Reverspective

from “Visual Phenomena & Optical Illusions”

In my office I have a cardboard object which produces a “wow” effect for most visitors. It's a “reverspective”, and the demonstrations here cannot come even close to the stunning reality of the effect. I bought that model at the “Turm der Sinne” when I gave a talk there and managed to bring it home without damage (it's just cardboard) and then carefully assembled it.

What to do

The movie (©Fergus Sullivan, with kind permission) conveys a little of the impression. While it runs, the object seemingly distorts. What does it look like, anyway? Somewhat like 3 corridors leading into the depth, and the entire arrangement rotates a little. Seen from top it appears to have this (green) profile:

In reality, the depth is inverted. This can be seen at the very beginning and end of the movie (stop it there for closer inspection). There it looks very different, and that’s what it really looks like:

Comments

The movie illustrates what is known as “Reverspective”, short for “reverse perspective”, a term that was, I believe, coined by Patrick Hughes. While the pyramids are extending out towards the viewer, the painting or texture on them is made increasingly smaller, as it would occur with increasing distance. Our visual system sees this size change, and “size constancy” kicks in, perspective is assumed, but in the wrong direction.

Once the depth is inverted, the seeming motion or distortion is just due to geometry: motion parallax shifts close objects relative to distant objects when we move sideways. Inversely, position of objects is deduced from their parallax. When the depth is inverted, the motion inverts too. Yes, this is a convoluted explanation.

When one does not just see the movie, but a real reverspective object, the effect becomes more striking: when one moves sideways, the object seems to become alive and rotate by itself (in the opposite direction). Real objects, when constructed right, can easily be seen in inverse depth. It works best if one covers one eye, then there is no contradiction between stereovision (what we deduce from the slight differences in the images of our two eyes) and (inverted) perspective. In fact, if you are observing a nice renaissance perspective painting in a book (thus from a short distance), the perceived depth of the image can be greatly enhanced by closing one eye.

I strongly suggest that you view a real reverspective object. Either buy one, or build one, below I give sources.

Reverspective is closely related to the “hollow mask” illusion, but there the depth inversion is even more compelling because the face percept is “stronger” then the knowledge that depth is inverted. The little dragon from “gathering for Gardener” is another cute example.

The next movie (again from Fergus Sullivan) helps to appreciate the inverted depth by including an entire 3d room scene.

Sources

Ben Backus has created a beautiful model (©1999) of the reverspective “cube illusion” for self-assembly

Norman D Cook’s website with a number of scientific references,   his “brief history of reverse perspective”

Dultz W (1984) Bust of the Tyrant: an optical illusion. Appl Opt 23:200–203

Patrick Hughe’s website,   his reverspective page

Fergus Sullivan’s website

Wade NH, Hughes P (1999) Fooling the eyes: trompe l'oeil and reverse perspective. Perception 28:1115–1119
Model for self-assemembly (PDF) , Mondrian movie