What methods exist to calculate the ellipticity of galaxies What methods exist to calculate the ellipticity of galaxies and what are their drawbacks? I have asked this question about ellipticity in the SDSS but I want to know about general methods for cases where I have just an image of a galaxy.

I do so far know these methods:


ellipticity from stoke parameters or the flux-weighted second moment as described here. 
from adaptive moments as described here (which would allow me to do shear calibration).
fit an ellipse on a particular isophote as decribed here.


My question is whether there are further methods I am not aware of. Does there also exist a method when I fit an ellipse to all isophotes? And how would I calculate the 'average' from it (such that the spherical center does not contribute to much)?

I would like to learn about the pro and cons of each method. I am especially interessted in methods that get close to what people would estimate by eye. I would also be glad to hear about references (textbooks or papers) for the different methods.
The first two methods mentioned in the question are really similar. They both use moments of the light distribution, only the weighting is different.

Another family of methods is 2D profile fitting to the image, with more or less sophisticated luminosity profile models. A simple case would be to fit a Sérsic profile. But instead, one could make a composite model with two or more elliptical profiles (say one exponential disk and a de Vaucouleur bulge). This would allow to separate the ellipticity of the disk from the ellipticity of the bulge. A widely used software for this is GALFIT by Chien Peng.