Re: 1D autocorrelation function
Posted by
Gabriel Landini on
URL: http://imagej.273.s1.nabble.com/1D-autocorrelation-function-tp3692494p3692502.html
Hi Larry,
I think that the two procedures you are comparing are different.
What I suggested was this:
http://books.google.co.uk/books?id=dSrgqo8POYIC&pg=PA22&lpg=PA22&dq=:+TWO+POINT+CORRELATION+FUNCTION+fractal&source=bl&ots=TMbKJT__fQ&sig=gghkBZ4eE51FW_Ufgoie1KtMpos&hl=en&ei=khgNSqmgGMKrjAf8s6i0Cg&sa=X&oi=book_result&ct=result&resnum=7#PPA22,M1
In case you cannot get the link above, this is from Fractal Growth Phenomena
(page 22) by T. Vicsek: "The expectation value that two points separated by r
belong to the structure. [...] ...the probability of finding a particle at the
position r + r' if there is one at r'. "
For fractal objects, this function is a power law.
Here is some recipe (look for "Correlation Dimension")
http://sprott.physics.wisc.edu/phys505/lect12.htmhttp://sprott.physics.wisc.edu/phys505/images/corrdim.gifI hope this clarifies it.
Regards
Gabriel