Curvilinearity, covariance, and regularity in perceptual groups

A curvilinear pattern among a series of visual items (e.g., dots) can be regarded as a kind of probabilistic inference, in which each consecutive angle, regarded independently, is more nearly collinear than would be expected by chance alone. This paper investigates judgments of curvilinearity as a function of the joint distribution of successive inter-dot angles. Subjects were asked to classify 4- and 5-dot configurations as having been generated by a curvilinear generating process, vs independently. Their results are distributed as a gaussian over the inter-dot angles with mean 0 deg (collinear), with a negative correlation between successive angles, but negligible correlation between non-successive angles. This suggests that curvilinearity is evaluated in a 4-dot window moving along the chain of dots, evaluating collinearity and smoothness but ignoring higher-order relationships. Moreover, the probabilistic model provides a remarkably precise numeric prediction of the magnitude of the correlation. Subjects also showed a reliable preference for equal spacing of dots along the virtual curve.