Do birds have peripheral vision?

For some reason, we manage to kill/injure a lot of birds at my house, on accident I will assure you.
Time #1 - It's a normal thing around my house for dad to get out the BBgun in attempt to scare away the birds after he's planted the winter lawn. Well, according to him it was an accident, but he actually nailed a bird. The poor guy collapsed and never woke.
Time #2 - My dog ate a baby bird, practically swallowed him whole. We locked him outside. Needless to say he hasn't done it again.
As of late - The following picture describes what has been happening on almost a daily basis since we replaced our living room and dining room windows. Apparently they're just too clean for the birds to handle, and apparently they don't have peripheral vision to notice that on each side of the window is a fairly large house. Poor guys.

(It's hard to see, but notice the leftover feathers that stuck to the window)

A word of warning to all the birds out there...The windows have been cleaned and dad is about to plant a winter lawn.