Signal Integration in Human Visual Speed Perception

Conflicts between short- and long-term experiences affect visual perception through modulating sensory or motor response systems: Evidence from Bayesian inference models

The independent effects of short- and long-term experiences on visual perception have been discussed for decades. However, no study has investigated whether and how these experiences simultaneously affect our visual perception. To address this question, we asked participants to estimate their self-motion directions (i.e., headings) simulated from optic flow, in which a long-term experience learned in everyday life (i.e., straight-forward motion being more common than lateral motion) plays an important role. The headings were selected from three distributions that resembled a peak, a hill, and a flat line, creating different short-term experiences. Importantly, the proportions of headings deviating from the straight-forward motion gradually increased in the peak, hill, and flat distributions, leading to a greater conflict between long- and short-term experiences. The results showed that participants biased their heading estimates towards the straight-ahead direction and previously seen headings, which increased with the growing experience conflict. This suggests that both long- and short-term experiences simultaneously affect visual perception. Finally, we developed two Bayesian models (Model 1 vs. Model 2) based on two assumptions that the experience conflict altered the likelihood distribution of sensory representation or the motor response system. The results showed that both models accurately predicted participants' estimation biases. However, Model 1 predicted a higher variance of serial dependence compared to Model 2, while Model 2 predicted a higher variance of the bias towards the straight-ahead direction compared to Model 1. This suggests that the experience conflict can influence visual perception by affecting both sensory and motor response systems. Taken together, the current study systematically revealed the effects of long- and short-term experiences on visual perception and the underlying Bayesian processing mechanisms.

Serial dependence bias can predict the overall estimation error in visual perception

Although visual feature estimations are accurate and precise, overall estimation errors (i.e., the difference between estimates and actual values) tend to show systematic patterns. For example, estimates of orientations are systematically biased away from horizontal and vertical orientations, showing an oblique illusion. Additionally, many recent studies have demonstrated that estimations of current visual features are systematically biased toward previously seen features, showing a serial dependence. However, no study examined whether the overall estimation errors were correlated with the serial dependence bias. To address this question, we enrolled three groups of participants to estimate orientation, motion speed, and point-light-walker direction. The results showed that the serial dependence bias explained over 20% of overall estimation errors in the three tasks, indicating that we could use the serial dependence bias to predict the overall estimation errors. The current study first demonstrated that the serial dependence bias was not independent from the overall estimation errors. This finding could inspire researchers to investigate the neural bases underlying the visual feature estimation and serial dependence.

The Associations between Results in Different Domains of Cognitive and Psychomotor Abilities Measured in Medical Students

We aimed to investigate the associations between intelligence quotient test scores obtained using the Raven's Advanced Progressive Matrices (APM) and psychomotor testing using the Complex Reactionmeter Drenovac (CRD) test battery, while taking into account previous theoretical approaches recognizing intelligent behavior as the cumulative result of a general biological speed factor reflected in the reaction time for perceptual detections and motor decisions. A total of 224 medical students at the University of Split School of Medicine were recruited. Their IQ scores were assessed using Raven's APM, while the computerized tests of CRD-series were used for testing the reaction time of perception to visual stimulus (CRD311), psychomotor limbs coordination task (CRD411), and solving simple arithmetic operations (CRD11). The total test-solving (TTST) and the minimum single-task-solving (MinT) times were analyzed. On the CRD11 test, task-solving times were shorter in students with higher APM scores (r = -0.48 for TTST and r = -0.44 for MinT; p < 0.001 for both). Negative associations between task-solving times and APM scores were reported on CRD311 (r = -0.30 for TTST and r = -0.33 for MinT, p < 0.001 for both). Negative associations between task-solving times in CRD411 and APM scores (r = -0.40 for TTST and r = -0.30 for MinT, p < 0.001 for both) were found. Faster reaction time in psychomotor limbs coordination tasks, the reaction time of perception to visual stimulus, and the reaction time of solving simple arithmetic operations were associated with a higher APM score in medical students, indicating the importance of mental speed in intelligence test performance. However, executive system functions, such as attention, planning, and goal weighting, might also impact cognitive abilities and should be considered in future research.

Perceived speed at low luminance: Lights out for the Bayesian observer?

To account for perceptual bias, Bayesian models use the precision of early sensory measurements to weight the influence of prior expectations. As precision decreases, prior expectations start to dominate. Important examples come from motion perception, where the slow-motion prior has been used to explain a variety of motion illusions in vision, hearing, and touch, many of which correlate appropriately with threshold measures of underlying precision. However, the Bayesian account seems defeated by the finding that moving objects appear faster in the dark, because most motion thresholds are worse at low luminance. Here we show this is not the case for speed discrimination. Our results show that performance improves at low light levels by virtue of a perceived contrast cue that is more salient in the dark. With this cue removed, discrimination becomes independent of luminance. However, we found perceived speed still increased in the dark for the same observers, and by the same amount. A possible interpretation is that motion processing is therefore not Bayesian, because our findings challenge a key assumption these models make, namely that the accuracy of early sensory measurements is independent of basic stimulus properties like luminance. However, a final experiment restored Bayesian behaviour by adding external noise, making discrimination worse and slowing perceived speed down. Our findings therefore suggest that motion is processed in a Bayesian fashion but based on noisy sensory measurements that also vary in accuracy.

Calibrating Vision: Concepts and Questions

The idea that visual coding and perception are shaped by experience and adjust to changes in the environment or the observer is universally recognized as a cornerstone of visual processing, yet the functions and processes mediating these calibrations remain in many ways poorly understood. In this article we review a number of facets and issues surrounding the general notion of calibration, with a focus on plasticity within the encoding and representational stages of visual processing. These include how many types of calibrations there are - and how we decide; how plasticity for encoding is intertwined with other principles of sensory coding; how it is instantiated at the level of the dynamic networks mediating vision; how it varies with development or between individuals; and the factors that may limit the form or degree of the adjustments. Our goal is to give a small glimpse of an enormous and fundamental dimension of vision, and to point to some of the unresolved questions in our understanding of how and why ongoing calibrations are a pervasive and essential element of vision.

Prior Expectations in Visual Speed Perception Predict Encoding Characteristics of Neurons in Area MT

Bayesian inference provides an elegant theoretical framework for understanding the characteristic biases and discrimination thresholds in visual speed perception. However, the framework is difficult to validate because of its flexibility and the fact that suitable constraints on the structure of the sensory uncertainty have been missing. Here, we demonstrate that a Bayesian observer model constrained by efficient coding not only well explains human visual speed perception but also provides an accurate quantitative account of the tuning characteristics of neurons known for representing visual speed. Specifically, we found that the population coding accuracy for visual speed in area MT ("neural prior") is precisely predicted by the power-law, slow-speed prior extracted from fitting the Bayesian observer model to psychophysical data ("behavioral prior") to the point that the two priors are indistinguishable in a cross-validation model comparison. Our results demonstrate a quantitative validation of the Bayesian observer model constrained by efficient coding at both the behavioral and neural levels.SIGNIFICANCE STATEMENT Statistical regularities of the environment play an important role in shaping both neural representations and perceptual behavior. Most previous work addressed these two aspects independently. Here we present a quantitative validation of a theoretical framework that makes joint predictions for neural coding and behavior, based on the assumption that neural representations of sensory information are efficient but also optimally used in generating a percept. Specifically, we demonstrate that the neural tuning characteristics for visual speed in brain area MT are precisely predicted by the statistical prior expectations extracted from psychophysical data. As such, our results provide a normative link between perceptual behavior and the neural representation of sensory information in the brain.

A unifying Bayesian framework accounting for spatiotemporal interferences with a deceleration tendency

Spatial and temporal levels of information processing interfere with each other. The Kappa effect is a well-known spatiotemporal interference in which the estimated time between two lights increases as the distance between them increases, showing a deceleration tendency. A classical model attributes this interference to constant speeds and predicts a linear relation, whereas a slowness model attributes the interference to slow speeds and proposes that the tendency is due to the uncertainty of stimuli locations. This study integrated a unifying Bayesian framework with the classical model and argued that this tendency is the result of the Weber-Fechner law. This hypothesis was tested via two time discrimination tasks that manipulated the uncertainty of stimuli locations and the distance between stimuli. Experiment 1 showed that the estimated time was not modulated by the uncertainty of the stimuli locations. Experiment 2 revealed that the behavioral predictions made by the Bayesian model on logarithmic scales were more accurate than those made by the linear model. Our results suggest that the deceleration tendency in the Kappa effect is the result of the Weber-Fechner law.

Adaptation to one perceived motion direction can generate multiple velocity aftereffects

Sensory adaptation is a useful tool to identify the links between perceptual effects and neural mechanisms. Even though motion adaptation is one of the earliest and most documented aftereffects, few studies have investigated the perception of direction and speed of the aftereffect at the same time, that is the perceived velocity. Using a novel experimental paradigm, we simultaneously recorded the perceived direction and speed of leftward or rightward moving random dots before and after adaptation. For the adapting stimulus, we chose a horizontally-oriented broadband grating moving upward behind a circular aperture. Because of the aperture problem, the interpretation of this stimulus is ambiguous, being consistent with multiple velocities, and yet it is systematically perceived as moving at a single direction and speed. Here we ask whether the visual system adapts to the multiple velocities of the adaptor or to just the single perceived velocity. Our results show a strong repulsion aftereffect, away from the adapting velocity (downward and slower), that increases gradually for faster test stimuli as long as these stimuli include some velocities that match some of the ambiguous ones of the adaptor. In summary, the visual system seems to adapt to the multiple velocities of an ambiguous stimulus even though a single velocity is perceived. Our findings can be well described by a computational model that assumes a joint encoding of direction and speed and that includes an extended adaptation component that can represent all the possible velocities of the ambiguous stimulus.

Image-Computable Ideal Observers for Tasks with Natural Stimuli

An ideal observer is a theoretical model observer that performs a specific sensory-perceptual task optimally, making the best possible use of the available information given physical and biological constraints. An image-computable ideal observer (pixels in, estimates out) is a particularly powerful type of ideal observer that explicitly models the flow of visual information from the stimulus-encoding process to the eventual decoding of a sensory-perceptual estimate. Image-computable ideal observer analyses underlie some of the most important results in vision science. However, most of what we know from ideal observers about visual processing and performance derives from relatively simple tasks and relatively simple stimuli. This review describes recent efforts to develop image-computable ideal observers for a range of tasks with natural stimuli and shows how these observers can be used to predict and understand perceptual and neurophysiological performance. The reviewed results establish principled links among models of neural coding, computational methods for dimensionality reduction, and sensory-perceptual performance in tasks with natural stimuli.

Interaction between motion scales: When performance in motion discrimination is worse for a compound stimulus than for its integrating components

Motion direction discrimination becomes impaired when combinations of drifting high spatial frequency (HSF) and static low spatial frequency (LSF) patterns are merged into a compound stimulus. Such impairment has been suggested to occur due to an interaction between motion sensors tuned to coarse and fine scale spatial patterns. This interaction is modulated by different stimulus parameters like temporal frequency, size, the spectral components mixed, and their relative contrast. The present research precisely aims to explore in a deeper way the interaction's dependency upon the spatial frequency and the relative contrast of the components when both move coherently. Two experiments were therefore performed measuring duration thresholds (Experiment 1) and proportion of correct responses (Experiment 2) in a motion direction discrimination task. Stimuli were vertical Gabor patches of 4 deg diameter horizontally drifting with a speed of 2 deg/sec. Simple LSF and HSF stimuli as well as complex stimuli where both components moved coherently (LSFm + HSFm) were used. These were grouped in the following LSF and HSF pairs: 0.25-0.75, 0.5-1.5, 1-3 and 2-6 c/deg. Each component had a Michelson contrast of 28% or 7%, giving rise to different relative contrast combinations. Most interestingly, the results show a decrease in performance for complex stimuli with respect to each of their simple components when the LSF component has a lower contrast than the HSF one. The decrease depends on the particular spatial frequencies mixed in a stimulus. Further knowledge about the inhibitory mechanism is thus provided, revealing its joint dependency upon contrast and spatial frequency.

Predicting the Partition of Behavioral Variability in Speed Perception with Naturalistic Stimuli

A core goal of visual neuroscience is to predict human perceptual performance from natural signals. Performance in any natural task can be limited by at least three sources of uncertainty: stimulus variability, internal noise, and suboptimal computations. Determining the relative importance of these factors has been a focus of interest for decades but requires methods for predicting the fundamental limits imposed by stimulus variability on sensory-perceptual precision. Most successes have been limited to simple stimuli and simple tasks. But perception science ultimately aims to understand how vision works with natural stimuli. Successes in this domain have proven elusive. Here, we develop a model of humans based on an image-computable (images in, estimates out) Bayesian ideal observer. Given biological constraints, the ideal optimally uses the statistics relating local intensity patterns in moving images to speed, specifying the fundamental limits imposed by natural stimuli. Next, we propose a theoretical link between two key decision-theoretic quantities that suggests how to experimentally disentangle the impacts of internal noise and deterministic suboptimal computations. In several interlocking discrimination experiments with three male observers, we confirm this link and determine the quantitative impact of each candidate performance-limiting factor. Human performance is near-exclusively limited by natural stimulus variability and internal noise, and humans use near-optimal computations to estimate speed from naturalistic image movies. The findings indicate that the partition of behavioral variability can be predicted from a principled analysis of natural images and scenes. The approach should be extendable to studies of neural variability with natural signals.SIGNIFICANCE STATEMENT Accurate estimation of speed is critical for determining motion in the environment, but humans cannot perform this task without error. Different objects moving at the same speed cast different images on the eyes. This stimulus variability imposes fundamental external limits on the human ability to estimate speed. Predicting these limits has proven difficult. Here, by analyzing natural signals, we predict the quantitative impact of natural stimulus variability on human performance given biological constraints. With integrated experiments, we compare its impact to well-studied performance-limiting factors internal to the visual system. The results suggest that the deterministic computations humans perform are near optimal, and that behavioral responses to natural stimuli can be studied with the rigor and interpretability defining work with simpler stimuli.

Optimality and heuristics in perceptual neuroscience

The foundation for modern understanding of how we make perceptual decisions about what we see or where to look comes from considering the optimal way to perform these behaviors. While statistical computation is useful for deriving the optimal solution to a perceptual problem, optimality requires perfect knowledge of priors and often complex computation. Accumulating evidence, however, suggests that optimal perceptual goals can be achieved or approximated more simply by human observers using heuristic approaches. Perceptual neuroscientists captivated by optimal explanations of sensory behaviors will fail in their search for the neural circuits and cortical processes that implement an optimal computation whenever that behavior is actually achieved through heuristics. This article provides a cross-disciplinary review of decision-making with the aim of building perceptual theory that uses optimality to set the computational goals for perceptual behavior but, through consideration of ecological, computational, and energetic constraints, incorporates how these optimal goals can be achieved through heuristic approximation.

Bayesian Modeling of Motion Perception Using Dynamical Stochastic Textures

A common practice to account for psychophysical biases in vision is to frame them as consequences of a dynamic process relying on optimal inference with respect to a generative model. The study presented here details the complete formulation of such a generative model intended to probe visual motion perception with a dynamic texture model. It is derived in a set of axiomatic steps constrained by biological plausibility. We extend previous contributions by detailing three equivalent formulations of this texture model. First, the composite dynamic textures are constructed by the random aggregation of warped patterns, which can be viewed as three-dimensional gaussian fields. Second, these textures are cast as solutions to a stochastic partial differential equation (sPDE). This essential step enables real-time, on-the-fly texture synthesis using time-discretized autoregressive processes. It also allows for the derivation of a local motion-energy model, which corresponds to the log likelihood of the probability density. The log likelihoods are essential for the construction of a Bayesian inference framework. We use the dynamic texture model to psychophysically probe speed perception in humans using zoom-like changes in the spatial frequency content of the stimulus. The human data replicate previous findings showing perceived speed to be positively biased by spatial frequency increments. A Bayesian observer who combines a gaussian likelihood centered at the true speed and a spatial frequency dependent width with a “slow-speed prior” successfully accounts for the perceptual bias. More precisely, the bias arises from a decrease in the observer's likelihood width estimated from the experiments as the spatial frequency increases. Such a trend is compatible with the trend of the dynamic texture likelihood width.

Weighted integration of short-term memory and sensory signals in the oculomotor system

Oculomotor behaviors integrate sensory and prior information to overcome sensory-motor delays and noise. After much debate about this process, reliability-based integration has recently been proposed and several models of smooth pursuit now include recurrent Bayesian integration or Kalman filtering. However, there is a lack of behavioral evidence in humans supporting these theoretical predictions. Here, we independently manipulated the reliability of visual and prior information in a smooth pursuit task. Our results show that both smooth pursuit eye velocity and catch-up saccade amplitude were modulated by visual and prior information reliability. We interpret these findings as the continuous reliability-based integration of a short-term memory of target motion with visual information, which support modeling work. Furthermore, we suggest that saccadic and pursuit systems share this short-term memory. We propose that this short-term memory of target motion is quickly built and continuously updated, and constitutes a general building block present in all sensorimotor systems.

Motion Perception: From Detection to Interpretation

Visual motion processing can be conceptually divided into two levels. In the lower level, local motion signals are detected by spatiotemporal-frequency-selective sensors and then integrated into a motion vector flow. Although the model based on V1-MT physiology provides a good computational framework for this level of processing, it needs to be updated to fully explain psychophysical findings about motion perception, including complex motion signal interactions in the spatiotemporal-frequency and space domains. In the higher level, the velocity map is interpreted. Although there are many motion interpretation processes, we highlight the recent progress in research on the perception of material (e.g., specular reflection, liquid viscosity) and on animacy perception. We then consider possible linking mechanisms of the two levels and propose intrinsic flow decomposition as the key problem. To provide insights into computational mechanisms of motion perception, in addition to psychophysics and neurosciences, we review machine vision studies seeking to solve similar problems.

A Switching Observer for Human Perceptual Estimation

Human perceptual inference has been fruitfully characterized as a normative Bayesian process in which sensory evidence and priors are multiplicatively combined to form posteriors from which sensory estimates can be optimally read out. We tested whether this basic Bayesian framework could explain human subjects' behavior in two estimation tasks in which we varied the strength of sensory evidence (motion coherence or contrast) and priors (set of directions or orientations). We found that despite excellent agreement of estimates mean and variability with a Basic Bayesian observer model, the estimate distributions were bimodal with unpredicted modes near the prior and the likelihood. We developed a model that switched between prior and sensory evidence rather than integrating the two, which better explained the data than the Basic and several other Bayesian observers. Our data suggest that humans can approximate Bayesian optimality with a switching heuristic that forgoes multiplicative combination of priors and likelihoods.

Near-optimal integration of facial form and motion

Human perception consists of the continuous integration of sensory cues pertaining to the same object. While it has been fairly well shown that humans use an optimal strategy when integrating low-level cues proportional to their relative reliability, the integration processes underlying high-level perception are much less understood. Here we investigate cue integration in a complex high-level perceptual system, the human face processing system. We tested cue integration of facial form and motion in an identity categorization task and found that an optimal model could successfully predict subjects’ identity choices. Our results suggest that optimal cue integration may be implemented across different levels of the visual processing hierarchy.

A Normalization Mechanism for Estimating Visual Motion across Speeds and Scales

Interacting with the natural environment leads to complex stimulations of our senses. Here we focus on the estimation of visual speed, a critical source of information for the survival of many animal species as they monitor moving prey or approaching dangers. In mammals, and in particular in primates, speed information is conceived to be represented by a set of channels sensitive to different spatial and temporal characteristics of the optic flow [1-5]. However, it is still largely unknown how the brain accurately infers the speed of complex natural scenes from this set of spatiotemporal channels [6-14]. As complex stimuli, we chose a set of well-controlled moving naturalistic textures called "compound motion clouds" (CMCs) [15, 16] that simultaneously activate multiple spatiotemporal channels. We found that CMC stimuli that have the same physical speed are perceived moving at different speeds depending on which channel combinations are activated. We developed a computational model demonstrating that the activity in a given channel is both boosted and weakened after a systematic pattern over neighboring channels. This pattern of interactions can be understood as a combination of two components oriented in speed (consistent with a slow-speed prior) and scale (sharpening of similar features). Interestingly, the interaction along scale implements a lateral inhibition mechanism, a canonical principle that hitherto was found to operate mainly in early sensory processing. Overall, the speed-scale normalization mechanism may reflect the natural tendency of the visual system to integrate complex inputs into one coherent percept.

The "Spinner" Illusion: More Dots, More Speed?

The perceived speed of a ring of equally spaced dots moving around a circular path appears faster as the number of dots increases (Ho & Anstis, 2013, Best Illusion of the Year contest). We measured this "spinner" effect with radial sinusoidal gratings, using a 2AFC procedure where participants selected the faster one between two briefly presented gratings of different spatial frequencies (SFs) rotating at various angular speeds. Compared with the reference stimulus with 4 c/rev (0.64 c/rad), participants consistently overestimated the angular speed for test stimuli of higher radial SFs but underestimated that for a test stimulus of lower radial SFs. The spinner effect increased in magnitude but saturated rapidly as the test radial SF increased. Similar effects were observed with translating linear sinusoidal gratings of different SFs. Our results support the idea that human speed perception is biased by temporal frequency, which physically goes up as SF increases when the speed is held constant. Hence, the more dots or lines, the greater the perceived speed when they are moving coherently in a defined area.

Integration of motion energy from overlapping random background noise increases perceived speed of coherently moving stimuli

The perception of visual motion can be profoundly influenced by visual context. To gain insight into how the visual system represents motion speed, we investigated how a background stimulus that did not move in a net direction influenced the perceived speed of a center stimulus. Visual stimuli were two overlapping random-dot patterns. The center stimulus moved coherently in a fixed direction, whereas the background stimulus moved randomly. We found that human subjects perceived the speed of the center stimulus to be significantly faster than its veridical speed when the background contained motion noise. Interestingly, the perceived speed was tuned to the noise level of the background. When the speed of the center stimulus was low, the highest perceived speed was reached when the background had a low level of motion noise. As the center speed increased, the peak perceived speed was reached at a progressively higher background noise level. The effect of speed overestimation required the center stimulus to overlap with the background. Increasing the background size within a certain range enhanced the effect, suggesting spatial integration. The speed overestimation was significantly reduced or abolished when the center stimulus and the background stimulus had different colors, or when they were placed at different depths. When the center- and background-stimuli were perceptually separable, speed overestimation was correlated with perceptual similarity between the center- and background-stimuli. These results suggest that integration of motion energy from random motion noise has a significant impact on speed perception. Our findings put new constraints on models regarding the neural basis of speed perception.

Ocular-following responses to white noise stimuli in humans reveal a novel nonlinearity that results from temporal sampling

White noise stimuli are frequently used to study the visual processing of broadband images in the laboratory. A common goal is to describe how responses are derived from Fourier components in the image. We investigated this issue by recording the ocular-following responses (OFRs) to white noise stimuli in human subjects. For a given speed we compared OFRs to unfiltered white noise with those to noise filtered with band-pass filters and notch filters. Removing components with low spatial frequency (SF) reduced OFR magnitudes, and the SF associated with the greatest reduction matched the SF that produced the maximal response when presented alone. This reduction declined rapidly with SF, compatible with a winner-take-all operation. Removing higher SF components increased OFR magnitudes. For higher speeds this effect became larger and propagated toward lower SFs. All of these effects were quantitatively well described by a model that combined two factors: (a) an excitatory drive that reflected the OFRs to individual Fourier components and (b) a suppression by higher SF channels where the temporal sampling of the display led to flicker. This nonlinear interaction has an important practical implication: Even with high refresh rates (150 Hz), the temporal sampling introduced by visual displays has a significant impact on visual processing. For instance, we show that this distorts speed tuning curves, shifting the peak to lower speeds. Careful attention to spectral content, in the light of this nonlinearity, is necessary to minimize the resulting artifact when using white noise patterns undergoing apparent motion.

Tactile length contraction as Bayesian inference

To perceive, the brain must interpret stimulus-evoked neural activity. This is challenging: The stochastic nature of the neural response renders its interpretation inherently uncertain. Perception would be optimized if the brain used Bayesian inference to interpret inputs in light of expectations derived from experience. Bayesian inference would improve perception on average but cause illusions when stimuli violate expectation. Intriguingly, tactile, auditory, and visual perception are all prone to length contraction illusions, characterized by the dramatic underestimation of the distance between punctate stimuli delivered in rapid succession; the origin of these illusions has been mysterious. We previously proposed that length contraction illusions occur because the brain interprets punctate stimulus sequences using Bayesian inference with a low-velocity expectation. A novel prediction of our Bayesian observer model is that length contraction should intensify if stimuli are made more difficult to localize. Here we report a tactile psychophysical study that tested this prediction. Twenty humans compared two distances on the forearm: a fixed reference distance defined by two taps with 1-s temporal separation and an adjustable comparison distance defined by two taps with temporal separation t ≤ 1 s. We observed significant length contraction: As t was decreased, participants perceived the two distances as equal only when the comparison distance was made progressively greater than the reference distance. Furthermore, the use of weaker taps significantly enhanced participants' length contraction. These findings confirm the model's predictions, supporting the view that the spatiotemporal percept is a best estimate resulting from a Bayesian inference process.

Speed Constancy or Only Slowness: What Drives the Kappa Effect

In the Kappa effect, two visual stimuli are given, and their spatial distance affects their perceived temporal interval. The classical model assumes constant speed while a competing Bayesian model assumes a slow speed prior. The two models are based on different assumptions about the statistical structure of the environment. Here we introduce a new visual experiment to distinguish between these models. When fit to the data, both the two models replicated human response, but the slowness model makes better behavioral predictions than the speed constancy model, and the estimated constant speed is close to the absolute threshold of speed. Our findings suggest that the Kappa effect appears to be due to slow speeds, and also modulated by spatial variance.