IdentifyTertiaryObjects, as a rule, is not an exclusive operation as it leaves an overlapping pixel in the larger object over the interior object. However, in terms of quantifying the intensities within the object generated, the result of this operation is that a pixel is counted twice. Is there a way to account for this problem, assuming it isn’t really possible to make them non-overlapping?
After some further reflection, you might be able to get what you want using MaskObjects to get your tertiary objects instead of IdentifyTertiaryObjs. If you select the secondary objects as the objects to be masked, the primary objects as the masking objects, invert the mask and retain numbering, I think you get the behavior you would want for the case you describe. Let me know if it works in the way that you want, and if so, we can modify IdentifyTertiaryObjs behavior accordingly.
Thank you for your suggestion. I just had a chance to try it out, and that seems to be exactly the behavior I’d like.