In the view of "analyzing" quickly some big numerical hydro simulations in which many complex galaxies form (with gaz, stars and all), one could maybe use the Gini coefficient to classify galaxies. These are home made galaxies (composed of a mixture of bulges with spiral disks). They are not designed to have perfect light profiles or colors.
We projected these 3D galaxies with random inclinations to get fake observed galaxies. And we measured the Gini coefficient for the pixels brighter than a given threshold. And just for fun, we computed the 3D Gini coefficient (we have the pixels in 3D space), thinking it would be more discriminating between ellipticals, spirals and irregular galaxies. But surprisingly, the Gini in 2D does a much better job than the 3D Gini coefficient in separating galaxy types.... It shows Gini3D (numbers in blue in the figure above) vs Gini 2D (numbers in red), for various brightness thresholds.