Robust cue integration : A Bayesian model and evidence 2 from cue - conflict studies with stereoscopic and figure

9 Most research on depth cue integration has focused on stimulus regimes in which stimuli contain the small cue conflicts that 10 one might expect to normally arise from sensory noise. In these regimes, linear models for cue integration provide a good 11 approximation to system performance. This article focuses on situations in which large cue conflicts can naturally occur in 12 stimuli. We describe a Bayesian model for nonlinear cue integration that makes rational inferences about scenes across the 13 entire range of possible cue conflicts. The model derives from the simple intuition that multiple properties of scenes or 14 causal factors give rise to the image information associated with most cues. To make perceptual inferences about one 15 property of a scene, an ideal observer must necessarily take into account the possible contribution of these other factors to 16 the information provided by a cue. In the context of classical depth cues, large cue conflicts most commonly arise when one 17 or another cue is generated by an object or scene that violates the strongest form of constraint that makes the cue 18 informative. For example, when binocularly viewing a slanted trapezoid, the slant interpretation of the figure derived by 19 assuming that the figure is rectangular may conflict greatly with the slant suggested by stereoscopic disparities. An optimal 20 Bayesian estimator incorporates the possibility that different constraints might apply to objects in the world and robustly 21 integrates cues with large conflicts by effectively switching between different internal models of the prior constraints 22 underlying one or both cues. We performed two experiments to test the predictions of the model when applied to estimating 23 surface slant from binocular disparities and the compression cue (the aspect ratio of figures in an image). The apparent 24 weight that subjects gave to the compression cue decreased smoothly as a function of the conflict between the cues but did 25 not shrink to zero; that is, subjects did not fully veto the compression cue at large cue conflicts. A Bayesian model that 26 assumes a mixed prior distribution of figure shapes in the world, with a large proportion being very regular and a smaller 27 proportion having random shapes, provides a good quantitative fit for subjects’ performance. The best fitting model 28 parameters are consistent with the sensory noise to be expected in measurements of figure shape, further supporting the 29 Bayesian model as an account of robust cue integration. 30