Visual factors that determine sensory uncertainty in rapid interceptive hand movements

Abstract

Tracking and intercepting a moving object requires predicting its trajectory, an ability that depends on the reliability of the available motion information. We investigated two common sources that limit the reliability (certainty) of visual motion information during laboratory object interception: how long an object is shown and how long it is occluded. A simulated flyball was shown briefly on a screen and then occluded before it entered a hit zone. Observers tracked the trajectory of the ball with their eyes and intercepted it in the hit zone with a rapid pointing movement. In a two-part experiment, we either varied the presentation of the ball or occlusion duration. Short presentation duration produced a strong center bias in hand movements, but long occlusion duration yielded only a weak center bias. Whereas the center bias merely improved with long presentation durations, it was fully resolved when occlusion duration was short. These findings indicate that sensorimotor decisions under uncertainty might have to rely more on priors when an object is presented briefly versus when it is occluded for longer periods. Eye and hand movement accuracy were correlated across levels of uncertainty, confirming that predictive processes guiding these effectors share a common readout of motion information.

Introduction

Visual uncertainty affects perception and movement

We move and act in a sensory world that provides a vast amount of visual information. Yet, the stream of visual information is often disrupted, and objects might be visible only for a moment or disappear behind other objects, rendering information about them uncertain. Under uncertainty, perceptual judgments about objects can be based on non-sensory attributes such as prior expectation or experience (Stocker & Simoncelli, 2006; Vilares & Kording, 2011; Petzschner, Glasauer, & Stephan, 2015; Hutchinson & Barrett, 2019; Gigerenzer, 2021). For example, when observers estimate the time to contact of a moving object, their perceptual judgments do not reflect true object speed but instead regress toward the mean distribution of speeds, reflecting the use of a Bayesian prior (Chang & Jazayeri, 2018). Congruently, when observers are asked to rapidly intercept a moving object with their hand, movement errors increase with decreasing availability of target motion information (e.g., Brouwer, Brenner, & Smeets, 2002; Fooken, Yeo, Pai, & Spering, 2016; Kreyenmeier, Schroeger, Cañal-Bruland, Raab, & Spering, 2023). These examples show that visual uncertainty affects perception and performance in systematic ways by biasing perceptual judgment and increasing movement errors. In this study, we selectively and systematically investigate two factors that can contribute to visual uncertainty—the duration a target is visible and the duration it is occluded—and compare their effects on eye and hand movements in a laboratory interception task. 

Uncertainty in limiting object viewing time

In perceptual time to contact (TTC) and manual interception tasks, available target information can be limited by either the duration for which a target is shown or the duration for which it is occluded (Villavicencio, de la Malla, & López-Moliner, 2024). Presentation and occlusion duration each determine and limit sensory uncertainty. However, most perceptual TTC and manual interception studies manipulate target presentation duration and occlusion duration simultaneously, and their potential effects on uncertainty are therefore confounded. Here, we independently manipulated presentation and occlusion duration to assess how each of these two factors contribute to performance accuracy in predictive actions. 

In general, the presentation duration of an object allows viewers to integrate visual position and velocity information to predict its trajectory. Longer presentation duration results in more available time to decode, accumulate, and continuously update visual motion information (Peterken, Brown, & Bowman, 1991; Brouwer et al., 2002; Brenner & Smeets, 2011; Zhao & Warren, 2015; Fooken et al., 2016; Brenner & Smeets, 2018; Fiehler, Brenner, & Spering, 2019). Longer presentation duration also provides more time to track a moving object with smooth pursuit eye movements, thereby enhancing perceptual motion prediction (Bennett, Baures, Hecht, & Benguigui, 2010; Spering, Schütz, Braun, & Gegenfurtner, 2011) and manual interception accuracy (Fooken, Kreyenmeier, & Spering, 2021). 

By contrast, target occlusion duration disrupts the processing, accumulation, and continuous updating of visual information. It might result in increased reliance on visual memory and extrapolation of the encoded object speed (Bennett et al., 2010; Battaglini & Mioni, 2019; de la Malla & López-Moliner, 2015; Aguado & López-Moliner, 2021; Battaglini & Ghiani, 2021). These visual memory signals may decay over time. Furthermore, longer occlusion duration leads to larger errors in perceptual TTC tasks (Lyon & Waag, 1995; DeLucia & Liddell, 1998; Benguigui, Broderick, & Ripoll, 2004) as well as in manual interception tasks (Sharp & Whiting, 1974; Whiting & Sharp, 1974; Teixeira, Chua, Nagelkerke, & Franks, 2006; Reid & Dessing, 2018; Menceloglu & Song, 2023). Larger errors with increasing occlusion duration are expected if we assume that any initial encoding error is extrapolated over longer periods of time. 

In sum, presentation duration and occlusion duration affect motion prediction and interception accuracy, but it is not known whether these visual factors influence performance in similar or different ways. In this study, we experimentally manipulated one factor while keeping the other constant. We expect that interception accuracy might increase continuously with increasing presentation duration (Fooken et al., 2021). However, not much is known about how manipulating occlusion duration alone might affect interceptive performance. We consider two alternatives. First, occlusion duration might have no or only small effects on interception accuracy, which would then remain largely constant across different occlusion durations. Even though unlikely, this scenario would indicate that occlusion duration does not affect target uncertainty and that therefore presentation duration is the major driver of target uncertainty. Alternatively, interception accuracy might increase with decreasing occlusion duration. This would suggest that both presentation duration and occlusion duration influence target uncertainty. 

We used a naturalistic task developed in our laboratory that requires the rapid and accurate interception of a visual target by making a three-dimensional (3D) pointing movement to the target. In contrast to previous perceptual TTC studies (e.g., Chang & Jazayeri, 2018; Villavicencio et al., 2024), this protocol allows us to investigate not only timing error but also the spatial accuracy of interceptive hand movements. Natural interception behavior, such as when catching prey or swatting a fly, must be both temporally and spatially accurate to be successful. We were interested in determining how temporal and spatial components of interceptive actions are affected by presentation and occlusion duration. 

Method

Human observers had to track and extrapolate the trajectory of a moving target before intercepting it with a rapid pointing movement. In two separate parts of the experiment, we manipulated either target presentation or occlusion durations while simultaneously recording observers’ eye and hand movements. 

Observers

We tested 10 observers (mean age ± SD, 25.8 ± 6.3 years; six females), one of them a study author; all observers participated in both study parts. Observers had normal or corrected-to-normal visual acuity, confirmed with a binocular visual acuity test using a standard Snellen chart and no history of neurological, psychiatric, or ophthalmic disease. Observers gave written informed consent before the study started and were paid $10 CAD per hour for their participation. The University of British Columbia Behavioral Research Ethics Board approved the study, and all procedures adhered to the tenets of the Declaration of Helsinki. 

Stimuli and apparatus

The target was a black disk (6.3 cd/m²), 0.35 degrees of visual angle (°) in radius, moving across a uniform gray background (270 cd/m²) toward a dark gray screen area (240 cd/m²), defined as the “hit zone.” The disk moved along the trajectory of a batted baseball presented in the fronto-parallel plane. The trajectories of the ball were simulated from the horizontal and vertical acceleration components, considering the mass of the ball, Magnus force, aerodynamic drag force, and gravitational acceleration (for details, see Fooken et al., 2016). The ball was launched at a constant angle of 35° at one of three launch speeds (13.6, 16.3, or 19.0 m/s). The simulated trajectories were then multiplied by a scaling factor, such that one meter of the simulated trajectory corresponded to 52 pixels on the screen (∼1.8°). Thus, the three simulated trajectories (Figure 1A) had initial launch speeds of 25°/s, 30°/s, and 35°/s. 

Figure 1.

 

(A) Ball trajectories defined by target speed (25°/s, 30°/s, 35°/s). (B) Trial timeline. The black disk indicates target, solid lines denote visible ball trajectory, and dotted lines indicate occluded trajectory. (C) Experiment parts in which we manipulated either presentation duration or occlusion duration while the other remained fixed. Total ball movement time was the sum of presentation duration and occlusion duration. (D) Calculation of hand spatial and timing error.

All visual stimuli were backprojected onto a translucent screen, 41.8 × 33.4 cm in size, using a PROPixx video projector (VPixx Technologies, Saint-Bruno, QC, Canada) at a frame rate of 120 Hz and a resolution of 1280 × 1024 pixels. Stimulus presentation and data acquisition were controlled by a PC (GeForce GTX 1060 graphics card; NVIDIA, Santa Clara, CA) using Psychtoolbox 3.0.18 (Brainard, 1997; Pelli, 1997; Kleiner et al., 2007) and MATLAB 9.10.0 (MathWorks, Natick, MA). Observers viewed the stimuli seated at a 44-cm distance to the screen with their head and forehead stabilized by a combined chin and forehead rest. An EyeLink 1000 tower mount eye tracker (SR Research, Kanata, ON, Canada) recorded the position of the observer's right eye at 1 kHz. A 3D Guidance trakSTAR electromagnetic hand tracker (Ascension Technology, Shelburne, VT) recorded the position of the observer's right index finger at a sampling rate of 120 Hz. Hand movements were recorded in three dimensions (x, horizontal; y, vertical; z, depth) in screen-centered coordinates. 

Procedure and task

At the start of each trial, observers had to place their right index finger at a designated start location on the desk in front of them and fixate their eyes on the stationary ball for a random period between 600 and 1000 ms. The target was always presented to the left of the screen center and moved from left to right toward the hit zone into the observer's ipsilateral reach space. After a brief presentation duration, and before it reached the hit zone, the ball was occluded from view. Observers had to extrapolate the ball trajectory and intercept it anywhere within the hit zone by hitting its estimated location on the screen with their right index finger. Upon interception, observers received visual feedback about their interception position and the position of the ball at the time of interception (Figure 1B). 

In separate parts of the experiment, we independently manipulated ball presentation or occlusion duration to investigate the effect of different sources of stimulus uncertainty (i.e., how long an object is visible or how long it is occluded) on interception performance. When manipulating presentation duration, the ball was visible for 100, 200, 300, 400, or 500 ms and occluded for 500 ms before reaching the hit zone. When manipulating occlusion duration, the ball disappeared for 100, 200, 300, 400, or 500 ms before reaching the hit zone while presentation duration was constant at 500 ms. Thus, total movement duration (presentation duration + occlusion duration) of the target until it reached the border of the hit zone was 600, 700, 800, 900, or 1000 ms in both experiment versions (Figure 1C). The target displacement between motion onset and the time the target reached the border of the hit zone (which was at a fixed position on the screen) depended on target speed and total movement duration. Thus, we shifted the target start position along the x-axis to account for the different target displacements. The manipulated occlusion duration (which was constant with varied presentation duration in experiment part A and was varied with constant presentation duration in experiment part B) was defined as the time from when the target disappeared until it entered the hit zone. However, because observers were free to choose when and where to intercept the target within the hit zone, the actual target occlusion duration (i.e., time between target disappearance and interception time) was slightly longer (mean = 149 ms; SD = 100 ms) than the manipulated occlusion duration and varied from trial to trial. 

Before starting the experiment, observers performed 12 practice trials where they were able to see the full trajectory of the target for the first six practice trials. This was to ensure that observers understood the task and the parabolic motion of the target, as well as to familiarize themselves with the setup. Both experiment parts used a 5 (presentation duration or occlusion duration) × 3 (target speed) within-subject design. Observers performed five blocks of 60 trials each, resulting in 300 trials for each experiment part. The experiment was completed in two separate sessions, one for each part, of 1 hour duration per session. The order of experimental versions was counterbalanced between observers. 

Eye and hand movement data processing and analyses

Eye and hand movement data were preprocessed and analyzed offline using custom-made routines in MATLAB. Eye position was filtered using a second-order Butterworth filter with a 15-Hz cut-off frequency. Eye velocity was derived by digital differentiation of the filtered eye position and then filtered with a second-order Butterworth filter with a cut-off frequency of 30 Hz. Saccades were defined as samples in which eye velocity exceeded a fixed velocity threshold of 30°/s for five consecutive samples. Saccade onsets and offsets were detected when the sign of acceleration changed (either from positive to negative or from negative to positive) before and after eye velocity surpassed the velocity threshold. We used the detected saccade onsets and offsets to calculate saccade probability as the likelihood of the observer making a saccade at each time point. We calculated mean eye velocity during smooth phases of the tracking response based on desaccaded, interpolated velocity data during the interval between stimulus motion onset and time of manual interception. 

We filtered the hand position using a second-order Butterworth filter (15-Hz cut-off) and upsampled it to 1 kHz (using spline interpolation) for better comparison with eye movement data. Interception position and time were detected online when the finger was less than 0.8 mm from the screen. If no interception was detected online, we determined each observer's interception time and position offline as the peak hand position in the z-dimension (depth) (Figure 2B). Note that the hand start position in the z-dimension was at approximately –20 cm and the screen position at 0 cm. Thus, the peak hand position indicated the closest distance to the screen. 

Figure 2.

 

(A) Example eye movement trace from a single observer for a single trial, showing saccades (dark blue) and smooth pursuit eye movements (light blue) for the visible (continuous black line) and occluded part of the trajectory (dashed black line). The black disk indicates the position of the target at time of interception. (B) Example 3D hand movement trace from a single observer and trial showing hand movement path, visible target trajectory, and occluded part of the target trajectory. The red “x” is the hand interception position, and the black disk is the target position at interception. (C, D) Kernel density plots of interception time for different presentation durations (C) and occlusion durations (D). Inverted triangles indicate median interception times, and vertical dashed lines indicate the times the target crossed into the hit zone.

We inspected all trials manually and excluded those in which observers blinked (less than 1.7% for each experiment part) and trials where no interception occurred (less than 0.2% for each experiment part). A within-subject z-score analysis was applied for each variable and each observer in each experiment part; data points that were more than 3 SD outside an individual's mean were flagged as outliers and excluded from further analysis. 

Our main variables of interest were the spatial and temporal components of the interception error, calculated as described in Kreyenmeier, Fooken, and Spering (2017). First, we calculated the spatial error as the difference in the distance between the two-dimensional (2D) hand interception position (labeled i in Figure 1D) and the closest point along the path of the ball trajectory (labeled t in Figure 1D). Positive values indicate that observers intercepted above the ball trajectory, and negative values indicate that observers intercepted below the ball trajectory. The same method was used to calculate the spatial error for the eye end position at time of interception. If observers made a saccade at time of interception, we used the saccade offset to calculate eye end position. 

Second, to determine the timing error, we calculated the difference in time between when observers intercepted the target and the moment the target reached the point along the trajectory closest to the interception position (labeled p in Figure 1D). Positive values refer to interceptions ahead of the target (too early), and negative values indicate interceptions behind the target (too late). 

Statistical analyses

To test how presentation duration and occlusion duration each affect interception performance accuracy, we analyzed hand spatial and timing errors. We calculated means across observers for each experimental condition and ran a repeated-measures analysis of variance (rmANOVA) with factors target speed and either occlusion duration or presentation duration. We used an alpha level of 0.05 and applied a sequential Bonferroni correction to correct for multiple comparison within multiway ANOVA (Cramer et al., 2016). 

To assess whether eye and hand movement accuracy was correlated during the interception task and whether this correlation was affected by uncertainty, we included a regression model with hand spatial error as the predicted variable and eye spatial error as the observed variable and then calculated the mean absolute error to evaluate the model. The mean absolute error measures the average of the absolute error (difference) between an observed variable and a predicted variable, with a lower mean absolute error indicating better model performance. We then performed linear mixed-effects models (LMM) with hand spatial error as the dependent variable, and eye spatial error, uncertainty (presentation duration or occlusion duration), and ball speed as fixed effects. Eye spatial error was entered as a random effect and observer was entered as a grouping variable. We used the following formula:  

\begin{eqnarray*} && \textit{Hand}\,spatial\,error\sim \textit{eye}\,\textit{spatial}\,error*target\,speed \\ && * \, uncertainty + \,\left( {1\, + \textit{eye}\,\textit{spatial}\,error \, | \, \textit{observer}} \right) \end{eqnarray*}

 

Uncertainty was defined as either presentation duration or occlusion duration in two separate LMMs. All predictor variables were centered and scaled before feeding the data into the LMM (Robinson & Schumacker, 2009). All statistical analyses were performed in R 4.2.2 (R Foundation for Statistical Computing, Vienna, Austria) using R Studio and libraries ez (Lawrence, 2016), afex (Singmann, Bolker, Westfall, Aust, & Ben-Shachar, 2023), and lme4 (Bates, Mächler, Bolker, & Walker, 2015). Statistical analyses were performed in MATLAB, Python, and JASP. 

Results

In our task, observers typically tracked the target using a combination of catch-up saccades and smooth pursuit eye movements (Figure 2A), as can be expected in the context of a fast-moving stimulus environment, where pursuit velocity errors are high (de Brouwer, Yuksel, Blohm, Missal, & Lefèvre, 2002; Schreiber, Missal, & Lefèvre, 2006; Orban de Xivry & Lefèvre, 2007; Goettker & Gegenfurtner, 2021). To intercept the target, the observer rapidly moved their hand from an initial start position on the table to the screen (Figure 2B). Across observers and conditions, hand movement duration was 543 ms on average (SD = 106 ms). Interception times depended on the total target movement duration (sum of presentation and occlusion duration). Observers intercepted earlier for shorter presentation durations (Figure 2C) or shorter occlusion durations (Figure 2D) and intercepted later for longer presentation durations or occlusion durations. For the different presentation durations (100–500 ms) in experiment part A, observers’ median interception times relative to the time that the target entered the hit zone were 187 ms, 145 ms, 109 ms, 104 ms, and 86 ms. For the different occlusion durations (100–500 ms) in experiment part B, observers’ median interception times were 179 ms, 132 ms, 100 ms, 68 ms, and 35 ms. In the following paragraphs, we describe the effects of presentation duration and occlusion duration on eye and hand movements. 

Effect of presentation duration on eye and hand movements

Across all observers, the first catch-up saccade was made on average 152 ms (SD = 33 ms) after target motion onset, reflected by the early peak in saccade probability shown in Figure 3. The timing of this early catch-up saccade was relatively constant across presentation durations. By contrast, congruent with previous studies using a similar task (Fooken et al., 2016; Kreyenmeier et al., 2022), saccades made to the interception location later in the trial occurred at increasingly longer delays with increasing presentation duration, indicated by a rightward shift of the second peak in saccade probability (light pink traces in Figure 3). Aligned with the observation that observers made later saccades with longer presentation duration, the magnitude (velocity) of smooth pursuit eye movements increased with increasing presentation duration (dark pink traces in Figure 3). These changes in saccades and pursuit with increasing presentation duration indicate that available time for information accrual improved observers’ ability to read out motion signals to guide smooth tracking eye movements. 

Figure 3.

 

Saccade probability and smooth pursuit velocity as a function of time for different presentation durations. Gray shaded areas indicate time after target occlusion.

We next assessed the effects of presentation duration on spatial and temporal interception accuracy as our main outcome variables. Figure 4A shows mean 2D hand positions at times of interception for different presentation durations for the three target speeds (different shades of red). Our results revealed a profound center bias when uncertainty was high: At short presentation durations, observers intercepted all targets close to the middle trajectory. With increasing presentation duration, observers’ ability to discriminate trajectories improved. Quantifying interception accuracy by analyzing the spatial error confirmed that observers systematically undershot targets moving at higher speeds and overshot targets moving at slower speeds (Figure 4B). This center bias was confirmed in a two-way rmANOVA, revealing a significant main effect of target speed, F(2, 18) = 77.69, p < 0.001, \(\eta_{p}^{2}\) = 0.90. In addition, spatial errors decreased with increasing presentation duration, F(4, 36) = 33.63, p < 0.001, \(\eta_{p}^{2}\) = 0.79. A significant target speed × presentation duration interaction revealed that the center bias decreased with increasing presentation duration, F(8, 72) = 3.09, p = 0.005, \(\eta_{p}^{2}\) = 0.26). Notably, even at the longest presentation duration, the center bias was not fully resolved. 

Figure 4.

 

(A) The x and y 2D hand positions at the time of interception for the different target speeds and presentation durations. (B) Hand spatial error for the different target speeds and presentation durations. (C) Hand timing error for the different target speeds and presentation durations. Horizontal dashed lines indicate zero error. Error bars in panel A indicate mean ± 1 SD for all observers. Error bars in panels B and C indicate ±1 SEM.

Target speed and presentation duration also systematically affected the interception timing error (Figure 4C). At short presentation durations, observers tended to intercept too late. At longer presentation durations, they were more accurate and tended to intercept too early for the timing error. This pattern was confirmed by a significant main effect of presentation duration in a two-way rmANOVA, F(4, 36) = 19.08, p < 0.001, \(\eta_{p}^{2}\) = 0.68. Moreover, compared with the middle trajectory, timing errors were more negative for faster targets and less negative for slower targets, indicating that observers generally underestimated the speed of faster targets and overestimated the speed of slower targets: main effect of target speed, F(2, 18) = 3.58, p = 0.049, \(\eta_{p}^{2}\) = 0.28. This center bias was stronger at short presentation durations compared with longer presentation durations. This was confirmed by a target speed × presentation duration interaction effect, F(8, 72) = 6.71, p < 0.001, \(\eta_{p}^{2}\) = 0.43. In contrast to results observed for the spatial error, the center bias in the timing error was fully resolved when presentation duration reached 400 ms. 

Together, these results show that observers’ ability to integrate target motion information for manual target interception improved with increasing presentation duration. At short presentation durations, spatial and temporal interception errors showed a striking center bias, indicating observers’ poor ability to accurately decode the true target trajectory under high visual uncertainty. Increasing presentation duration improved the observers’ ability to discriminate trajectories and helped to fully resolve the center bias in the temporal interception error. 

Effect of occlusion duration on eye and hand movements

Next, we assessed how eye and hand movements were affected when visual uncertainty was varied by manipulating the occlusion duration of the target while keeping its presentation duration constant at 500 ms. Figure 5 shows observers’ eye movements for different target occlusion durations. Pursuit velocity and the timing of the first catch-up saccade were relatively unaffected by occlusion duration. Yet, later saccades toward the interception location were strongly influenced by occlusion duration. For long occlusion durations, we observed a clear second peak in saccade probability around the time of target occlusion (see second peak in the light turquoise trace in Figure 5), identical to observations shown in the rightmost panel in Figure 3 (presentation duration, 500 ms; occlusion duration, fixed at 500 ms). The probability of these later saccades decreased with decreasing occlusion duration. Whereas observers made later saccades across all levels of uncertainty when presentation duration was manipulated (Figure 3), they might have relied less on saccades to move their eyes to the predicted interception location when occlusion duration was short, in line with previous observations that observers relied primarily on smooth pursuit eye movements when intercepting fully visible targets (Mrotek & Soechting, 2007; Schroeger, Goettker, Braun, & Gegenfurtner, 2024). 

Figure 5.

 

Saccade probability and smooth pursuit velocity as a function of time for different occlusion durations. Gray shaded areas indicate time after target occlusion.

Plotting the 2D hand interception position for each occlusion duration (Figure 6A) showed that observers accurately intercepted targets along their true trajectory across occlusion durations. Although we did not observe a strong center bias in the 2D interception position, our analysis of the spatial error revealed that a small, yet systematic, bias was present for most occlusion durations (Figure 6B). This was confirmed by a significant main effect of target speed, F(2, 18) = 19.72, p < 0.001, \(\eta_{p}^{2}\) = 0.69, in a two-way rmANOVA. Occlusion duration also affected spatial errors, F(4, 36) = 19.72, p < 0.001, \(\eta_{p}^{2}\) = 0.69, indicating that spatial accuracy improved with decreasing occlusion duration. Moreover, a significant occlusion duration × target speed interaction effect, F(8, 72) = 6.88, p < 0.001, \(\eta_{p}^{2}\) = 0.43, revealed that the center bias was strongest for long occlusion durations (high uncertainty) and decreased with decreasing occlusion duration. 

Figure 6.

 

(A) The x and y 2D hand positions at the time of interception for the different target speeds and occlusion durations. (B) Hand spatial error at the time of interception for the different target speeds and occlusion durations. (C) Hand timing error at the time of interception for the different target speeds and occlusion durations. Horizontal dashed lines indicate zero error. Error bars in panel A indicate mean ± 1 SD for all observers. Error bars in panels B and C indicate ±1 SEM.

The analysis of the timing error revealed that observers generally intercepted ahead of the targets at long occlusion durations and behind the targets at short occlusion durations: main effect of occlusion duration, F(4, 36) = 33.28, p < 0.001, \(\eta_{p}^{2}\) = 0.79 (Figure 6C). There was no significant effect of target speed, F(2, 18) = 0.46, p = 0.64, \(\eta_{p}^{2}\) = 0.05. There was, however, a small, yet significant, occlusion duration × target speed interaction effect, F(8, 72) = 2.39, p = 0.048, \(\eta_{p}^{2}\) = 0.21. These results indicate that observers might overestimate target speed at long occlusion durations and underestimate target speed at short occlusion durations. 

Eye–hand coordination across different levels of sensory uncertainty

Next, we asked whether eye and hand movements were correlated across uncertainty manipulations during this rapid-intercept task. Figure 7 shows trial-by-trial correlations between eye and hand spatial error for a single observer. Insets show individual mean absolute error for all observers. When varying presentation duration, spatial errors in eye and hand movements were strongly correlated across presentation durations, and the mean absolute error was similar across conditions (Figure 7A). This was confirmed by a linear mixed-effects model that included eye spatial error, target speed, and presentation duration as fixed effects. Eye spatial error was a significant predictor of hand spatial error, β = 0.87, F(1, 519.27) = 125.40, p < 0.001, across presentation durations and target speeds (all interaction effects p > 0.07). Neither a main effect of presentation duration, β = –0.39, F(1, 2936.23) = 1.48, p = 0.22, nor target speed, β = –0.038, F(1, 2913.85) = 0.38, p = 0.54, was significant. 

Figure 7.

 

(A) Mean absolute error for a single observer for varying presentation durations and target speeds. (B) Mean absolute error for the same observer for varying occlusion durations and target speeds. Black lines indicate the regression line across target speeds. Individual mean absolute errors for all observers are shown in the insets of each panel.

Similarly, when varying occlusion duration, spatial errors in eye and hand movements were correlated on a trial-by-trial basis (Figure 7B). In a separate linear mixed-effects model, we found that eye spatial error was also a significant predictor of hand spatial error, β = 0.73, F(1, 195.32) = 25.50, p < 0.001. Similar to presentation duration, the model prediction using mean absolute error was similar across conditions (Figure 7B). Accordingly, eye spatial error did not interact with occlusion duration or target speed (all p > 0.35). In addition, occlusion duration, β = 1.31, F(1, 2946.97) = 15.59, p < 0.001; target speed, β = 0.24, F(1, 2941.21) = 17.18, p < 0.001; and the occlusion duration × target speed interaction, β = –0.52, F(1, 2942.34) = 9.87, p = 0.002, were significant predictors of hand spatial error. Together, these findings show that eye and hand movements were strongly coupled. The strength of the eye–hand correlation varied only marginally across different levels of sensory uncertainty, indicating that eye and hand movements responded similarly to manipulations of presentation and occlusion duration. 

Discussion

In many everyday tasks, humans have to make sensorimotor decisions based on uncertain visual information. The presentation duration and occlusion duration of visual objects are two factors that are commonly used to manipulate uncertainty in laboratory studies on visual perception (Bennett, Orban de Xivry, Barnes, & Lefèvre, 2007; Spering et al., 2011; López-Moliner, Supèr, & Keil, 2013; Reid & Dessing, 2018) and visually guided action (Brenner & Smeets, 2011; Fooken et al., 2016; Fooken & Spering, 2019; Kreyenmeier et al., 2023). However, because these two factors are often manipulated simultaneously, they can be confounded. In our study, we aimed at understanding how each of these factors might contribute individually to visual uncertainty in a naturalistic interception task. We report four key findings: First, the quality of the observers’ eye movements during our rapid track-intercept task scaled with both presentation duration and occlusion duration. Long presentation durations promoted more smooth pursuit and later catch-up saccades toward the interception location. Varied occlusion duration did not affect pursuit quality but decreasing occlusion durations led to fewer saccades towards the interception location, allowing observers to track the target until interception. Second, observers’ interception positions discriminated poorly between target trajectories when presentation duration was short and regressed toward the mean target trajectory, resulting in a strong center bias. This bias was reduced but not fully resolved as presentation duration increased. Thus, presentation duration profoundly affects uncertainty and limits visually guided interception. Third, occlusion duration had a smaller effect on uncertainty than presentation duration. Observers showed only a weak center bias at long occlusion durations, and this bias was fully resolved when occlusion duration was short. Fourth, spatial errors in eye and hand movements were strongly correlated across presentation and occlusion durations, confirming known close links between eye and hand movements during manual interception. 

Sensorimotor decisions under uncertainty

The task used in this study involved a time-critical decision about when and where to intercept a visual target that was presented only briefly and then occluded. When visual information about a target is uncertain, performance accuracy decreases (e.g., Schroeger, Tolentino-Castro, Raab, & Cañal-Bruland, 2021; Brenner, de la Malla, & Smeets, 2023). Under uncertainty, sensorimotor decisions are influenced by heuristics (Tversky & Kahneman, 1974; Gigerenzer, 2021), naturalistic priors (Stocker & Simoncelli, 2006), or priors that build up over time and reflect statistical regularities of a given stimulus set (e.g., the range of target speeds) (Chang & Jazayeri, 2018). Reliance on heuristics or priors in the face of noisy sensory information often results in a regression toward the center of the range of possible stimulus features (center bias) (Petzschner et al., 2015). Congruent with these reports, we observed a strong center bias when observers intercepted a moving target after a very brief presentation duration. This center bias was strongly reduced, and interception performance improved with increasing time available to accrue information. Notably, even when presentation duration was long, a small center bias remained when observers had to extrapolate target motion throughout a long occlusion duration. This bias was only fully resolved when presentation duration was long and occlusion duration was short. 

Our finding that the center bias increased with increasing occlusion duration (while keeping presentation duration constant) may be explained by at least two possible mechanisms. At longer occlusion durations, observers have to extrapolate the trajectory of the ball over longer periods of time. If observers slightly misjudge the trajectory of the ball during the viewing period, such errors would increase with the duration over which the trajectory must be extrapolated. Additionally, observers presumably rely on their memory of the trajectory of the ball when intercepting an occluded target (Rust & Palmer, 2021; Teichmann, Edwards, & Baker, 2021). With increasing occlusion duration, memory signals may decay and lead to increased uncertainty and stronger reliance on prior experience. 

Although our task design does not allow us to isolate each mechanism, we suggest that information decay provides a valid explanation of our current findings for two reasons: First, initial misjudgments of the trajectory of the ball would predict larger interception errors but not necessarily a center bias. Instead, a center bias may reflect the use of a prior based on the different trajectories observers encounter throughout the experiment (e.g., Chang & Jazayeri, 2018; for a review, see Petzschner et al., 2015). Second, we did not observe any systematic errors at the shortest occlusion duration, indicating that observers were able to accurately judge the trajectory of the ball in principle. However, we do acknowledge that errors in this condition might be too small to be detected and only become evident when occlusion durations are longer. 

Temporal and spatial components of interception performance are differently affected by uncertainty

Extrapolating and predicting the trajectory of a moving object throughout temporary perceptual gaps is a fundamental ability that allows humans to interact with a highly dynamic and crowded visual environment (Teichmann et al., 2021). Perceptual gaps are frequently caused by eye blinks or when objects in the foreground temporarily occlude other objects in the background. Perceptual TTC tasks, in which observers press a button to indicate the time required for a moving object to pass an occluder, have been widely used to investigate the mechanisms of motion prediction (Benguigui et al., 2004; Bennett et al., 2010; Chang & Jazayeri, 2018; Battaglini & Mioni, 2019; Villavicencio et al., 2024). TTC tasks are typically restricted to the analysis of observers’ temporal accuracy and variability. Yet, most real-world tasks require both temporal and spatial motion prediction. In our interception task, observers had to extrapolate the motion of a 2D moving object, congruent with the real-world requirement of catching an object. 

Using a perceptual TTC task, Villavicencio and colleagues (2024) compared manipulations of presentation and occlusion duration on observers’ TTC estimates. Accuracy of perceptual TTC estimates was low when presentation duration was short and occlusion duration was long. These authors identified the ratio between presentation and occlusion duration as the critical factor that determines performance accuracy in TTC tasks. For ratios close to 1 (i.e., presentation and occlusion duration were equally long), performance was optimal and further increasing presentation duration while decreasing occlusion duration did not result in improved performance. Our study extended these previous findings. Comparing spatial and temporal aspects of interception accuracy, we found that both types of error behaved differently in response to manipulations of uncertainty. We showed that observers failed to accurately adjust the timing of their hand movements to match target speed when presentation duration was short. This resulted in systematic interceptions that were too late when the target speed was high and interceptions that were too early when target speed was low (i.e., timing errors showed a strong center bias) (Figure 4C). Congruent with the findings of Villavicencio and colleagues (2024), this bias was resolved when presentation duration was long (>400 ms); that is, the ratio of presentation duration to occlusion duration was ∼1. In contrast, the spatial error revealed a strong center bias that was still present even when presentation and occlusion duration were equal (see Figure 4B). This center bias on the spatial interception error was only fully resolved when presentation duration exceeded occlusion duration by a factor of 5, indicating that ratios well above 1 were necessary to minimize spatial errors. Our finding is congruent with studies showing that continuous updating and extrapolation of target motion information improves interception performance (McLeod, Reed, & Dienes, 2003; McLeod, Reed, & Dienes, 2006; Brenner & Smeets, 2018). 

In addition, when comparing TTC estimates between occluded and fully visible objects, a previous study (Menceloglu & Song, 2023) found that observers tended to overestimate target motion duration during target occlusion. We showed that observers underestimated the duration of target occlusion at long occlusions, resulting in early interceptions ahead of the target (left data points in Figure 6C), in line with our previous studies (Fooken et al., 2016; Kreyenmeier et al., 2017). At shorter occlusion durations, observers slightly overestimated occlusion duration, resulting in late interceptions (right data points in Figure 6C). These differences in findings may be due to differences in the motor task. Menceloglu and Song (2023) found that the bias in their study was stronger when participants responded by making a button press versus when they intercepted the target with a computer mouse. In our task, observers had to make a more ecologically valid, large-amplitude hand movement in 3D space, taking 543 ms on average. Future studies should investigate how different action tasks with different movement durations might modulate interception accuracy and TTC estimates. 

Eye–hand coordination during naturalistic interceptive behavior

Humans move their eyes to actively gather relevant visual information about objects in their environment with which they plan to interact (Land & MacLeod, 2000; Hayhoe, McKinney, Chajka, & Pelz, 2012; Leclercq, Blohm, & Lefèvre, 2013; de Brouwer, Flanagan, & Spering, 2021; Lavoie, Hebert, & Chapman, 2024). It has been reported that the eye leads the hand, and eye and hand movement are tightly coupled during goal-directed actions, including manual interception (Land & MacLeod, 2000; Hayhoe et al., 2012; for a review, see de Brouwer et al., 2021). When intercepting moving objects, observers naturally track the path of the target with smooth pursuit eye movements before intercepting it (Mrotek & Soechting, 2007; Schroeger et al., 2024), with different gaze strategies flexibly deployed depending on context and task (Danion & Flanagan, 2018; Coudiere & Danion, 2024; for reviews and commentaries, see de Brouwer et al., 2021; Fooken et al., 2021; Kreyenmeier & Spering, 2024). Tracking the target enhances temporal and spatial motion prediction, compared with when observers are fixating (Bennett et al., 2010; Spering et al., 2011). Accordingly, interception accuracy can be enhanced when observers track a moving target with their eyes (van Donkelaar & Lee, 1994). By varying presentation duration, we found that the duration and velocity of smooth pursuit eye movements increased with increasing presentation duration. This may suggest that observers relied on smooth pursuit eye movements to accurately read out trajectory information, in line with previous findings showing correlations between tracking accuracy and interception accuracy (Fooken et al., 2016). When targets are occluded prior to interception, observers typically make a series of predictive saccades to move their eyes to the estimated interception location. Although these predictive saccades occur several hundred milliseconds before interception, they are temporally and spatially coupled to the interceptive hand movement, congruent with similar reports in the literature (Diaz, Cooper, Rothkopf, & Hayhoe, 2013; Fooken et al., 2016; Jana, Gopal, & Murthy, 2017; Kreyenmeier et al., 2017; Li, Wang, & Cui, 2018; Binaee & Diaz, 2019; Fooken & Spering, 2020; Jana & Murthy, 2020; Kreyenmeier, Kämmer, Fooken, & Spering, 2022). Here, we showed that the spatial errors of predictive eye movements and manual interception were strongly correlated on a trial-by-trial basis. Importantly, the coordination of eye and hand movements was robust across manipulations of presentation and occlusion durations. Together, these findings indicate that interceptive eye and hand movements might share a similar predictive mechanism (Fooken et al., 2021). 

Acknowledgments

Supported by a Natural Sciences and Engineering Research Foundation of Canada Discovery Grant to MS. 

Commercial relationships: none. 

Corresponding author: Abibat A. Akande. 

Email: [email protected]. 

Address: Graduate Program in Neuroscience, University of British Columbia, Vancouver, BC V6T 1Z4, Canada.