Intercepting free falling objects: better use Occam's razor than internalize Newton's law

Embeddedness of Earth's gravity in visual perception

Falling objects are commonplace in daily life, requiring precise perceptual judgments for interception and avoidance. We argue that human judgments of projectile motion arise from the interplay between sensory information and predictions constrained by Newtonian mechanics. Our study investigates how individuals perceive falling objects under various gravitational conditions, aiming to understand the role of internalized gravity in visual perception. Through meticulously controlling the available information, we demonstrated that these phenomena cannot be explained solely by simple heuristics nor representational momentum. Instead, we found that the perceptual judgments of humans (n = 11, 13, 14, and 11, respectively, in Experiments 1, 2, 3, and 4) are influenced by a combination of sensory information and gravity predictions, highlighting the role of internalized physical constraints in the perception of projectile motion.

Grounding Intuitive Physics in Perceptual Experience

This review article explores the foundation of laypeople's understanding of the physical world rooted in perceptual experience. Beginning with a concise historical overview of the study of intuitive physics, the article presents the hypothesis that laypeople possess accurate internalized representations of physical laws. A key aspect of this hypothesis is the contention that correct representations of physical laws emerge in ecological experimental conditions, where the scenario being examined resembles everyday life experiences. The article critically examines empirical evidence both supporting and challenging this claim, revealing that despite everyday-life-like conditions, fundamental misconceptions often persist. Many of these misconceptions can be attributed to a domain-general heuristic that arises from the overgeneralization of perceptual-motor experiences with physical objects. To conclude, the article delves into ongoing controversies and highlights promising future avenues in the field of intuitive physics, including action-judgment dissociations, insights from developmental psychology, and computational models integrating artificial intelligence.

Evidence for an internal model of friction when controlling kinetic energy at impact to slide an object along a surface toward a target

Although the role of an internal model of gravity for the predictive control of the upper limbs is quite well established, evidence is lacking regarding an internal model of friction. In this study, 33 male and female human participants performed a striking movement (with the index finger) to slide a plastic cube-like object to a given target distance. The surface material (aluminum or balsa wood) on which the object slides, the surface slope (-10°, 0, or +10°) and the target distance (25 cm or 50 cm) varied across conditions, with ten successive trials in each condition. Analysis of the object speed at impact and spatial error suggests that: 1) the participants chose to impart a similar speed to the object in the first trial regardless of the surface material to facilitate the estimation of the coefficient of friction; 2) the movement is parameterized across repetitions to reduce spatial error; 3) an internal model of friction can be generalized when the slope changes. Biomechanical analysis showed interindividual variability in the recruitment of the upper limb segments and in the adjustment of finger speed at impact in order to transmit the kinetic energy required to slide the object to the target distance. In short, we provide evidence that the brain builds an internal model of friction that makes it possible to parametrically control a striking movement in order to regulate the amount of kinetic energy required to impart the appropriate initial speed to the object.

Flexible prediction of opponent motion with internal representation in interception behavior

Skilled interception behavior often relies on accurate predictions of external objects because of a large delay in our sensorimotor systems. To deal with the sensorimotor delay, the brain predicts future states of the target based on the current state available, but it is still debated whether internal representations acquired from prior experience are used as well. Here we estimated the predictive manner by analyzing the response behavior of a pursuer to a sudden directional change of the evasive target, providing strong evidence that prediction of target motion by the pursuer was incompatible with a linear extrapolation based solely on the current state of the target. Moreover, using neural network models, we validated that nonlinear extrapolation as estimated was computationally feasible and useful even against unknown opponents. These results support the use of internal representations in predicting target motion, suggesting the usefulness and versatility of predicting external object motion through internal representations.

Gravity and Known Size Calibrate Visual Information to Time Parabolic Trajectories

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.

Slacklining: A narrative review on the origins, neuromechanical models and therapeutic use

Slacklining, the neuromechanical action of balance retention on a tightened band, is achieved through self-learned strategies combining dynamic stability with optimal energy expenditure. Published slacklining literature is recent and limited, including for neuromechanical control strategy models. This paper explores slacklining's definitions and origins to provide background that facilitates understanding its evolution and progressive incorporation into both prehabilitation and rehabilitation. Existing explanatory slacklining models are considered, their application to balance and stability, and knowledge-gaps highlighted. Current slacklining models predominantly derive from human quiet-standing and frontal plane movement on stable surfaces. These provide a multi-tiered context of the unique and complex neuro-motoric requirements for slacklining's multiple applications, but are not sufficiently comprehensive. This consequently leaves an incomplete understanding of how slacklining is achieved, in relation to multi-directional instability and complex multi-dimensional human movement and behavior. This paper highlights the knowledge-gaps and sets a foundation for the required explanatory control mechanisms that evolve and expand a more detailed model of multi-dimensional slacklining and human functional movement. Such a model facilitates a more complete understanding of existing performance and rehabilitation applications that opens the potential for future applications into broader areas of movement in diverse fields including prostheses, automation and machine-learning related to movement phenotypes.

Intuitive physics of gravitational motion as shown by perceptual judgment and prediction-motion tasks

In Experiment 1, we explored participants' perceptual knowledge of vertical fall by presenting them with virtually simulated polystyrene or wooden spheres falling to the ground from about two meters high. Participants rated the perceived naturalness of the motion. Besides the implied mass of the sphere, we manipulated the motion pattern (i.e., uniform acceleration vs. uniform velocity), and the magnitude of acceleration or velocity. Results show that relatively low values of acceleration or velocity were judged as natural for the polystyrene sphere, whereas relatively high values of acceleration or velocity were judged as natural for the wooden sphere. In Experiment 2, the same stimuli of Experiment 1 were used, but the sphere disappeared behind an invisible occluder at some point of its trajectory. Participants were asked to predict the time-to-contact (TTC) of the sphere with the ground by pressing a key at the exact time of impact of the lower edge of the sphere with the floor of the room. Results show that the estimated TTC for the simulated wooden sphere was slightly but consistently smaller than the estimated TTC for the simulated polystyrene sphere. The influence of the implied mass on participants' responses might be the manifestation of two processes, namely an explicit 'heavy-fast, light-slow' heuristic, and/or an implicit, automatic association between mass and falling speed.

Continuously updating one’s predictions underlies successful interception

This paper reviews our understanding of the interception of moving objects. Interception is a demanding task that requires both spatial and temporal precision. The required precision must be achieved on the basis of imprecise and sometimes biased sensory information. We argue that people make precise interceptive movements by continuously adjusting their movements. Initial estimates of how the movement should progress can be quite inaccurate. As the movement evolves, the estimate of how the rest of the movement should progress gradually becomes more reliable as prediction is replaced by sensory information about the progress of the movement. The improvement is particularly important when things do not progress as anticipated. Constantly adjusting one’s estimate of how the movement should progress combines the opportunity to move in a way that one anticipates will best meet the task demands with correcting for any errors in such anticipation. The fact that the ongoing movement might have to be adjusted can be considered when determining how to move, and any systematic anticipation errors can be corrected on the basis of the outcome of earlier actions.

The use of visual cues in gravity judgements on parabolic motion

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.

Gravity as a Strong Prior: Implications for Perception and Action

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.

Hand interception of occluded motion in humans: a test of model-based vs. on-line control

Two control schemes have been hypothesized for the manual interception of fast visual targets. In the model-free on-line control, extrapolation of target motion is based on continuous visual information, without resorting to physical models. In the model-based control, instead, a prior model of target motion predicts the future spatiotemporal trajectory. To distinguish between the two hypotheses in the case of projectile motion, we asked participants to hit a ball that rolled down an incline at 0.2 g and then fell in air at 1 g along a parabola. By varying starting position, ball velocity and trajectory differed between trials. Motion on the incline was always visible, whereas parabolic motion was either visible or occluded. We found that participants were equally successful at hitting the falling ball in both visible and occluded conditions. Moreover, in different trials the intersection points were distributed along the parabolic trajectories of the ball, indicating that subjects were able to extrapolate an extended segment of the target trajectory. Remarkably, this trend was observed even at the very first repetition of movements. These results are consistent with the hypothesis of model-based control, but not with on-line control. Indeed, ball path and speed during the occlusion could not be extrapolated solely from the kinematic information obtained during the preceding visible phase. The only way to extrapolate ball motion correctly during the occlusion was to assume that the ball would fall under gravity and air drag when hidden from view. Such an assumption had to be derived from prior experience.

Fourier decomposition of spatial localization errors reveals an idiotropic dominance of an internal model of gravity

Given its conspicuous nature, gravity has been acknowledged by several research lines as a prime factor in structuring the spatial perception of one's environment. One such line of enquiry has focused on errors in spatial localization aimed at the vanishing location of moving objects - it has been systematically reported that humans mislocalize spatial positions forward, in the direction of motion (representational momentum) and downward in the direction of gravity (representational gravity). Moreover, spatial localization errors were found to evolve dynamically with time in a pattern congruent with an anticipated trajectory (representational trajectory). The present study attempts to ascertain the degree to which vestibular information plays a role in these phenomena. Human observers performed a spatial localization task while tilted to varying degrees and referring to the vanishing locations of targets moving along several directions. A Fourier decomposition of the obtained spatial localization errors revealed that although spatial errors were increased "downward" mainly along the body's longitudinal axis (idiotropic dominance), the degree of misalignment between the latter and physical gravity modulated the time course of the localization responses. This pattern is surmised to reflect increased uncertainty about the internal model when faced with conflicting cues regarding the perceived "downward" direction.

On-line and model-based approaches to the visual control of action

Two general approaches to the visual control of action have emerged in last few decades, known as the on-line and model-based approaches. The key difference between them is whether action is controlled by current visual information or on the basis of an internal world model. In this paper, we evaluate three hypotheses: strong on-line control, strong model-based control, and a hybrid solution that combines on-line control with weak off-line strategies. We review experimental research on the control of locomotion and manual actions, which indicates that (a) an internal world model is neither sufficient nor necessary to control action at normal levels of performance; (b) current visual information is necessary and sufficient to control action at normal levels; and (c) under certain conditions (e.g. occlusion) action is controlled by less accurate, simple strategies such as heuristics, visual-motor mappings, or spatial memory. We conclude that the strong model-based hypothesis is not sustainable. Action is normally controlled on-line when current information is available, consistent with the strong on-line control hypothesis. In exceptional circumstances, action is controlled by weak, context-specific, off-line strategies. This hybrid solution is comprehensive, parsimonious, and able to account for a variety of tasks under a range of visual conditions.

Synergies between optical and physical variables in intercepting parabolic targets

Interception requires precise estimation of time-to-contact (TTC) information. A long-standing view posits that all relevant information for extracting TTC is available in the angular variables, which result from the projection of distal objects onto the retina. The different timing models rooted in this tradition have consequently relied on combining visual angle and its rate of expansion in different ways with tau being the most well-known solution for TTC. The generalization of these models to timing parabolic trajectories is not straightforward. For example, these different combinations rely on isotropic expansion and usually assume first-order information only, neglecting acceleration. As a consequence no optical formulations have been put forward so far to specify TTC of parabolic targets with enough accuracy. It is only recently that context-dependent physical variables have been shown to play an important role in TTC estimation. Known physical size and gravity can adequately explain observed data of linear and free-falling trajectories, respectively. Yet, a full timing model for specifying parabolic TTC has remained elusive. We here derive two formulations that specify TTC for parabolic ball trajectories. The first specification extends previous models in which known size is combined with thresholding visual angle or its rate of expansion to the case of fly balls. To efficiently use this model, observers need to recover the 3D radial velocity component of the trajectory which conveys the isotropic expansion. The second one uses knowledge of size and gravity combined with ball visual angle and elevation angle. Taking into account the noise due to sensory measurements, we simulate the expected performance of these models in terms of accuracy and precision. While the model that combines expansion information and size knowledge is more efficient during the late trajectory, the second one is shown to be efficient along all the flight.

Catching what we can't see: manual interception of occluded fly-ball trajectories

Control of interceptive actions may involve fine interplay between feedback-based and predictive mechanisms. These processes rely heavily on target motion information available when the target is visible. However, short-term visual memory signals as well as implicit knowledge about the environment may also contribute to elaborate a predictive representation of the target trajectory, especially when visual feedback is partially unavailable because other objects occlude the visual target. To determine how different processes and information sources are integrated in the control of the interceptive action, we manipulated a computer-generated visual environment representing a baseball game. Twenty-four subjects intercepted fly-ball trajectories by moving a mouse cursor and by indicating the interception with a button press. In two separate sessions, fly-ball trajectories were either fully visible or occluded for 750, 1000 or 1250 ms before ball landing. Natural ball motion was perturbed during the descending trajectory with effects of either weightlessness (0 g) or increased gravity (2 g) at times such that, for occluded trajectories, 500 ms of perturbed motion were visible before ball disappearance. To examine the contribution of previous visual experience with the perturbed trajectories to the interception of invisible targets, the order of visible and occluded sessions was permuted among subjects. Under these experimental conditions, we showed that, with fully visible targets, subjects combined servo-control and predictive strategies. Instead, when intercepting occluded targets, subjects relied mostly on predictive mechanisms based, however, on different type of information depending on previous visual experience. In fact, subjects without prior experience of the perturbed trajectories showed interceptive errors consistent with predictive estimates of the ball trajectory based on a-priori knowledge of gravity. Conversely, the interceptive responses of subjects previously exposed to fully visible trajectories were compatible with the fact that implicit knowledge of the perturbed motion was also taken into account for the extrapolation of occluded trajectories.

The Effect of Body Posture on Long-Range Time-to-Contact Estimation

On Earth, gravity accelerates freely moving objects downward, whereas upward-moving objects are being decelerated. Do humans take internalised knowledge of gravity into account when estimating time-to-contact (TTC, the time remaining before the moving object reaches the observer)? To answer this question, we created a motion-prediction task in which participants saw the initial part of an object's trajectory moving on a collision course prior to an occlusion. Observers had to judge when the object would make contact with them. The visual scene was presented with a head-mounted display. Participants lay either supine (looking up) or prone (looking down), suggestive of the ball either rising up or falling down toward them. Results showed that body posture had a significant effect on time-to-contact estimation, but only when occlusion times were long (2.5 s). The effect was also rather small. This lack of immediacy in the posture effect suggests that TTC estimation is initially robust toward the effect of gravity, which comes to bear only as more time is allowed for post-processing of the visual information.

Timing of anticipatory muscle tensing control: responses before and after expected impact

It is widely accepted that human motor control is anticipatory in nature. Previous studies have used electromyography (EMG) to examine muscle responses to falling objects and identified anticipatory muscle tensing (AMT) as a spike in activation that occurs prior to object impact. Some studies have suggested that humans use an internal model of gravity to mediate precisely timed AMT responses. The present study further examines predictive motor control through the analysis of AMT during an object catching task. For some trials, participants watched an object falling toward the hand; for other trials, their eyes were closed. For some trials, the object fell downward and impacted the hand; for other randomly selected trials, the object abruptly stopped 12 cm above the hand, enabling an assessment of the effect of impact anticipation independent of the reflexive tactile response associated with an actual impact. In Experiment 1, AMT did not shift for approximately 113 ms after the abrupt stop of the ball. In Experiment 2, we randomly varied the start height of the object and found well-timed AMT with a 129-ms lag time. A control system based on simple memory for fall time duration cannot explain these findings. We argue that an AMT control system with a lag time of approximately 121 ms could not perform with human levels of accuracy without accounting for the acceleration of downward moving objects.

Egocentric and allocentric reference frames for catching a falling object

When programming movement, one must account for gravitational acceleration. This is particularly important when catching a falling object because the task requires a precise estimate of time-to-contact. Knowledge of gravity's effects is intimately linked to our definition of 'up' and 'down'. Both directions can be described in an allocentric reference frame, based on visual and/or gravitational cues, or in an egocentric reference frame in which the body axis is taken as vertical. To test which frame humans use to predict gravity's effect, we asked participants to intercept virtual balls approaching from above or below with artificially controlled acceleration that could be congruent or not with gravity. To dissociate between these frames, subjects were seated upright (trunk parallel to gravity) or lying down (body axis orthogonal to the gravitational axis). We report data in line with the use of an allocentric reference frame and discuss its relevance depending on available gravity-related cues.

Internal models and prediction of visual gravitational motion

Baurès et al. [Baurès, R., Benguigui, N., Amorim, M.-A., & Siegler, I. A. (2007). Intercepting free falling objects: Better use Occam's razor than internalize Newton's law. Vision Research, 47, 2982-2991] rejected the hypothesis that free-falling objects are intercepted using a predictive model of gravity. They argued instead for "a continuous guide for action timing" based on visual information updated till target capture. Here we show that their arguments are flawed, because they fail to consider the impact of sensori-motor delays on interception behaviour and the need for neural compensation of such delays. When intercepting a free-falling object, the delays can be overcome by a predictive model of the effects of gravity on target motion.