Important question of the week: Pigeon pupils

So, why do Woodpigeons have odd shaped pupils? I thought this bird photographed in my garden, which has an asymmetric pupil, might just have an odd eye, but having looked at a few pictures, they all have this... but why?

I tried looking up "woodpigeon pupil" (surely one of the least googled phrases ever?), but just got a load of references to schoolchildrens' projects on pigeons. And do other birds have odd-shaped pupils? A quick search through my photos reveals this (all over-enlarged so we can see the pupil):

All nice and round, or at worst, slightly oval, but nothing compared to the asymmetry of the Pigeon pupil! So is it a Pigeon thing? After all, the above three species are all fish-eaters. So, lets have a look at a close relative of the pigeon, the Collared Dove:
Perfectly round pupils (honest)! What is going on here? Answers on a postcard to Cuddesdon please...