Posted by
Gabriel Landini on
Jun 21, 2016; 8:39am
URL: http://imagej.273.s1.nabble.com/Convert-macro-from-NIH-Image-to-ImageJ-tp5015304p5016704.html
On Tuesday 21 Jun 2016 11:59:22 Dini Nurfiani wrote:
> I noted your explanation regarding to make sure the largest dilation has to
> fit completely within the frame. I want to make sure something else again.
> Can I dilate an image up to high iteration? as long as the largest dilation
> still fit within the frame? For example, the following shape:
>
> 3 iterations
>
> 4 iterations (in the upper right corner, there is pixel touching each
> other. Will this influence the dilated area measured?)
>
> 40 iterations (or I can go until higher/largest dilation?)
The purpose of the dilation is to remove detail on the curve, so you can
measure how 'shorter' it gets with less detail.
Once the dilation kernel gets close to the size of the largest detail in
object itself, the length of increase slows down, so part of your plot will
have a shallower slope (likely approach D=1, and the slope will get closer to
0).
If you apply too many dilations you will notice this shallowing of the log-log
plot. So it is best to be careful in deciding what is an appropriate range of
dilation sizes to be used to estimate the slope. Too small discs will not pick
up detail as you are close to the pixel matrix, too large and you approach the
object size.
There are various papers dealing with this including some trying to estimate
not only the fractal slope, but also the transition to an Euclidean range.
See: "Rigaut J.P. An empirical formulation relating boundary lengths to
resolution in specimens showing 'non-ideally fractal' dimensions. Journal of
Microscopy 133, 41-54. 1984."
That is quite a remarkable paper (by a remarkable scientist), way ahead of its
time. People were struggling to understand "just" fractals after Mandelbrot
published his famous book and JPR came up with his extended model for
asymptotic fractals very soon afterward.
Hope it is useful.
Gabriel
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