Fractal dimension calculated using the box counting method depends on the grid location. I have attached a file which contains the fractal dimensions obtained using ImageJ with FracLac plugin at different grid locations. There is a significant difference between the values of fractal dimension at different grid locations. Which value of fractal dimension should I choose?
You can rotate the grid or off-set the grid to a number of locations - say 8 around a central grid and then take the average. Rotation is probably best because of pixilation issues when a line is not either horizontal or vertical on the screen
i suggest you to make many computations varying the position and others parameter (you can do directly with Image J) and take the average values as result.
Hi! Herbert, can I do the rotation of grid with ImageJ while using Box Counting Method to find fractal dimension?
Hi
Yes you can. In fact have a look in the macros section for Audrey Karperien's fractal analysis macros. They may include the option for rotation already. Otherwise it is not difficult to add a couple of lines of code or depending on the number of images rotate them before analysis
I am trying to measure the fractal dimensions of Brewseter Angle Microscope images.
Hi David. Images of 2D phases of langmuir monolayer at a/w interface. 2D phases change when the interaction between the surface molecules and the subphase is changed. My goal is to see whether the fractal dimension of 2D phases has any thing to do with the interaction. I have binirized the image considering what I want to see. I don't get your point - "How the fractal ....to answer!". Can you clarify me, please ?
Using the box-counting method to estimate fractal dimension can be very tricky depending on the object you're using it. Anyway this method has a lot of side/borders effect that you should be aware of when trying to estimate the fractal dimension this way. I strongly suggest you to read about it:
Falconer, K. 1990. Fractal geometry : mathematical foundation and applications. John Wiley and Sons.
Falconer, K. 1997. Techniques in fractal geometry. John Wiley and Sons.
Foroutan-Pour, K., Dutilleul, P., and Smith 1999. Advances in the implementation of the box-counting method of fractal dimension estimation. Applied Mathematics and Computation 105:195-210.
Reeve, R. 1992. A warning about standard errors when estimating the fractal dimension. Comput. Geosci. 18:89-91.
Of for a quick reviews of the pitfalls you may check chapter3 of my thesis, full text should be available from my RG profile.
Hi David Barry,
Great idea using the local fractal dimension. Landini has a book chapter where he discusses this and I also have a paper on using local connected fractal dimension. You need to watch the scale though that you are using. Also using local connected fractal dimension is good for some microscope images where you have a lot of empty space.
David da Silva - thanks for pointing out some more refs. I have not come across the Foroutan-Pour reference. Will check it out.
The box-counting fractal dimension, is actually, scale dependent. See the attached paper.
are you sure your phenomena is mono fractal? If not, BCD should give little information about it.
it's probably not a monofractal, but a multifractal object, more adequate approach is the multifractal analysis, with leader coefficients, or 2D-WTMM methode, then you get the multifractal spectrum not just the fractal dimension,
dear
please let me know anyone has matlab code for Fractal dimensions(Fd) calculating?please send to my email:[email protected]
Hi, Toushmalani. Follow the link http://fraclab.saclay.inria.fr/ to Fraclab which is written in matlab.
If any one has the MATLAB code for finding the fractal dimension, then please inbox me this code.email addresses: [email protected]
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