A Two-Tiered Model of the Perception of Aspect Ratio in Binocularly Viewed Surfaces

Standard Bayesian models of the perception of aspect ratio in binocularly viewed surfaces predict that observers will accurately perceive the aspect ratio of a surface given reliable binocular-disparity cues to slant. However, there is psychophysical evidence that this prediction is not borne out. Specifically, Hibbard et al. (2012) showed that observers underestimate the aspect ratio of surfaces by about 13% when the binocularly specified surface slant is 0. This has been taken to show that the standard Bayesian model is inadequate. We agree but argue that a different kind of Bayesian model can explain the recalcitrant data. We propose a two-tiered model based on an explanation of previous data that shows that line length is (mis)perceived as a function of image orientation (Howe and Purves 2002). According to that argument, the misperception of line length is driven by the correlation between line image orientation and its 3D slant (from natural scene statistics). In our model, the misperception of length in the vertical direction leads to an overestimation of aspect ratio in the first tier. Moreover, this first tier is informationally encapsulated insofar as the bias it introduces cannot be corrected by cues to slant available to higher-level modules. The information from the first tier is then fed into a second tier that uses Bayes’ theorem to compute an estimate of surface aspect ratio given the biased image aspect ratio plus binocularly specified slant. This two-tiered model can explain why observers underestimate surface aspect ratio despite having binocular-disparity cues to slant. The model thus shows how percepts that appear inconsistent with Bayes can nevertheless be understood in terms of a hierarchy of modules, even if the processing within each module is Bayesian. This model also explains how percepts that are not projectively consistent with the image data are possible.