn.cnr.ittel: +39 051-639-8526fax: +39 051-639-8540
Hi Andreas,
I did use the box-counting method to analyze some lipid monolayer domain images for my dissertation. We only looked at a couple images and we didn't consider it a very critical analysis, so we didn't put any work into automating the analysis or otherwise making it easy. I forget the exact details, but we literally just drew different size grids on printouts of the AFM images and counted boxes manually. In our case the boundary was not so well defined either, which introduced more uncertainty.
Here's what I wrote about it in my dissertation:
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There exist several ways to estimate the fractal dimension, D , of an experimentally observed shape. We used the box counting technique described by Birdi (1993). This technique is applied by taking a grid of box length "l" and defining x = 1/l as the “precision” of the grid. The grid is placed over the shape being analyzed and the number of boxes, N , containing any portion of the border of the shape are counted. This is repeated for several grids of different box sizes. One finds that the number of non-empty boxes asymptotically approaches the dependence: N= K * x^D, for some constant K. The fractal dimension, D, can then be determined by regression of the line: log(N) = log(K) + D*log(x) . This technique was validated on a known fractal, the Koch snowflake, for which the fractal dimension can be calculated analytically to be 1.262 (Mandelbrot, 1983).
The Birdi reference is: Birdi, K. S. 1993. Fractals in chemistry, geochemistry, and biophysics : an introduction. Plenum, New York
Note the idea to check your analysis on a fractal of known fractal dimension. That might help resolve the discrepancy between the two methods you have already used.
I wish I had a better answer for you. Hopefully someone else will be able to direct you to a more automated analysis.
Regards,
-Ben
Dear Andreas,
You can try WSxM software. You can download it for free at www.nanotec.es. There is an option called Flooding that allows you to detect the highest (islands) or lowest (holes) points of an image. Then it allows to get different information about perimeters, areas, volumes... of the islands, including a fractal analysis, where you can get the fractal dimension.
Greetings,
Pablo Ares.