Zooming Diamonds: A New Illusion, and a Warning on the Biological Relevance of Parallel Projection

A new illusion is described. Observers watch parallel projections of ‘diamonds’ (rhombi) tumbling in 3-D. The displays are generated by moving a viewpoint round a fixed rhombus on a trajectory with two components—a circle parallel to the plane of the diamond, and a superimposed change in elevation which varies sinusoidally. To a greater or lesser extent, depending on the phase of the sinusoid, elevation change is misinterpreted as ‘zooming’ in and out—though in fact the projection always corresponds to an object at a fixed distance. The illusion was devised to underline the questions surrounding the treatment of parallel projection in biological systems. The standard formulations considered in computational vision preclude the kind of size - distance trade-off that the illusion demonstrates, but they do imply that observers should be able to register the shape of an object from this kind of display. A less familiar formulation, ‘paraperspective projection’, allows size - distance trade-off as in perspective projection, but it suggests the shape of a lamina should be impossible to recover from motion. Stimuli which promote ‘zooming’ do weaken shape discrimination, but the trade-off is incomplete. A possible solution is that human vision picks out size change in a way that is appropriate when either object or motion path is ‘friendly’, but that misleads when awkward combinations occur. Certainly vision research should avoid assuming that the attractively simple consequences associated with standard parallel projection govern the way biological systems operate.