Posted by
Gabriel Landini on
Dec 11, 2016; 3:14pm
URL: http://imagej.273.s1.nabble.com/Ever-decreasing-circles-tp5017755p5017756.html
Hi,
On Sunday, 11 December 2016 13:38:23 GMT John M Brear wrote:
> Calculating the circularities of our observed precipitates shows that we
> would obtain much better discrimination by selecting on circularity values
> greater than 1. At present ImageJ does not allow this.
Not sure I understand your question, but that seems impossible from the
definition of circularity. A circle has the maximum theoretical circularity of
1.
Regions with a circularity >1, would mean that a region has a shorter
perimeter than a circle enclosing the same area.
To avoid large errors generated on small regions, you could take images with
higher magnification, so the pixellation error are relatively less prominent.
However, the discretisation problem, will not go away. You cannot get
circularity of 1. While you get closer and closer to the true area of your
region by increasing magnification, the perimeter is always overestimated due
to the polygonation of the discrete representation of your objects.
> it appears that perimeters in ImageJ are of the form a + b x sqrt(2), where
> a, b are integers. This gives a limiting circularity (for a single pixel)
> of Pi / 2.
A single pixel has no circularity because it is a sample (with neither area
nor perimeter), so I would not make assumptions as what is the limiting
circularity in that case.
IJ uses the number of pixels as area and the length of the polygon as the
perimeter. There are alternatives to this. For example my plugin (Particles8,
downloadable from my page) uses the area inside the perimeter polygon as the
estimate of "area". The circularity values are slightly different from those
in IJ
The problem of the length of the perimeter, however, remains, but this is well
understood and there have been many papers on this and the representation of
"digital lines".
Freeman's papers in the 1960s are the classic reference to this. This was
discussed a bit in the ImageJ Forum some time ago and I posted some more
references
http://forum.imagej.net/t/polygon-mesh-boundary/3153Strange things happen in discrete space! :-)
Cheers
Gabriel
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