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Margination

It is unclear how to use margination in segmentation.  I have read the definition for margination, but is there a fuller explanation/example available for this measurement and how to use it?
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    The Margination measurement is an estimate of the radial angular moment of inertia, normalized to a range of 0 to 1 (more details below).  Unfortunately at some time in the far past (prior to Image-Pro version 9.0), a change was made that caused all objects to report a Margination value of 0.33, no matter their shape or radial distribution of intensity.  This has been fixed in the just released Image-Pro version 11.1, but the measurement is useless in prior versions. Clearly, few users of Image-Pro have been using this measurement since no one has ever complained.  And our tests missed the problem because the expected values for our internal testing were also wrong.

    In any case, in the current version of Image-Pro 11.1 Margination is computed correctly.  A distance map of each object is computed and the sum of the intensity at each pixel times the square of the distance from the point(s) most distal from the object boundary is computed.  This sum is normalized to a range of zero to one.  The result is a normalized estimate of the radial angular moment of inertia (also known as "rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body" according to Wikipedia).

    I have attached two images, each of which has a single circular measurement object when opened in Image-Pro 11.1.  In one image all of the intensity is at the center of the object, which results in a Margination measurement of zero. In the other image all of the intensity is on the boundary of the circle, resulting in a Margination value of one.  However in cases of more typical radial intensity distributions, the values tend to fall within a quite narrow range of values (e.g., between 0.30 and 0.37 will be usually observed). Like rotational inertial itself, mass (i.e., intensity) at object boundaries is most heavily weighted in the measurement.

    In summary, the Margination measurement is costly to compute and will not vary much unless object intensities differ substantially close to the objects' outer boundaries.  So most of the time we would not recommend using it. On the other hand, for some situations the measurement will capture object characteristics that no other measurement can.
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    Thank you for your detailed answer.  Still not sure I totally understand, but will continue to consider.
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