http://imagej.273.s1.nabble.com/Convert-macro-from-NIH-Image-to-ImageJ-tp5015304p5016709.html
Noted. Thank you. I will read the paper.
> 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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