Paul King, Computational Neuroscientist, Software Entrepreneur
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This is a tricky question because so much of the brain is involved in multiple things.
It is often said that 2/3 (60%+) of the brain is "involved" in vision. However possibly less than 20% of the brain is dedicated to "visual-only" functioning. The other 40% is doing vision+touch, or vision+motor, or vision+attention, or vision+spatial navigation, or vision+meaning, etc. There is generally a smooth gradation from areas fully-specialized to one thing to areas involved in many things.
This image shows the approximate area dedicated to each sensory function (smell is underneath the brain and not visible):
Amazingly, a recent study found that neurons in "V1", the primary visual area, are modulated by motor behavior! [1] If there was any part of the brain at all that was "vision only", for sure it would be V1, and yet even V1 is being affected by something that would seem to be the opposite of perception.
The very rough answer I've heard is that about 2/3 of the brain is used for processing visual information. This include areas that are multimodal, like the superior colliculus and some visual association areas.