Difference between Major-/Minor-Axis and Ferets Diameter

Hello together,

I have a question about the terms “Major-/Minor-Axis” and “Feret-Diameter”. What is the difference between those two? When I imagine a perfect circle, both values should be the same. But what about an ellipse? Are the Major- and Minor-Axis not the same as the Feret diameter?
And especially, what about a rotated ellipse? It would be great, if someone could explain me the difference between those two :slight_smile:

Best regards,
Björn

Hi @Bjoern

Major-/Minor-Axis are the two axis of the fitted ellipse to your object. For a circle the best fitting ellipse is a circle. For an ellipse it’s the ellipse.

Feret-Diameter is coupled to an angle. You can either compute it for an angle or compute Min-/Max-Feret-Diameter. Min-Feret-Diameter can be imagined as the diameter of the tube through which you just can push (can be orientation dependent) your object. Max-Feret-Diameter is the diameter of the tube through which you always can push (orientation independent) your object.

So Min-/Max-Feret-Diameter should also be the same as Minor-/Major-Axis for an ellipse. For an arbitrary angle this does not hold.

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Hey @tibuch,

so if I understand you correctly, the Major-/Minor-Axis should be in most cases the same as the Max- and Min-Feret-Diameter, e. g. like this:

So then what is the difference, if the ellipse is rotated in a certain angle like this?

Is the measurement of the Major-/Minor-Axis different or that of the Feret-Diameter? I mean, are the Major- and Minor-Axis still measured as in the picture above? It would be great if you could outline this for me :slight_smile:

Best regards,
Björn

Major-/Minor-Axis and Min-/Max-Feret-Diameter will still be the same. But Feret-Diameter about an angle will change.

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Ok, so basically both “diameters” are the same?! I thought, if the term is different that there has to be a difference between thos two…but now it seems, that the only difference is, that with Feret-Diameter calculation an angle is calculated, which indicates the degree of rotation of the object.

Thanks for the explanation!

Not for all objects! It depends on the ellipse fitted to the object. In the case of a circle/ellipse it is the same, because the fitted ellipse is the same. But it can be different. As far as I know, the best fitting ellipse in imagej is the one, with the least difference with respect to area. And then the Minor-Major-Axis are computed from this fitted ellipse, whereas the Min-Max-Feret-Diameter is computed from the object directly.

But I have never performed a big test regarding the difference between the two features for different shapes.

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Ok, I think that clears everything up for me. I hadn’t in mind, that one parameter was calculated by fitting an ellipse to the object, while the other is calculated on the object directly.
Thank you very much for your patience! :wink: