Re: Questions about equations of Shape Descriptors
Posted by Gabriel Landini on Feb 26, 2010; 10:16am
URL: http://imagej.273.s1.nabble.com/Questions-about-equations-of-Shape-Descriptors-tp3688338p3688342.html
On Friday 26 Feb 2010 09:06:33 you wrote:
> The "sqr" in the above equation does mean "square" (though it's not macro
> syntax).
That is right.
> Major axis and max Feret diameter are not the same. The
> best-fitting ellipse is a much more robust measurement than the Feret
> diameter, as all pixels inside an object are taken into account, not only
> the perimeter pixels.
Well it depends of what one is trying to characterise. For instance if one
needs to know something related to their length for very thin particles like a
latin cross, the fitted ellipse (that has the same area as the cross) has a
very small maximum diameter and so it underestimates the extent of the shape
(I know, it correlates with the area, but we already know that!). For convex
particles with no holes the fitted ellipse might approach the particle other
stats. So it really depends.
Just in case, I think that most "major" and "minor axis" instances of
morphological parameters (such as those in Russ' book) relate to the maximum
Feret and breadth (and should not be confused with the Major, Minor of the
fitted ellipse found in the IJ results table when one uses "Fit ellipse").
Otherwise one would end up measuring the shape descriptors of ellipses. I
mention this because it might become confusing when computing parameters like
the "equivalent ellipse area" that represents the area of an ellipse that has
the same long and short axis (ie Max Feret and breadth) as the particle.
As mentioned in Russ' book there are tons of morphological parameters which
are small variations of others, sometimes with different names or just
factored by a constant.
Cheers
G.