In the LEM paper, it looks like they're using only lines at the highest resolution. It might be interesting to also match lines at other scales.

The ARP method is interesting, but it seems very special-purpose. Since it's an FT approach, it needs to combine information over a large area. I imagine you'd need to have very good centerpoint localization and limited changes in aspect ratio. Aspect ratio for face regions does change with expression, I've found, and I'd think the centerpoint could shift as well.