Saccade crossing avoidance as a visual search strategy

Abstract

Although visual search appears largely random, several oculomotor biases exist such that the likelihoods of saccade directions and lengths depend on the previous scan path. Compared to the most recent fixations, the impact of the longer path history is more difficult to quantify. Using the step-selection framework commonly used in movement ecology, and analyzing data from 45-second viewings of "Where's Waldo?", we report a new memory-dependent effect that also varies significantly between individuals, which we term self-crossing avoidance. This is a tendency for saccades to avoid crossing those earlier in the scan path, and is most evident when both have small amplitudes. We show this by comparing real data to synthetic data generated from a memoryless approximation of the spatial statistics (i.e. a Markovian nonparametric model with a matching distribution of saccade lengths over time). Maximum likelihood fitting indicates that this effect is strongest when including the last $\approx 7$ seconds of a scan path. The effect size is comparable to well-known forms of history dependence such as inhibition of return. A parametric probabilistic model including a self-crossing penalty term was able to reproduce joint statistics of saccade lengths and self-crossings. We also quantified individual strategic differences, and their consistency over the six images viewed per participant, using mixed-effect regressions. Participants with a higher tendency to avoid crossings displayed smaller saccade lengths and shorter fixation durations on average, but did not display more horizontal, vertical, forward or reverse saccades. Together, these results indicate that the avoidance of crossings is a local orienting strategy that facilitates and complements inhibition of return, and hence exploration of visual scenes.

Figures (4)

• Figure 1: (a) List of predictors used (left), sorted by the number of most recent fixations $L_{hist}$ required to calculate them; and an example of a scanpath illustrating key quantities and case-control sampling (right). Saccades are approximated as straight lines between mean fixation locations. In the illustration, predictors are calculated for fixation $Q_{t+1}$ by generating four random control saccades (light dotted lines) in addition to the saccade from the data (dark dotted line). The center of the screen is indicated by a cross. (b) The panels on the left illustrate parametric predictor values for test points $Q'_{t+1}$ given a scanpath up to $Q_t$ indicated by an X. The panels on the right show overall spatial log likelihoods for the nonparameteric model (top) the combined parameteric model (middle) and the difference (bottom).
• Figure 2: Task comparison. The panels in (a) compare the spatial distributions of fixations in terms of sparsity and distance from the centre of the image. Overlaid are moving averages over time, with a window length of 5 seconds, ending in the red crosses. The arrows in (b) shows the direction and slope of maximum gradient in log-odds from fitted parametric models evaluated at the small-saccade limit $Q'_{t+1}\approx Q_{t}$ (see Supplementary Information). The half-width of the image is approximately 15.2 degrees. Panel (c) compares normalized z-scores for the main predictors in the model. The color of each cell gives the z-score when including only a linear term for this predictor and all interactions for all other terms. Terms that do not decrease the AIC are given a z-score of zero. Log-length, horizontal bias and cardinality are not included due to strong dependence on the saccade model.
• Figure 3: (a) Mean number of crossings (including intersections with both past and future saccades within $\tau_3$) divided by saccade length, plotted against saccade length, for the models and test data. The grey area shows the density of saccade lengths in the test data, while the grey line shows the density of saccades with crossings. (b) Cumulative number of crossings over time for data generated from each model along with the test data. Shown are means and standard deviations over all 70 trials in each set.
• Figure 4: Waldo task individual differences. (a) Intraclass correlation coefficients for predictors where there was significant variation among both trials and participants. (b) Corresponding standard deviations of the participant-level random effect. (c) Pearson correlation coefficients between each significant random participant effect $(y)$ and the mean of the trial-level median fixation duration $t_\mathrm{fix}$. Hatched bars indicate lack of significance at the $p<0.05$ level. (d) Loadings of the first principal component given the fitted means for each participant and each significant predictor.