So I am no expert here... but here is something you can at least start with and see if it helps... it's not perfect (as there is overlap between some objects, making them more difficult to individualize - but you can always remove those objects as outliers based on area or so...).
Here is a little macro I came up with to segment/measure your objects:
run("Analyze Particles...", "display exclude add");
If you look at the list of measurements calculated in Set Measurements. The major axis of the ellipse for Fit Ellipse might do the trick.
But perhaps others have more refined methods... I'd be happy to learn them myself.