I have been attempting to use analyze particles to measure the major and minor axes of these eggs (for an estimate of volume). However, I have found that any eggs which are touching cannot be recognized for measurement (example overlay image). Are there any recommendations for how to deal with this issue?
Going out on a limb here, but you may want to try a pixel classifier like Weka or Ilastik (lots of posts on those) for segmentation, by creating a class of pixels for the crease between where two objects are touching. So you would have 3 classes, “egg” “crease” and “background.” How well this works in practice will likely depend on how consistent your imaging conditions are. In the above image your grid appears warped as it goes out of focus, so I have a feeling that will make things difficult for any type of classification without quality of image improvements.
Even lighting, and a flat surface are probably going to have a significant impact on any results you might want to get. Or change imaging methods to something that is maybe heatsensitive, or check for autofluorescence.
Hopefully someone else will have a better idea, but I did not have much luck trying a pixel classifier on that one image. Too much is context dependent. Maybe deep learning could handle it.
Adding to this: transillumination (x-ray light box) may push light through the goo in between the eggs for better separation. Or use a soft light box to get a more even illumination and hence more unifor egg color, for better separation. And if you can put a yard stick beside the eggs rather than having them on wireglass (?) you still have the magnification but an easier thresholding for separation.
On the other end of the spectrum (pun intended) three light sources in a triangle that throw a circular spot and make a more or less, depending on the angle of incidence, oval reflection on each egg combined with some trigonometry may tell you the center of the egg, as defined by the shape of each oval and bearing of the axis of each reflection. The three light sources need to be relatively far away, but, as @Research_Associate mentions, your fisheye lens also warps, another reason for wanting to be further away with the camera too, in order to fight barrel distortion. Nice resolution, though.