Imagining circles: empirical data and a perceptual model for the arc-size illusion

An essential part of visual object recognition is the evaluation of the curvature of both an object's outline as well as the contours on its surface. We studied a striking illusion of visual curvature--the arc-size illusion (ASI)--to gain insight into the visual coding of curvature. In the ASI, short arcs are perceived as flatter (less curved) compared to longer arcs of the same radius. We investigated if and how the ASI depends on (i) the physical size of the stimulus and (ii) on the length of the arc. Our results show that perceived curvature monotonically increases with arc length up to an arc angle of about 60°, thereafter remaining constant and equal to the perceived curvature of a full circle. We investigated if the misjudgment of curvature in the ASI translates into predictable biases for three other perceptual tasks: (i) judging the position of the centre of circular arcs; (ii) judging if two circular arcs fall on the circumference of the same (invisible) circle and (iii) interpolating the position of a point on the circumference of a circle defined by two circular arcs. We found that the biases in all the above tasks were reliably predicted by the same bias mediating the ASI. We present a simple model, based on the central angle subtended by an arc, that captures the data for all tasks. Importantly, we argue that the ASI and related biases are a consequence of the fact that an object's curvature is perceived as constant with viewing distance, in other words is perceptually scale invariant

Visual after-effect of perceived regularity

Aim: Regular repeating patterns are prominent features in a visual scene. Here I consider whether regularity is an adaptable feature that produces a subsequent after-effect and whether a first- or second-order process mediates that after-effect. Method: Stimuli consisted of a 7 by 7 arrangement of elements on a baseline grid. The position of each element was randomly jittered from its baseline position by an amount that determined its degree of pattern irregularity. The elements of the pattern consisted of dark Gaussian blobs (GB), difference of Gaussians (DOG) or random binary patterns (RBP). Observers adapted for 60 seconds to a pair of patterns above and below fixation with a different degree of regularity, then adjusted the relative degree of regularity of two subsequently presented test patterns. The size of the after-effect at the point of subjective equality (PSE) was given by the baseline removed difference in regularity at the PSE or log ratio of the physical element jitter of the two test patterns at the PSE. Results: PSEs revealed that regularity is an adaptable feature that produces a unidirectional after-effect; specifically that adaptation only causes test patterns to appear less regular. The after-effect displayed transfer from GB adaptors to both DOG and RB test patterns and from DOG and (RBP) adaptors to GB patterns. Conclusion: Pattern regularity is an adaptable feature in vision, which produces a novel unidirectional after-effect I have termed Regularity After-Effect, or RAE. I propose second-order spatial-frequency channels as candidate mechanisms of regularity processing.Objectif: Les motifs réguliers répétitifs sont des caractéristiques de premier plan dans la scène visuelle. Cette communication a comme objectif de découvrir si la régularité est une caractéristique adaptable du système visuel produisant un effet consécutif et si cet effet-consécutif est lié à un processus de premier- ou de second-ordre. Méthode: Les stimuli étaient constitués en un arrangement 7 par 7 éléments sur une grille. La position de chaque élément a été giguer au hasard à partir de sa position d'origine avec une valeur qui détermine son degré d'irrégularité. Les éléments qui constituent chaque grille pouvaient être des blobs de Gaussiennes (GB), des différence de Gaussiennes (DOG) ou de motif binaire aléatoire (RBP). Les participants ont été adaptés pour 60 secondes à une paire de motifs placée de part et d'autre d'un point de fixation ou chaque motif avait un degré différent de régularité. Les participants devaient ajuster le degré relatif de régularité de deux motifs présentés après. La taille de l'effet-consécutif est obtenue par la différence de régularité au point subjectif d'égalité soustrait à la régularité mesurée entre les deux motifs test ou par le logarithme du ratio de la différence de régularité entre les deux motifs test au point subjectif d'égalité. Résultats: Les point-subjectif d'égalité mesurée ont montrées que la régularité est une caractéristique adaptable qui produit un effet-consécutif unidirectionnel, plus précisément que les motifs sont perçus comme plus irréguliers après adaptation. On a observe un transfert à partir des stimuli d'élément GB a des motifs de test RBP et DOG et un transfert a partir des stimuli DOG et RBP vers des test de GB. Conclusion: La régularité est un élément du système visuel adaptable, produisant effet-consécutif unidirectionnel nouveau que appelé l'effet consécutif de la régularité. Je propose les canaux de fréquence-spatial de second-ordre comme mécanisme candidat au traitement de la régularité

After effect of perceived regularity

Regularity is a ubiquitous feature of the visual world. We demonstrate that regularity is an adaptable visual dimension: The perceived regularity of a pattern is reduced following adaptation to a pattern with a similar or greater degree of regularity. St

Mean Phi coefficients for the bi-stable target condition are plotted against those obtained for the rivalrous target condition by each context condition.

<p>The matched target was always presented to the observer’s dominant eye. A, context presented to both eyes; B, context presented to the same eye as the matched target; C, context presented to the opposite eye as the matched target. The upper panel is for when the target was presented above the fixation cross, the lower panel when below it.</p

Mean Phi coefficients for context-target coherence averaged across trials.

<p>Each graph plots the bi-stable target coefficients against the rivalrous target coefficients. Different graphs are for different context condition. A, context presented to both eyes; B, context presented to the same eye as the matched target; C, context presented to the opposite eye as the matched target. The upper panel is for when the target figure was presented above the fixation cross, the lower panel when below it.</p

Mean Phi coefficients for the ambiguous target are plotted against those for the rivalrous target, for each context condition.

<p>The matched target was always presented to the observer’s non-dominant eye. A, context presented to both eyes; B, context presented to the same eye as the matched target; C, context presented to the opposite eye as the matched target. The upper panel is for when the target figure was presented above the fixation cross, the lower panel when below it.</p

Example of context motion sequence (top), observer response (second), and extracted perceived motion of the target sequence (three from the bottom) taken from a sample trial for three example shifts of the timeline.

<p>Example of context motion sequence (top), observer response (second), and extracted perceived motion of the target sequence (three from the bottom) taken from a sample trial for three example shifts of the timeline.</p

Correlations r between the mean Phi coefficients of the ambiguous and rivalrous targets for Experiment 2.

<p>Correlations r between the mean Phi coefficients of the ambiguous and rivalrous targets for Experiment 2.</p

Sample frames illustrating each context and target condition for the rivalrous target (top), and ambiguous target (bottom).

<p>The context figure was presented either to both eyes (left hand side), the same eye (middle), or the opposite eye (right hand side) of the target. For each condition, the context was presented either above or below the fixation dot.</p

Example of the ambiguous Necker cube (left) and binocularly rivalrous skeleton cube (right pair).

<p>One of the skeleton cubes also served as the context figure. Orthographic projection was used to render ambiguous the motion direction of the Necker cube, while the addition of shading and color difference disambiguated the motion directions of skeleton cubes.</p