Ellipsoid factor


I would like to use the ellipsoid factor on CT images. The voxel resolution is 80 μm.
Even when I raise the Vectors (up to 500), I decrease the Sampling increment (down to 0.02) and I use only one point per ellipsoid, the results are bad.
Is the resolution too high, compared to the size of trabecular elements, or is it because of the parameters ? I precise that the samples come from bovine femurs, the structure is a mix of plates and rodes.

Thank you,
Nicolas Rogalski

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Hi Nicolas,

Do you know the trabecular thickness in pixels of your images? Is there a (cropped-down) individual sample you could provide us for testing?

Estimating the trabecular thickness of cattle from two samples measured in Doube et al 2011 (see supplemental material) suggests 240-340 um, so 3-4 pixels at your resolution, average trabecular thickness. In my view, that’s just a little bit too low resolution for any trabecular analysis, so unfortunately, I doubt it’s worth trying.

Should you still want to go ahead with Ellipsoid Factor, in the latest BoneJ, there are some additional EF parameters that you can attempt to tune, and some recommendations for how to do this should be in this preprint.
You might in particular want to try adding more distance-ridge based seeds (i.e. tick the distance-ridge seed box and, from my experience, experiment with thresholds between 0.6 and 0.9 or so). For what it’s worth, 500 vectors and 0.02 step seem excessive to me - in my experience 100 vectors and as step between 0.5 and 0.8 should be OK.

Hope this helps!

Hi Alessandro,

thank you very much for this answer. The Tb.Th values of my samples are indeed in this range.
I will try to tune the other parameters.
What is the minimum resolution you believe is enough to run the EF ? (For the same range of thicknesses).

You’re welcome!

For me, in an ideal scenario, you’d have >10 pixels across a trabecula, so a good resolution in your case would be ~20-30 um or better. I think it’s worth trying while acknowledging the limits of your resolution if you get to >5 pixels across a trabeculae, so that would be ~50um or lower voxel size in your case.

Hi Alessandro,

I am trying to calculate EF for a structure. When I get the output Flinn plots, I am not sure that the axis are the same as axis shown in Fig.2 (C,G,K) in this article (vertical axis is a/b 0 to1 and, horizontal axis b/c 0 to 1):

Frontiers | The Ellipsoid Factor for Quantification of Rods, Plates, and Intermediate Forms in 3D Geometries | Endocrinology (frontiersin.org)

The output I see is like the below picture:

I appreciate your clearance.
Thanks a lot.


There may be some confusion over axis labelling here.

It is conventional to list axes as x × y (although “y upon x” convention is also common in spoken English at least, which confuses things a bit).

In image processing the origin (0,0) is by convention at the top left.

In Cartesian plots like the Flinn plot here, the origin (0,0) is by convention at the lower left of the +/+ quadrant, which means the polarity of the y-axis, a/b, has to be inverted.

What all this means is that the status bar information:

1 b/c x-1 a/b (512 x512)

means that b/c is on the x-axis, and a/b is on the y-axis. Additionally, the y-axis values are inverted by multiplying by -1, which puts the origin at the lower left. The numbers 1, -1 and (512x512) mean that the range 0-1 is spread along 512 pixels left to right (on the x-axis) and bottom to top (on the y-axis).

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Thanks for your detailed and clear explanations, Michael.