Eye Contact via Multiple Cameras

Video chat has an eye-contact problem. You look at the image of the person, but the camera's in a corner so they see you staring off into space:

camera lower right camera lower left

camera upper right camera upper left

The fancy way to fix this is you put the camera behind the screen. No one seems to have figured out how to do this with cell phones, though, and it seems hard. What if we just put four cameras on the phone, one in each corner? Then you integrate the images and construct a new one with the eyes looking where they should:

(image not actually product of proposed method)

Fixing eye contact would be really nice. So: how hard is the image processing problem? How expensive is it to put on three more front-facing cameras? Or could we just do two cameras, top and bottom?

(I do see some work on this (2001) but nothing recent.)

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