Ambiguous pictorial depth cues and perceptions of nonrigid motion in the three-loop figure

The three-loop figure is a two-dimensional (2-D) pattern that generates (mis)perceptions of nonrigid three-dimensional (3-D) structure when rotated about its centre. Such observations have been described as counterexamples to the principle whereby a moving object is presumed to be rigid, provided that a rigid interpretation is possible (ie the 'rigidity constraint'). In the present investigation we demonstrated that stationary three-loop figures exhibit many of the classic properties of multistable/ambiguous figures, with any one of several possible 3-D configurations being reported at any one instant. Further investigation revealed that perceived nonrigidity during rotation was markedly reduced (and rigidity enhanced) when the figure was modified with static pictorial depth cues (eg shading, interposition). These cues had no effect on the overall proportion of time that observers reported 3-D organisations in stationary versions of the figure, but significantly reduced the frequency of perceptual reorganisation, and increased the duration for reporting a particular organisation. Since each of the perceived 3-D structures in a stationary ambiguous 2-D figure has a unique kinetic counterpart (ie rigid transformation), we attribute the nonrigid structure perceived when the figure rotates to the integration of these otherwise inconsistent kinetic components; and have further illustrated this with modified versions of a Penrose impossible triangle. Under kinetic versions of the classical size/distance invariance hypothesis, the rigidity constraint may be considered to represent a special instance of size/shape constancy, in which case counterexamples involving (mis)perceptions of nonrigid structure are comparable to other well-known exceptions to such principles of minimum object change (eg classical illusions).