Missing-fundamental motion inversion

From Michael’s “Optical Illusions & Visual Phenomena”

Warning: this is a rather subtle effect for “vision insiders”.

What to observe – The two top and bottom grating strips move, obviously. Do they move to the left or to the right? The top one to the left, no doubt. And the bottom one? It looks like it’s moving to the right, but if you follow the contours you notice this also moves leftwards.

Increasing speed enhances the effect, at very low speeds it diminishes; contrast has little effect; blurring (i.e. removing high spatial frequencies) decreases the illusion.

Comment – The bottom grating is a square-wave grating where the lowest spatial frequency, the ‘fundamental’ has been removed, hence “missing fundamental”. When looking at the Fourier spectrum of the grating, most power moves to the right, so the illusion is no surprise (Adelson & Bergen 1985).
As with nearly all motion illusions, it would look better were I able to synchronise to your display’s frame rate.

History – I had heard & read (A&B 1985) of this, but never seen it. Luckily, Kelvin Chen showed it as background material for his VSS talk 2004 (T207). This looked so nice that it motivated me to revive this illusion from 1982.

Sources

Adelson EH (1982) Some new illusions and some old ones analyzed in terms of their Fourier components. IOVS (Suppl.) 22:144

Adelson EH & Bergen JR (1985) Spatiotemporal energy models for the perception of motion. J Opt Soc Am A 2:284–299

Alan B. Cobo-Lewis’ demo