[Insight-users] Circularity and Compactness Measure

[José Santamaría López]

Perhaps, what I am going to say could be
trivial, but may help you:

The radius of the largest possible circle can be
computed by the distance between the center of
mass of the segmented image and the furthest point
at the segmented one.

And, the smallest possible radious that will enclose
it can be computed by the distance between the center of
mass and its closest point on the segmented image.

This could be an ill scheme for solving your
requeriments, mainly when the noise is a relevant
factor present in the images you are using. You can
make use of a more robust mechanism, for instance,
take a median value for each one of the rules.

I don't know whether it is implemented in ITK, but
some components of it could help you, for instance
a Kd-Tree to compute the closest point rule.

Regards.

Karthik Krishnan
> On Sun, 2006-04-02 at 19:25 -0500, Matt Kelsey wrote:
>> Hello All,
>> I need to measure the circularity and compactness of a 2D segmented
>> object. To do so, I'd like to compute the radius of the largest possible
>> circle that will fit in the shape and the smallest possible that will
>> enclose it. Does anyone know of a built-in ITK function that will do
>> this?
>
> The largest medial radius is the smallest possible circle that encloses
> your segmentation.
>
> The filter:
> http://www.itk.org/Insight/Doxygen/html/classitk_1_1BinaryThinningImageFilter.html
> will find the skeleton of your 2D shape.
>
> The largest binary ball when centered on the skeletal pixels that has
> all pixels inside it "on" is the largest medial radius.
>
>
>
> I have no knowledge of algorithms that compute the circumcircle of an
> arbitrary shape, but it seems to me that you can approximate that
> computing the largest image extents along the x/y axis by rotating it
> from 1 through 90 degrees in steps of 1.
>
> -karthik
>
>> Thanks for any ideas,
>> Matt
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