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We constantly perform tasks within complex and dynamic environments. Some of these tasks (e.g., road crossing or playing team sports) require predicting future states of the world to decide which action to unfold and when to do so. However, it remains largely unexplored how the variability in a scene influences perceptual decision-making. Here we examine how increasing the scene variability influences our ability to make perceptual judgements and decisions by using a go/no-go decision task in a dynamic scenario mimicking a road-crossing situation with different levels of stimuli variability. Parameters of psychometric functions revealed that differences in variability do not influence judgements about the objects' time-to-contact, or the difficulty in making such judgements. Nevertheless, increases in the scene variability influence the go/no-go decisions leading people to adopt more conservative criteria. How much the criterion changes across levels of variability is well accounted for by the actual amount of variance in the scene, but the overall criterion is tightly linked to the precision or reliability with which one can estimate perceptual information about the objects' arrival time. These results suggest that the reliability on our own perceptual estimates modulate our criterion when completing perceptual decision-making tasks under different scene variabilities. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

People usually follow a moving object with their gaze if they intend to interact with it. What would happen if they did not? We recorded eye and finger movements while participants moved a cursor toward a moving target. An unpredictable delay in updating the position of the cursor on the basis of that of the invisible finger made it essential to use visual information to guide the finger's ongoing movement. Decreasing the contrast between the cursor and the background from trial to trial made it difficult to see the cursor without looking at it. In separate experiments, either participants were free to hit the target anywhere along its trajectory or they had to move along a specified path. In the two experiments, participants tracked the cursor rather than the target with their gaze on 13% and 32% of the trials, respectively. They hit fewer targets when the contrast was low or a path was imposed. Not looking at the target did not disrupt the visual guidance that was required to deal with the delays that we imposed. Our results suggest that peripheral vision can be used to guide one item to another, irrespective of which item one is looking at.

We often need to interact with targets that move along arbitrary trajectories in the 3D scene. In these situations, information of parameters like speed, time-to-contact, or motion direction is required to solve a broad class of timing tasks (e.g., shooting, or interception). There is a large body of literature addressing how we estimate different parameters when objects move both in the fronto-parallel plane and in depth. However, we do not know to which extent the timing of interceptive actions is affected when motion-in-depth (MID) is involved. Unlike previous studies that have looked at the timing of interceptive actions using constant distances and fronto-parallel motion, we here use immersive virtual reality to look at how differences in the above-mentioned variables influence timing errors in a shooting task performed in a 3D environment. Participants had to shoot at targets that moved following different angles of approach with respect to the observer when those reached designated shooting locations. We recorded the shooting time, the temporal and spatial errors and the head’s position and orientation in two conditions that differed in the interval between the shot and the interception of the target’s path. Results show a consistent change in the temporal error across approaching angles: the larger the angle, the earlier the error. Interestingly, we also found different error patterns within a given angle that depended on whether participants tracked the whole target’s trajectory or only its end-point. These differences had larger impact when the target moved in depth and are consistent with underestimating motion-in-depth in the periphery. We conclude that the strategy participants use to track the target’s trajectory interacts with MID and affects timing performance.

Catching a ball in a parabolic flight is a complex task in which the time and area of interception are strongly coupled, making interception possible for a short period. Although this makes the estimation of time-to-contact (TTC) from visual information in parabolic trajectories very useful, previous attempts to explain our precision in interceptive tasks circumvent the need to estimate TTC to guide our action. Obtaining TTC from optical variables alone in parabolic trajectories would imply very complex transformations from 2D retinal images to a 3D layout. We propose based on previous work and show by using simulations that exploiting prior distributions of gravity and known physical size makes these transformations much simpler, enabling predictive capacities from minimal early visual information. Optical information is inherently ambiguous, and therefore, it is necessary to explain how these prior distributions generate predictions. Here is where the role of prior information comes into play: it could help to interpret and calibrate visual information to yield meaningful predictions of the remaining TTC. The objective of this work is: (1) to describe the primary sources of information available to the observer in parabolic trajectories; (2) unveil how prior information can be used to disambiguate the sources of visual information within a Bayesian encoding-decoding framework; (3) show that such predictions might be robust against complex dynamic environments; and (4) indicate future lines of research to scrutinize the role of prior knowledge calibrating visual information and prediction for action control.

Obtaining reliable estimates of the time-to-contact (TTC) in a three-dimensional (3D) parabolic trajectory is still an open issue. A direct analysis of the optic flow cannot make accurate predictions for gravitationally accelerated objects. Alternatively, resorting to prior knowledge of gravity and size can provide accurate estimates of TTC in parabolic head-on trajectories, but its generalization depends on the specific geometry of the trajectory and particular moments. The aim of this work is to explore the preferred viewing windows to estimate TTC and how the available visual information affects these estimations. We designed a task in which participants, wearing an head-mounted display (HMD), had to time the moment a ball in a parabolic path returned at eye level. We used five trajectories for which accurate temporal predictions were available at different points of flight time. Our results show that our observers can predict both the trajectory of the ball and TTC based on the available visual information and previous experience with the task. However, the times at which our observers chose to gather the visual evidence did not match those in which visual information provided accurate TTC. Instead, they looked at the ball at relatively fixed temporal windows depending on the trajectory but not of TTC.

In a 2-alternative forced-choice protocol, observers judged the duration of ball motions shown on an immersive virtual-reality display as approaching in the sagittal plane along parabolic trajectories compatible with Earth gravity effects. In different trials, the ball shifted along the parabolas with one of three different laws of motion: constant tangential velocity, constant vertical velocity, or gravitational acceleration. Only the latter motion was fully consistent with Newton’s laws in the Earth gravitational field, whereas the motions with constant velocity profiles obeyed the spatio-temporal constraint of parabolic paths dictated by gravity but violated the kinematic constraints. We found that the discrimination of duration was accurate and precise for all types of motions, but the discrimination for the trajectories at constant tangential velocity was slightly but significantly more precise than that for the trajectories at gravitational acceleration or constant vertical velocity. The results are compatible with a heuristic internal representation of gravity effects that can be engaged when viewing projectiles shifting along parabolic paths compatible with Earth gravity, irrespective of the specific kinematics. Opportunistic use of a moving frame attached to the target may favour visual tracking of targets with constant tangential velocity, accounting for the slightly superior duration discrimination.

Movement execution is not always optimal. Understanding how humans evaluate their own motor decisions can give us insights into their suboptimality. Here, we investigated how humans time the action of synchronizing an arm movement with a predictable visual event and how well they can evaluate the outcome of this action. On each trial, participants had to decide when to start (reaction time) and for how long to move (movement duration) to reach a target on time. After each trial, participants judged the confidence they had that their performance on that trial was better than average. We found that participants mostly varied their reaction time, keeping the average movement duration short and relatively constant across conditions. Interestingly, confidence judgements reflected deviations from the planned reaction time and were not related to planned movement duration. In two other experiments, we replicated these results in conditions where the contribution of sensory uncertainty was reduced. In contrast to confidence judgements, when asked to make an explicit estimation of their temporal error, participants' estimates were related in a similar manner to both reaction time and movement duration. In summary, humans control the timing of their actions primarily by adjusting the delay to initiate the action, and they estimate their confidence in their action from the difference between the planned and executed movement onset. Our results highlight the critical role of the internal model for the self-evaluation of one's motor performance.

Every time we use our smartphone, tablet, or other electronic devices we are exposed to temporal delays between our actions and the sensory feedback. We can compensate for such delays by adjusting our motor commands and doing so likely requires establishing new temporal mappings between motor areas and sensory predictions. However, little is known about the neural underpinnings that would support building new temporal correspondences between different brain areas. We here address the possibility that communication through coherence, which is thought to support neural interareal communication, lies behind the neural processes accounting for how humans cope with additional delays between motor and sensory areas. We recorded EEG activity while participants intercepted moving targets while seeing a cursor that followed their hand with a delay rather than their own hand. Participants adjusted their movements to the delayed visual feedback and intercepted the target with the cursor. The EEG data shows a significant increase in coherence of beta and gamma bands between visual and motor areas during the hand on-going movement towards interception. However, when looking at differences between participants depending on the level of adaptation, only the increase in gamma band correlated with the level of temporal adaptation. We are able to describe the time course of the coherence using coupled oscillators showing that the times at which high coherence is achieved are within useful ranges to solve the task. Altogether, these results evidence the functional relevance of brain coherence in a complex task where adapting to new delays is crucial.AUTHOR SUMMARYHumans are often exposed to delays between their actions and the incoming sensory feedback caused by actions. While there have been advances in the understanding of the conditions at which temporal adaptation can occur, little is known about the neural mechanisms enabling temporal adaptation. In the present study we measure brain activity (EEG) to investigate whether communication through coherence between motor and sensory areas might be responsible for one’s ability to cope with externally imposed delays in an interception task. We show evidence that neural coherence at gamma band between visual and motor areas is related to the degree of adaptation to temporal delays.

In this article we present a temporal extension of the slow motion prior model to generate predictions regarding the temporal evolution of the contrast induced speed bias. We further tested these predictions using a novel experimental paradigm that allows us to measure the dynamic perceptual difference between stimuli through a series of manual pursuit open loop tasks. Results show good agreement with our model’s predictions. The main findings reveal that hand speed dynamics are affected by stimulus contrast in a way that is consistent with a dynamic model of motion perception that assumes a slow motion prior. The proposed model also confirms observations made in previous studies that suggest that motion bias persisted even at high contrast as a consequence of the dynamics of the slow motion prior.

Correction on the basis of previous errors is paramount to sensorimotor learning. While corrections of spatial errors have been studied extensively, little is known about corrections of previous temporal errors. We tackled this problem in different conditions involving arm movements (AM), saccadic eye movements (SM) or button presses (BP). The task was to intercept a moving target at a designated zone (i. e. no spatial error) either with the hand sliding a pen on a graphics tablet (AM), a saccade (SM) or a button press (BP) that released a cursor moving ballistically for a fixed time of 330 ms. The dependency of the final temporal error on action onset varied from "low" in AM (due to possible online corrections) to "very high" in the other conditions (i.e. open loop). The lag-1 cross-correlation between action onset and the previous temporal error were close to zero in all conditions suggesting that people minimized temporal variability of the final errors across trials. Interestingly, in conditions SM and BP, action onset did not depend on the previous temporal error. However, this dependency was clearly modulated by the movement time in the AM condition: faster movements depended less on the previous actual temporal error. An analysis using a Kalman filter confirmed that people in SM, BP and AM involving fast movements used the prediction error (i.e. intended action onset minus actual action onset) for next trial correction rather than the final target error. A closer look at the AM condition revealed that both error signals were used and that the contribution of each signal follows different patterns with movement time: as movement progresses the reliance on the prediction error decreases non-linearly and that on the final error increases linearly.

The increased reliance on electronic devices such as smartphones in our everyday life exposes us to various delays between our actions and their consequences. Whereas it is known that people can adapt to such delays, the mechanisms underlying such adaptation remain unclear. To better understand these mechanisms, the current study explored the role of eye movements in interception with delayed visual feedback. In two experiments, eye movements were recorded as participants tried to intercept a moving target with their unseen finger while receiving delayed visual feedback about their own movement. In Experiment 1, the target randomly moved in one of two different directions at one of two different velocities. The delay between the participant’s finger movement and movement of the cursor that provided feedback about the finger movements was gradually increased. Despite the delay, participants followed the target with their gaze. They were quite successful at hitting the target with the cursor. Thus, they moved their finger to a position that was ahead of where they were looking. Removing the feedback showed that participants had adapted to the delay. In Experiment 2, the target always moved in the same direction and at the same velocity, while the cursor’s delay varied across trials. Participants still always directed their gaze at the target. They adjusted their movement to the delay on each trial, often succeeding to intercept the target with the cursor. Since their gaze was always directed at the target, and they could not know the delay until the cursor started moving, participants must have been using peripheral vision of the delayed cursor to guide it to the target. Thus, people deal with delays by directing their gaze at the target and using both experience from previous trials (Experiment 1) and peripheral visual information (Experiment 2) to guide their finger in a way that will make the cursor hit the target.

In daily life, we often need to make accurate and precise movements. However, our movements do not always end up as intended. When we are consistently too late to catch a ball for example, we need to update the predictions of the temporal consequences of our motor commands. These predictions can be improved when the brain evaluates sensory error signals. This is thought to be an optimal process, in which the relative reliabilities of the error signal and the prediction determine how much of an error is updated. Perturbation paradigms are used to identify how the brain learns from errors. Temporal perturbations (delays) between sensory signals impede the multisensory integration of these signals. Adaptation to these perturbations is often incomplete. We propose that the lack of adaptation is caused by an increased measurement noise that accompanies the temporal perturbation. We use a modification of the standard Kalman filter that allows for increases in measurement uncertainty with larger delays, and verify this model with a timing task on a screen. Participants were instructed to press a button when a ball reached a vertical line. Temporal feedback was given visually (unisensory consequence) or visually and auditory (multisensory consequence). The consequence of their button press was delayed incrementally with one ms per trial. Participants learned from their errors and started pressing the button earlier, but did not adapt fully. We found that our model, a Kalman filter with non-stationary measurement variance, could account for this pattern. Measurement variance increased less for the multisensory than the unisensory condition. In addition, we simulated our model's output for other perturbation paradigms and found that it could also account for fast de-adaptation. Our paper highlights the importance of evaluating changes in measurement noise when interpreting the results motor learning tasks that include perturbation paradigms.

There is evidence that humans rely on an earth gravity (9.81 m/s²) prior for a series of tasks involving perception and action, the reason being that gravity helps predict future positions of moving objects. Eye-movements in turn are partially guided by predictions about observed motion. Thus, the question arises whether knowledge about gravity is also used to guide eye-movements: If humans rely on a representation of earth gravity for the control of eye movements, earth-gravity-congruent motion should elicit improved visual pursuit. In a pre-registered experiment, we presented participants (n = 10) with parabolic motion governed by six different gravities (−1/0.7/0.85/1/1.15/1.3 g), two initial vertical velocities and two initial horizontal velocities in a 3D environment. Participants were instructed to follow the target with their eyes. We tracked their gaze and computed the visual gain (velocity of the eyes divided by velocity of the target) as proxy for the quality of pursuit. An LMM analysis with gravity condition as fixed effect and intercepts varying per subject showed that the gain was lower for −1 g than for 1 g (by −0.13, SE = 0.005). This model was significantly better than a null model without gravity as fixed effect (p

Many tasks require synchronizing our actions with particular moments along the path of moving targets. However, it is controversial whether we base these actions on spatial or temporal information, and whether using either can enhance our performance. We addressed these questions with a coincidence timing task. A target varying in speed and motion duration approached a goal. Participants stopped the target and were rewarded according to its proximity to the goal. Results showed larger reward for responses temporally (rather than spatially) equidistant to the goal across speeds, and this pattern was promoted by longer motion durations. We used a Kalman filter to simulate time and space-based responses, where modeled speed uncertainty depended on motion duration and positional uncertainty on target speed. The comparison between simulated and observed responses revealed that a single position-tracking mechanism could account for both spatial and temporal patterns, providing a unified computational explanation.

Previous studies have shown that the angle of approach is consistently overestimated for approaching (but passing-by) objects. An explanation based on a slow-motion prior has been proposed in the past to account for this bias. The mechanism relies on the (less reliable) in-depth component of the motion being more attracted towards the slow motion prior than the (more reliable) lateral component. This hypothesis predicts that faster speeds in depth will translate into a greater bias if the perception of velocity in depth follows Weber’s law. Our approach is different than the one used in previous studies where perceived speed and direction were measured in different experiments. To test our hypothesis, we conducted an experiment in which participants estimated approaching angles via a pointing device, while at the same time comparing the speed of the approaching object with a lateral velocity reference. This way, we couple perceived speed with perceived trajectory for each approaching angle in the same trial. Our results show that the directional bias is larger for faster objects, which is consistent with motion in depth following Weber’s law. The differential biases can be accounted for by a Bayesian model that includes a slow motion prior.

Evidence suggests that humans rely on an earth gravity prior for sensory-motor tasks like catching or reaching. Even under earth-discrepant conditions, this prior biases perception and action towards assuming a gravitational downwards acceleration of 9.81 m/s2. This can be particularly detrimental in interactions with virtual environments employing earth-discrepant gravity conditions for their visual presentation. The present study thus investigates how well humans discriminate visually presented gravities and which cues they use to extract gravity from the visual scene. To this end, we employed a Two-Interval Forced-Choice Design. In Experiment 1, participants had to judge which of two presented parabolas had the higher underlying gravity. We used two initial vertical velocities, two horizontal velocities and a constant target size. Experiment 2 added a manipulation of the reliability of the target size. Experiment 1 shows that participants have generally high discrimination thresholds for visually presented gravities, with weber fractions of 13 to beyond 30 %. We identified the rate of change of the elevation angle (ẏ) and the visual angle (θ) as major cues. Experiment 2 suggests furthermore that size variability has a small influence on discrimination thresholds, while at the same time larger size variability increases reliance on ẏ and decreases reliance on θ. All in all, even though we use all available information, humans display low precision when extracting the governing gravity from a visual scene, which might further impact our capabilities of adapting to earth-discrepant gravity conditions with visual information alone.

We easily adapt to changes in the environment that involve cross-sensory discrepancies (e.g., between vision and proprioception). Adaptation can lead to changes in motor commands so that the experienced sensory consequences are appropriate for the new environment (e.g., we program a movement differently while wearing prisms that shift our visual space). In addition to these motor changes, perceptual judgments of space can also be altered (e.g., how far can I reach with my arm?). However, in previous studies that assessed perceptual judgments of space after visuomotor adaptation, the manipulation was always a planar spatial shift, whereas changes in body perception could not directly be assessed. In this study, we investigated the effects of velocity-dependent (spatiotemporal) and spatial scaling distortions of arm movements on space and body perception, taking advantage of immersive virtual reality. Exploiting the perceptual illusion of embodiment in an entire virtual body, we endowed subjects with new spatiotemporal or spatial 3D mappings between motor commands and their sensory consequences. The results imply that spatiotemporal manipulation of 2 and 4 times faster can significantly change participants’ proprioceptive judgments of a virtual object’s size without affecting the perceived body ownership, although it did affect the agency of the movements. Equivalent spatial manipulations of 11 and 22 degrees of angular offset also had a significant effect on the perceived virtual object’s size; however, the mismatched information did not affect either the sense of body ownership or agency. We conclude that adaptation to spatial and spatiotemporal distortion can similarly change our perception of space, although spatiotemporal distortions can more easily be detected.

A basic function of the visual system is to estimate the location of objects. Among other sensory inputs, the coding of an object's position involves the integration of visual motion, such as that produced by other moving patterns in the scene. Psychophysical evidence has shown that motion signals can shift, in the direction of motion, both the perceived position and the directed action to a stationary object. The neural mechanisms that sustain this effect are generally assumed to be mediated by feedback circuits from the middle temporal area to the primary visual cortex. However, evidence from neural responses is lacking. We used measures of ERPs and Granger causality analysis-a tool to predict the causal connectivity of two brain responses-to unravel the circuit by which motion influences position coding. We found that the motion-induced hand shift is tightly related to a neural delay: Participants with larger shifts of the pointing location presented slower sensory processing, in terms of longer peak latencies of the primary visual evoked potentials. We further identified early neural activity in the vicinity of the extrastriate cortex as the cause of this delay, which likely reflects the early processing of motion signals in position coding. These results suggest the rapid transfer of visual motion through feedforward circuits as a putative neural substrate in charge of the motion-induced shift in reaching.

Hitting a moving target requires that we do not miss the target when it is around the aimed position. The time available for us not to miss the target when it is at the position of interest is usually called the time window and depends on target's speed and size. These variables, among others, have been manipulated in previous studies but kept constant within the same trial or session. Here, we present results of a hitting task in which targets underwent simple harmonic motion, which is defined by a sinusoidal function. Target velocity changes continuously in this motion and so does the time window which is shorter in the centre (peak velocity) and longer at the turning points (lowest velocity) within a single trial. We studied two different conditions in which the target moved with a reliable (across trials) amplitude displacement or reliable peak velocity, respectively, and subjects were free to decide where and when to hit it. Results show that subjects made a compromise between maximum and minimum target's speed, so that they did hit the target at intermediate speed values. Interestingly, the reliability of target peak velocity (or displacement) modulated the point of interception. When target's peak velocity was more reliable, subjects intercepted the target at positions with smaller temporal windows and the reverse was true when displacement was reliable. Subjects adapted the interceptive behaviour to the underlying statistical structure of the targets. Finally, in a control condition in which the temporal window also depended on the instant size and not only on speed, subjects intercepted the target when it moved at similar speeds than when the size was constant. This finding suggests that velocity rather than the temporal window contributed more to controlling the interceptive movements.

The integration of vision and proprioception for estimating the hand’s starting location prior to a reach has been shown to depend on the modality of the target towards which the reach is planned. Here we investigated whether the processing of online feedback is also influenced by target modality. Participants made reaching movements to a target that was defined by vision, proprioception, or both, and visual feedback about the unfolding movement was either present or absent. To measure online control we used the variability across trials; we examined the course of this variability for the different target modalities and effector conditions. Our results showed that the rate of decrease in variability in the later part of the movements (an indicator of online control) was minimally influenced by effector vision when participants reached towards a proprioceptive target, whereas the rate of decrease was clearly influenced by effector vision when participants reached towards a visual target. In other words, when participants reached towards a proprioceptively defined target they relied less on visual information about the moving hand than when they reached towards a visually defined target. These results suggest that target modality influences visual processing for online control.

In the future, humans are likely to be exposed to environments with altered gravity conditions, be it only visually (Virtual and Augmented Reality), or visually and bodily (space travel). As visually and bodily perceived gravity as well as an interiorized representation of earth gravity are involved in a series of tasks, such as catching, grasping, body orientation estimation and spatial inferences, humans will need to adapt to these new gravity conditions. Performance under earth gravity discrepant conditions has been shown to be relatively poor, and few studies conducted in gravity adaptation are rather discouraging. Especially in VR on earth, conflicts between bodily and visual gravity cues seem to make a full adaptation to visually perceived earth-discrepant gravities nearly impossible, and even in space, when visual and bodily cues are congruent, adaptation is extremely slow. We invoke a Bayesian framework for gravity related perceptual processes, in which earth gravity holds the status of a so called “strong prior”. As other strong priors, the gravity prior has developed through years and years of experience in an earth gravity environment. For this reason, the reliability of this representation is extremely high and overrules any sensory information to its contrary. While also other factors such as the multisensory nature of gravity perception need to be taken into account, we present the strong prior account as a unifying explanation for empirical results in gravity perception and adaptation to earth-discrepant gravities.

International audience; Previous studies have shown that performing a motor action toward a target decreases the perceptual asynchrony observed in a temporal order judgment (TOJ) of a change in the target's visual attributes. We examined the temporal limit of this effect and whether this temporal limit can be extended through sensorimotor adaptation. Participants performed a TOJ task related to changes of the position and color of a visual stimulus in a perceptual and a motor task. A fixed change (color or position) occurred 250 or 500 ms following an auditory cue (perceptual task) or the end of a manual reaching action (motor task), whereas the variable change (position or color) occurred randomly within a time window of ±200 ms locked to the fixed change. The points of subjective simultaneity (PSSs) revealed that performing a voluntary action decreased the temporal asynchrony observed in the perceptual task, but only in the 250-ms delay condition. In Experiment 2, the fixed change occurred 1 s after either an auditory cue or the end of a manual reaching action, and the variable change occurred either simultaneously (new sensorimotor contingencies, 60 % of trials) or within a time window of ±200 ms (40 % of trials). The PSSs revealed that temporal asynchrony decreased in the motor task, but only after adaptation to the 1-s delay. Taken together, these data show that voluntary motor action affects the temporal binding of visual attributes for a period of less than 500 ms after the end of the action. Sensorimotor adaptation can nevertheless extend this time interval, at least up to 1 s.

The different sources of information that can be used to estimate time-to-contact may have different degrees of reliability across time. For example, after a given presentation or display time, an absolute change of angular size can be more reliable than the corresponding estimation of the rate of angular expansion (e.g. motion information). One could then expect systematic biases in the observer’s responses for different times of stimulus exposure. In one experiment, observers judged whether approaching objects arrived at the point of observation before or after a reference beep (1.2 s) under monocular, and binocular plus monocular vision. Five display times from 0.1 to 0.9 s were used. Unlike monocular viewing, where accuracy increased monotonically with display time, an interesting non-linearity occurred for objects with small size when binocular information was available. Accuracy reached maximum values for small objects with only 0.3 s of vision with stereopsis. This accuracy, however, dropped significantly after 0.4 s of exposure and increased again linearly with time. This is consistent with subjects switching from using binocular information to using monocular motion information when it started to become more reliable. We also explored whether monocular cues were combined differently across time by fitting a model that relates visual angle to its rate of expansion. Results show that subjects relied more on angular motion information (i.e. rate of expansion) with presentation time but interrupting this motion integration process led to a loss of accuracy in time-to-contact judgments.

quickpsy is a package to parametrically fit psychometric functions. In comparison with previous R packages, quickpsy was build to easily fit and plot data for multiple groups. Here, we describe the standard parametric model used to fit psychometric functions and the standard estimation of its parameters using maximum likelihood. We also provide examples of usage of quickpsy, including how allowing the lapse rate to vary can sometimes eliminate the bias in parameter estimation, but not in general. Finally, we describe some implementation details, such as how to avoid the problems associated to round-off errors in the maximisation of the likelihood or the use of closures and non-standard evaluation functions.