As I understand it, Magic Eye stereoscopic images were originally developed by brain scientists studying how we see in 3D (i.e., how the brain processes 2 eye inputs into a 3D image).

There were two competing theories:

1. The brain first does a recognition pass (that's a house, that's a person, etc.) and compares the two eyes to see which objects have moved.

2. The brain compares the two eye inputs first, at the "pixel" level and figures out which pattern of pixels has moved, then afterwards, applies recognition to the resulting 3D image.

Magic Eye would only work if #2 is the correct theory (because in Magic Eye, there is nothing to recognize until AFTER you convert to 3D).