[zeroca]

To explain the told above phenomenon isn’t hard: As I mentioned in my previous posts Flashing light reversal (posts #24, 25, 26), exact overlapping of images happens only in focal point (central vision) and all other points of scenario, i.e. all rest part of whole field of vision is doubling when looking at them with binocular vision (with both eyes), so contours of circles at crosses are coincided with color of background (squares), so the effect of illusion is the result of physiological doubling that takes place within the whole field of vision except for a small field of central vision. So that’s the reason of eliminating of illusion when narrowing the eyes (as narrowing of eyes covers peripheral vision and leaves functioning only central one).
When looking at the picture with monocular vision (with one eye open) illusion takes place because of shifting of eye slightly, so if you fix the vision with it, you’ll notice that illusion eliminates.
The truth, this illusion arises only when circles and background are contrasting.