Curvilinearity, covariance, and regularity in perceptual groups

Area of Science:

• * Cognitive psychology
• * Visual perception
• * Probabilistic inference

Background:

• * Curvilinear patterns are often perceived as a form of probabilistic inference.
• * Previous research suggests that visual systems may process sequential information to infer patterns.

Purpose of the Study:

• * To investigate how humans judge curvilinearity based on the distribution of successive inter-dot angles.
• * To determine the cognitive window used for evaluating curvilinear visual sequences.
• * To model human judgments of curvilinearity using probabilistic principles.

Main Methods:

• * Participants classified 4- and 5-dot configurations as either curvilinear or independently generated.
• * Analysis focused on the joint distribution of successive inter-dot angles.
• * A probabilistic model was developed to predict human judgments.

Main Results:

• * Human judgments of curvilinearity align with a Gaussian distribution of inter-dot angles centered on collinearity (0 degrees).
• * A negative correlation was found between successive angles, indicating a focus on local smoothness.
• * Non-successive angles showed negligible correlation, suggesting a limited cognitive window (approximately 4 dots).
• * The probabilistic model accurately predicted the magnitude of observed correlations.
• * Participants demonstrated a preference for equally spaced dots along perceived curves.

Conclusions:

• * Curvilinear pattern perception relies on evaluating local collinearity and smoothness within a limited perceptual window.
• * Human visual processing of sequential data for pattern recognition is based on probabilistic inference.
• * The findings support a model where curvilinearity is assessed by a moving 4-dot window, prioritizing immediate angular relationships over long-range dependencies.