Re: Feret's dimeter

Posted by Michael Schmid on Jan 11, 2015; 10:54am
URL: http://imagej.273.s1.nabble.com/Feret-s-dimeter-tp5011144p5011172.html

Hi Slobodan,

yes, if you create a circle (oval selection) with a diameter of 3 pixels
it and fill it, you will get a square of 3x3 pixels. This square has a
minFeret of 3 (if you measure it with calipers touching two sides) and a
maxFeret of 3*sqrt(2) = 4.24 pixels (calipers measuring the diagonal).

For larger circles (diameter >= 4), filling does not result in a square
any more, but the maxFeret will be still too large.

In any case, for calculating Feret diameters and areas, pixels are assumed
to be small squares with a side length of 1, not single points.

[ImageJ reports the same Feret values for a the circle and the shape
obtained by filling it. In principle one could change this by handling
oval selections separately when calculating the Feret diameters, but I am
not sure whether it would be worthwhile.]

You can easily try it yourself. It is best to create a small image and
zoom in, then you can nicely see the pixels.


Michael


On Sat, January 10, 2015 10:22, Slobodan Dražić wrote:

> Hi Michael,
>
> thanks once more.
>
> I think I understand, but just to be sure: If a circle with radius 1.5
> pixels is digitized such that it digitization is 3X3 neighborhood  of
> pixels (a square of size 9 pixels) the maximal Feret's diameter would be
> 3*\sqrt(2) estimated from the farthest pixel corners (when angle is 45
> degrees)?  It will not be 2*\sqrt(2) if it is estimated from pixel
> centers?
>
> Best regards,
> Slobodan
>

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