Regularity Vs Genericity in the Perception of Collinearity

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Abstract
The perception of collinearity is investigated, with the focus on the minimal case of three dots. As suggested previously, from the standpoint of probabilistic inference, the observer must classify each dot triplet as having arisen either from a one-dimensional curvilinear process or from a two-dimensional patch. The normative distributions of triplets arising from these two classes are unavailable to the observer, and are in fact somewhat counterintuitive. Hence in order to classify triplets, the observer invents distributions for each of the two opposed types, ‘regular’ (collinear) triplets and ‘generic’ (ie not regular) triplets. The collinear prototype is centered at 0° (ie perfectly straight), whereas the generic prototype, contrary to the normative statistics, is centered at 120° away from straight—apparently because this is the point most distant in triplet space from straight and thus creates the maximum possible contrast between the two prototypes. By default, these two processes are assumed to be equiprobable in the environment. An experiment designed to investigate how subjects' judgments are affected by conspicuous environmental deviations from this assumption is reported. The results suggest that observers react by elevating or depressing the expected probability of the generic prototype relative to the regular one, leaving the prototype structure otherwise intact.

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