We used 156 real-world images representing a large variety of scenes (landscapes, buildings, indoor scenes) (Figure 1). Scenes were presented in grayscale and had a resolution of 768 by 1024 pixels and were presented in full screen subtending a visual angle of 30° × 40°. All scenes were equalized to an average luminance of 127 (luminance values were between 0 and 255).

The distractor, a Gabor patch, was inserted into the scene. The patch had a radius R_d of 2.2° (i.e. 56.4 pixels) with maximal luminance contrast. The distractor shape corresponded to a 2D Gaussian function modulated by a vertical sinusoid with a spatial frequency of 2.2 cycles per degree. It appeared at the onset of the second detected fixation1. Note that “fixation 1” refers to the first fixation that occurred after scene onset (and not the fixation that started before scene onset). To speed up the display of the scene with the distractor at the second fixation, this scene was computed before the experiment. For each scene, four different locations for the distractor were chosen randomly on a 4° radius-centered circle.

Eye movements were recorded using the SR Research Eyelink II (500 Hz) infrared eye tracking system. Stimuli were presented on a 20-inch ViewSonic CRT monitor, with a resolution of 768 by 1024 pixels, a refresh rate of 85 Hz, at a viewing distance of 57 cm. Experiments were run using SoftEye ( 10 ).

Each trial started with a white fixation cross presented for 1 s on a gray screen. This fixation cross was located on the screen diagonals 5° from the center. After 1 s, and if gaze had stabilized for 100 ms (gaze contingent display), the scene was displayed. If the participant did not gaze at the cross, the scene was still displayed after 5 s, but the trial was considered invalid and recorded data were not analyzed.

In the control condition, the scene was displayed for 2.5 s. Three distractor conditions were used. The distractor always appeared at the onset of fixation 2, an early fixation known to be mainly guided by the visual properties of the scene. As already mentioned, the starting point of exploration was on the screen diagonals 5° from the center of the screen. The probability that fixation 1 would appear on the scene center was therefore very high, due to the “central bias” observed during eye movement experiments ( 24 ). The distractor was displayed for 50 ms (Short Presentation Time: SPT), 210 ms (Medium Presentation Time: MPT) or until the end of the exploration (Long Presentation Time: LPT). The duration of scene presentation was therefore different in these three distractor conditions. In the SPT condition, scenes containing a distractor were displayed for 50 ms, and then, scenes with no distractor were shown for 2250 ms. In the MPT condition, a scene featuring the distractor was displayed for 210 ms and followed by the same scene without the distractor for 2090 ms. In the LPT condition, a scene with the distractor was displayed for 2300 ms. Distractor onset was synchronized with the onset of fixation 2 for each scene and each observer. On average, it appeared 580 ms after scene onset. Finally, at the end of the trial, a gray screen appeared for 1 s (Figure 2).

Observers were asked to look carefully at scenes in preparation for a questionnaire on scene content. The questionnaire was never actually given. A 9-point calibration routine was completed and repeated every 50 trials or if the drift correction, completed every ten trials, detected an error above 0.5°.

Forty-eight naïve healthy volunteers with normal or corrected-to-normal vision took part in the experiment (17 female; age range: 21-27, M=24.12, SD=2.46). Participants were assigned randomly to one of four experimental conditions: the control condition (without the distractor) or one of the three distractor conditions (SPT, MPT or LPT). In the control condition, participants viewed all 156 scenes. In the distractor conditions, each participant viewed only 52 of the 156 scenes. In the MPT and LPT conditions, all participants reported perceiving the distractor. However, in the SPT condition only 10 out of 12 reported it. We analyzed only the data from these 10 participants in order to maintain consistency. Analyses indicated that the two observers who did not notice the distractor differed from the other participants in their eye movement patterns but showed no increase in fixation durations.

Raw eye-movement data were preprocessed by removing fixations that occurred around eye blinks or outside the presentation screen. Fixations whose duration was shorter than 50 ms or longer than 1000 ms were excluded. In total, less than 10% of the data was removed, including invalid trials.

Because the distributions of fixation durations were skewed, median values were used for each subject per condition. Eye fixation locations were also extracted and the proportion of fixations that landed on the distractor was computed. In order to test if the proportions of fixations that landed on the distractor location were greater in the distractor conditions than in the control condition, we calculated the proportion of fixations recorded at the distractor location in the control condition (with no distractor). Fixations were represented by a circle of 1° around the fixation location and classified as being on the distractor if there was an intersection between the circle with a radius of 2.2° representing the distractor and the circle with a radius of 1° representing the fixation.

For each scene, we computed a map highlighting all the regions of interest. These maps were called empirical saliency maps. They were created using fixations recorded during the control condition. Empirical saliency maps were obtained for each scene by summing a 2D Gaussian with a standard deviation of 1° centered on fixations. The size of Gaussians was chosen in relation to foveal size and eye-tracker accuracy. It should be noted that only fixations 2 to 8 were used; we did not use fixation 1, mainly due to central bias ( 24 ). Empirical saliency maps were then converted into binary maps using a threshold of 0.2 (for eye movement analysis) or normalized to 1 to correspond to probability density function (for the modeling part). These maps obtained using the eye fixations of several observers predict the fixations of other observers about as well as the best saliency models do. Even if individual differences do exist between observers, consistency between the fixations of several observers has been reported, making the prediction of fixation locations of one observer by using the fixations of other observers efficient ( 26, 12 ).

A repeated-measure ANOVA was conducted with Fixation (fixation 1 to 8) as a within-subjects factor and Condition (control/SPT/MPT/LPT) as a between-subjects factor. We found main effects of Condition, F(3,41) = 9.65, p < .001, η_p² = 0.41, and Fixation, F(7,287) = 10.59, p < .001, η_p² = 0.20. The interaction Condition × Fixation was also significant, F(21,287) = 2.47, p < .001, η_p² = 0.15 (Figure 3). Multiple comparisons of distractor conditions to the control condition were assessed with Dunnett post-hoc tests. The distractor effect was particularly noticeable at fixation 2, during which the distractor appeared. Its duration significantly increased in the three distractor conditions compared to the control condition (p < .05 – marginal effect for LPT, p = 0.06). We observed an equal increase of the duration of fixation 2 in the three distractor conditions. The fixation following distractor onset (fixation 3) also increased in duration compared to the control condition in the MPT and LPT conditions (p < .05). Moreover, in the LPT condition, fixations 4 to 8 were longer than in the control condition (p < .05). Finally, the fixation preceding distractor onset (fixation 1) was more prolonged in the LPT condition than in the control condition (p < .05).

A repeated-measure ANOVA was conducted with Fixation (fixation 2 to 8) as a within-subjects factor and Condition (control/SPT/MPT/LPT) as a between-subjects factor. The analysis revealed main effects of Condition, F(3,41) = 9.55, p < .001, η_p² = 0.41, and Fixation, F(6,246) = 37.82, p < .001, η_p² = 0.48. The interaction Condition × Fixation was also significant, F(18,246) = 6.78, p < .001, η_p² = 0.33 (Figure 4). Multiple comparisons of distractor conditions to the control condition were assessed with Dunnett post-hoc tests. The proportion of fixation 3s on the distractor, i.e. the fixation immediately following distractor onset, was higher in all distractor conditions compared to the control condition (p < .01). The proportion of fixation 4s on distractor location was also higher for MPT and LPT than in the control condition (p < .01). In the LPT condition, the proportion of fixations 5 to 7 that landed on the distractor was again higher than in the control condition (p < .05).

Results on fixation durations and fixation locations were coherent: the current fixation increased in duration and the following fixation had a high probability of landing on the distractor location. The following analysis directly tested the link between the distractor effect on the duration of fixation 2 and the location of fixation 3.

In line with previous studies ( 12, 13 ), an increase in the mean duration of fixation 2s and a high probability of observing fixation 3s on the distractor location, were observed. These parameters were linked when the distractor was presented for longer durations: more fixation 3s were observed inside the distractor location when fixation 2s were of longer duration. Although the effect of the distractor was the same on the duration of fixation 2 in the three distractor conditions, we observed differences on subsequent fixations. Distractors of longer duration had a greater impact on the location and even on the duration of subsequent fixations. Finally, the distractor effect was influenced by scene saliency at the distractor location: a stronger distractor effect was observed with an increase in the proportion of fixation 3s on the distractor location, when the distractor appeared in a salient location. We measured the distractor effect only on fixations that landed on the distractor location with these eye movement analyses. Furthermore, the analysis presented did not allow us to quantify the contribution of the distractor in relation to scene saliency, which is known to drive fixation location during the exploration of scenes.

The proposed statistical model explains the distribution of recorded eye fixation locations using a linear weighted summation of three possible guiding factors. We used the Expectation-Maximization (EM) algorithm, a statistical method using the recorded eye movements to calculate the relative contribution of each guiding factor in order to maximize the global likelihood of the mixture model ( 21 ).

The first factor known to guide eye movement during scene exploration is the saliency of a scene. We used the experiment saliency map: S_m(p), with p=(x,y) the 2D fixation position.

The second factor in the model was the impact of distractor2 appearance on a given position. In line with previous results showing the attractiveness of the distractor, this factor was modeled by a 2D Gaussian function: Ν(p;μ(t),σ(t)). In other words, μ(t) (mean) was the spatial position and the parameter σ(t) (standard deviation) represented the size of the Gaussian. The parameters μ(t) and σ(t) were estimated for each fixation order . This factor acted as a “localizer Gaussian” and indicated that fixation locations were gathered on a particular spatial location modeled by the Gaussian. The ability of this factor to reflect the influence of the distractor on fixation locations was related to the parameters μ(t), σ(t) of the Gaussian function. For this reason we named this second factor the “Gaussian” and not the “distractor” factor.

Finally, even if the saliency of the scene and the distractor were the two main factors which explained eye movements, a third factor was added to cover any other non-controlled processes which may have influenced eye movements. This third factor was a noise factor, and explains any fixations that were not explained by the two other factors. The lower the weight of this factor was, the better the other factors explained the data. It was simply modeled by a uniform spatial distribution on the whole image: U(p) and was called “noise factor” for simplicity.

The guiding factors that explain fixation locations after distractor onset could be confounded: when the distractor appeared in a salient location, the contributions of the scene saliency and the distractor could not be distinguished. Consequently, only trials where the distractor was not in a salient location were used in the proposed model. 49% of the trials were therefore used. This also allowed us to avoid instability in the convergence of the parameters of the model.

The density function f(p,t) of the fixation position p=(x,y) at each fixation order t was expressed in terms of an additive mixture of the three spatial maps, each associated with a given prior probability or weight α_i(t),i = 1,2,3:

f(p,t)=α₁(t)×S_m(p)+ α₁(t)×Ν(p;μ(t),σ(t))+α₃(t)×U(p)

with p=(x,y) the 2D fixation position, f(p,t) the eye fixation map for one distractor condition (SPT, MPT, or LPT) at each fixation order t (t= 2:8) and α_i(t) the estimated weights of the factor with α₁(t)+α₁(t)+α₃(t) = 1. α₁(t) represented the weight of the saliency map, α₁(t) the weight of the Gaussian factor and α₃(t) the weight of the “noise factor”.

The EM algorithm was used for each distractor condition, for each fixation order, to calculate unknown parameters. To deal with the sensitivity of the estimated parameters to initial conditions, ten randomly chosen values for the initialization were used.

The parameters μ(t) and σ(t) of the Gaussian factor, which were free parameters across fixation order, were calculated. For each fixation order , and each distractor condition, the number of estimated parameters was six (α₁(t),α₁(t),α₃(t),μ_x(t),μ_y(t) and σ(t) with σ_x(t)=σ_y(t)=σ(t)), and five degrees of freedom (α₁(t)+α₁(t)+α₃(t)=1). The attractiveness of the distractor was analyzed by both the weight, and the spatial parameters (μ(t),σ(t)) at the convergence. Consequently, interpretation of this factor as a guiding factor during the exploration could be carried out only once estimated parameters had been obtained at the EM convergence. More precisely, the interpretation of this “localized Gaussian” factor as the “distractor factor” was only justified when the mean corresponded to the physical position of the distractor. To evaluate it, the Euclidean distance d_μ(t)=d_E(μ(t),D₀) between μ(t) and the spatial location D₀ of the distractor, was computed, in function of the fixation order t. If this distance was different from zero, the nature of this factor changed. In other words, its interpretation depends on the distance d_μ(t). If the distance is high, this Gaussian factor does not represent the distractor accurately, but rather indicates that fixation locations are gathered at a particular spatial location modeled by the Gaussian function. That is why we chose to call this guiding factor the “localized Gaussian” factor.

The saliency map weight α₁(t) was the highest for all fixations and distractor conditions (Figure 5). Although the scene saliency map had the highest weight, the weight of the Gaussian factor was not negligible. As expected, the temporal evolution of the Gaussian factor (σ(t) and d_μ(t) was different in the various distractor conditions (Figure 7).

In the three distractor conditions, at fixation 2, the standard deviation σ(2) was larger and the distance d_μ(2) close to zero, showing a mode close to the image center (Figure 6). At this fixation, the distractor had not yet been displayed. The fact that this mode was close to the scene center illustrated the central bias currently observed in eye movement data ( 24 ).

For SPT and MPT conditions, the evolution of σ(t) and d_μ(t) was divided into three phases. Firstly, between fixations 2 and 3, the Gaussian weight α₁(t) increased slightly (Figure 5). At the same time, the deviation σ(t) decreased and became smaller than the size R_d of the distractor. Secondly, after fixation 3, d_μ(t) decreased to almost zero and σ(t) was slightly larger than R_d (Figure 7). In the MPT condition, the Gaussian factor was more attractive, as we can see for fixations 3 and 4. We observed smaller values for σ(3) and σ(4), which in turn were even smaller than R_d (Figure 7A). The mean μ was at the location of the distractor (Figure 6). From fixations 4 to 6, σ(t) and d_μ(t) increased, resulting in the Gaussian factor moving towards the image center (Figure 6). Finally, from fixation 6, all parameters were stabilized.

For the LPT condition, the Gaussian factor weight α₁(t increased from fixation 2 to fixation 3, until it was almost equal to the weight α₁(3) of the saliency mode. The contribution of saliency remained stable, while from fixation 3, the contribution of the distractor decreased, and the “noise factor” weight α₃ increased (Figure 5). From fixation 3, we also observed a decrease in the parameter σ(t) and a decrease in the distance d_μ(t) (Figure 7). σ(t) which was twice as small as R_d from fixation 4 to the end of the exploration. Contributions of this factor and of the “noise factor” were similar from fixation 6. Furthermore, the position of the Gaussian mode converged at the spatial location D₀ of the distractor (Figure 6).

Interestingly, when comparing the three distractor conditions, we observed that the larger distractor effect on eye movements observed in LPT than in MPT and in MPT than in SPT was illustrated by the results of the model. The influence of the distractor on fixation 3, α₁(3), was higher in LPT than in MPT, which in its turn was slightly higher than in SPT.