The role of sensory uncertainty in simple contour integration

Abstract

Perceptual organization is the process of grouping scene elements into whole entities. A classic example is contour integration, in which separate line segments are perceived as continuous contours. Uncertainty in such grouping arises from scene ambiguity and sensory noise. Some classic Gestalt principles of contour integration, and more broadly, of perceptual organization, have been re-framed in terms of Bayesian inference, whereby the observer computes the probability that the whole entity is present. Previous studies that proposed a Bayesian interpretation of perceptual organization, however, have ignored sensory uncertainty, despite the fact that accounting for the current level of perceptual uncertainty is one of the main signatures of Bayesian decision making. Crucially, trial-by-trial manipulation of sensory uncertainty is a key test to whether humans perform near-optimal Bayesian inference in contour integration, as opposed to using some manifestly non-Bayesian heuristic. We distinguish between these hypotheses in a simplified form of contour integration, namely judging whether two line segments separated by an occluder are collinear. We manipulate sensory uncertainty by varying retinal eccentricity. A Bayes-optimal observer would take the level of sensory uncertainty into account-in a very specific way-in deciding whether a measured offset between the line segments is due to non-collinearity or to sensory noise. We find that people deviate slightly but systematically from Bayesian optimality, while still performing "probabilistic computation" in the sense that they take into account sensory uncertainty via a heuristic rule. Our work contributes to an understanding of the role of sensory uncertainty in higher-order perception.

Fig 1. Tasks and generative model.

A: Collinearity judgment task. After stimulus offset, participants reported if the line segments belonged to the same line or different lines. B: Height judgment task. Participants reported whether the left line segment was higher or the right line segment was higher. C: Generative model of the collinearity judgment task. Trial type C = 1 when the two lines segments are collinear, and C = 0 when line segments are non-collinear. On a given trial, the stimulus pair y_L, y_R randomly appeared around one of four eccentricity levels (y = 0, 4.8, 9.6, 16.8), measured by degrees of visual angle (dva). For all models, the observer’s measurements x_L, x_R are assumed to follow a Gaussian distribution centered on the true stimulus y_L, y_R, respectively, with standard deviation σ_x(y) dependent on eccentricity level y. D: Possible eccentricity levels (in dva). E: Stimulus distribution for collinearity judgment task. When C = 1, the vertical position of the left line segment y_L is drawn from a Gaussian distribution centered at y with fixed standard deviation σ_y; the vertical position of the right segment y_R is then set equal to y_L. When C = 0, y_L and y_R are independently drawn from the same Gaussian.

Fig 2. Collinearity judgement task data.

A: Accuracy as a function of retinal eccentricity level (chance probability = 0.5). B: Proportion of reporting “collinear” as a function of vertical offset between the two line segments. C: Proportion of reporting “collinear” as a function of vertical offset of the two line segments at each eccentricity level. Error bars indicate Mean ± 1 SEM across 8 subjects.

Fig 3. Decision boundaries for fixed-criterion (Fixed), bayesian (Bayes) and linear heuristic (Lin) models (left to right).

The probability of reporting “collinear” given stimulus and eccentricity condition is equal to the probability that the observer’s measurements of vertical positions of left and right line segments fall within the boundary defined by the model.

Fig 4. Model fits and model comparison for fixed-criterion (Fixed), bayesian (Bayes) and linear heuristic (Lin) models (from left to right).

A: Model fits to proportion of responding collinear as a function of vertical offset of the two line segments. Error bars indicate Mean ± 1 SEM across subjects. Shaded regions indicates Mean ± 1 SEM of fits for each model, with each model on a separate column. B: Model comparison via leave-one-out cross-validation score (LOO). Bars indicate individual subjects’ LOO scores for every model, relative to the fixed-criterion model. A positive value indicates that the model in the corresponding column had a better LOO score than the fixed-criterion model. Shaded regions indicate Mean ± 1 SEM in LOO differences across subjects. The Lin model won the model comparison, whereas Fixed was the worst model.

Fig 5. Height judgment task results.

A: Height judgment task data. Proportion of reporting “right line segment higher” is plotted as a function of vertical offset between line segments. Error bars indicate Mean ± 1 SEM across subjects. B: Noise parameters estimated from the best-fitting model, linear heuristic (Lin), on collinearity judgment task vs. noise parameters estimated from the height judgment task, in dva. Each dot corresponds to a subject’s estimated noise parameters (posterior means) for a given eccentricity level. C: Models’ fits to collinearity judgment task data when noise parameters estimated from the height judgment task were imported into the models. Shaded regions indicate Mean ± 1 SEM of fits. See Fig 4A for comparison. D: Model comparison on collinearity judgment task data via LOO, constrained by importing noise parameters from the height judgment task. Results are consistent with the model comparison ordering we found in the original unconstrained fits, with free noise parameters (see Fig 4B for comparison).

Fig 6. Suboptimality analysis.

Black line: Observed accuracy across four eccentricity levels (chance probability = 0.5). Error bars indicate Mean ± 1 SEM across subjects. Green line: Estimated accuracy if subjects perform Bayes-optimally, with noise parameters obtained via the collinearity judgement task. Blue line: Estimated accuracy with noise parameters obtained via the height judgment task. Performance was slightly suboptimal across participants.

Fig 7. Nonparametric model.

A: Decision boundary estimates of linear heuristic model (Lin) vs. decision boundary estimates of the Nonparametric model at different eccentricity levels (Mean ± 1 SEM). B: Decision boundary at every eccentricity level fitted non-parametrically vs. Decision boundary at every eccentricity level fitted from the Lin model. Even when allowed to vary freely (“non-parametrically”), the decision boundaries are approximately linear in the sensory noise associated with each eccentricity level (and, incidentally, approximately linear in the eccentricity level itself), as per the Lin model.