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University of Nevada, Reno

The Effects of Motion on Perceived Size and Other Perceptual Processes

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Psychology

by

Lauren N. Gregg

Dr. Gideon Caplovitz/Thesis Advisor

May, 2021 THE GRADUATE SCHOOL

We recommend that the thesis prepared under our supervision by

Lauren Gregg

entitled The Effects of Motion on Perceived Size and Other Perceptual Processes

be accepted in partial fulfillment of the requirements for the degree of

Master of Science

Dr. Gideon Caplovitz Advisor Dr. Ryan Mruczek Committee Member

Dr. Lorainne Benuto rte ereettie

ee rte

May, 2021 i Abstract

Optical provide important insights into how we process visual information and illusions that alter the perceived size of an object are a valuable tool to study size . Studied for over a century, the classic size illusions have informed us about the complex mechanisms underlying how our brains derive the experience of how big or small objects appear to be. However, these illusions have all been static in nature and thus have ignored motion’s effect on size perception. This review discusses observations of novel dynamic versions of these illusions. Motion has a profound impact on the strength of the illusions tested, with added motion typically creating a stronger effect. Some dynamic versions of these images create an twice as strong as the classic static version. Motion-related manipulations lead to uncertainty in the image size representation of the target, specifically due to added noise at the level of retinal input. We propose a hypothesis that each visual cue involved in size perception is reweighted based on the level of precision or uncertainty in their neural representation. Thus, more weight is given to contextual information when the stimulus and/or eye is moving. Biologically accurate models of size perception need to be able to account for the observed effects of motion. ii Acknowledgements

I would like to express deep gratitude to my advisor and mentor Dr. Gideon Caplovitz, whose encouragement and support led me down this rewarding path of inquiry. I also want to thank every member past and present of Dr. Caplovitz’s C-Lab who supported me, especially my colleague Taissa Lytchenko.

Much gratitude goes to Dr. Ryan Mruczek for his continued guidance through this material and assistance in bringing it all together for this review.

I would also like to thank the entire Cognitive & Brain Science and Neuroscience Departments at University of Reno, Nevada, for the opportunity to study here and for all the knowledge imparted to me by my professors and colleagues. Thank you as well to Dr. Lorraine Benuto for your participation on my graduate committee.

And finally, thank you to my family and friends for your support and encouragement through this process. iii Table of Contents !

Introduction 1 Principles Revealed by Classic Size Illusions 2 The Precision Uncertainty Hypothesis 9 Observed Effects 9 Bayesian modeling and multisensory integration 13 Related Illusions 14 Future Directions and Open Questions 16 iv List of Figures !

Figure 1 Classic Size Illusions pg. 6 Figure 2 Muller-Lyer Fins pg. 7 Figure 3 Dynamic Moving Ebbinghaus pg. 8 Figure 4 Static vs. Dynamic Corridor Illusion pg. 12 Figure 5 Bayesian Cue Integration pg. 14 1 The Effects of Motion on Perceived Size and Other Perceptual Processes

Introduction

Illusions have long been thought to provide important insights about how we process visual information. “Can it be that illusions arise from information processing mechanisms that under normal circumstances make the visible world easier to comprehend?” (Gregory, 1968, p.66). In this review, we will discuss how motion affects the magnitude of size illusions and what these observations reveal about size perception in general. Size perception can be defined as the process by which our brains derive the subjective experience of how big something we are looking at appears to be. Estimating the size of an object across the room may feel simple, but this process is not as straightforward as it first may seem. Although the world around us is three dimensional, we do not have direct visual access to this 3D world. Instead, perception is constrained by the flat, two dimensional images projected on the in the back of our eyes. The fundamental constraint of size perception is that the size of an object’s retinal image scales with viewing distance. An elephant far off in the distance appears as a tiny dot on the savannah. Therefore, at the level of the , a small object viewed from up close projects the same retinal image as a large object viewed from far away. With perfect information about an object’s image size on our retina plus the exact distance of that object, the would be able to compute the exact size of the object. However, in real world visual experiences, perfect information about viewing distance and image size is simply not available, as our visual system cannot measure distance. This creates ambiguities that prevent an object’s real-world size from being directly detected. Instead, the perceived size of an object must be constructed through the integration of visual cues in the scene that can be directly detected.

One way vision scientists and experimental psychologists have tackled the mystery of size perception is through the study of illusions that alter the perceived size of an object. For over a century, size illusions have been used to characterize the factors that contribute to size perception. Some of the most well studied size illusions include the Ebbinghaus, Delboeuf, Müller-Lyer and Ponzo (Figure 1 A-D) illusions, discussed below. Size illusions can be caused by multiple factors- some are caused by inaccurate estimation of distance, however many misperceptions are mainly due to the misestimation of angular size (McCready, 1985). We now know that size perception involves integrating multiple sources of visual 2 information including estimates of both the image size of the object and its distance (Berryhill, Fendrich & Olson, 2009), as well as contextual cues surrounding the object (Coren & Girgus, 1978; Delboeuf, 1865; Titchener, 1901, Mruczek, Blair, Strother, & Caplovitz, 2017), and these processes of integration also contribute to illusions of size.

As we will highlight in the following sections, one key aspect that classic size illusions have in common is they are all static (motionless) in nature. In reality, however, our visual environment is defined by movement. We move through the world as do many of the objects around us, and as such the images on our retinas are constantly in motion. While the classic size illusions have revealed foundational elements of size perception, it was surprising to us that the potential influence of motion on size perception has been largely ignored. This presents a problem when trying to develop a fully formed theory of size perception. To address this issue, we have taken classic size illusions and created novel variants incorporating stimulus dynamics and motion. In each case, we have found that motion significantly impacts the strength of the underlying illusion, most often making the illusion stronger but in some cases reducing its magnitude. In this review, we first discuss in more detail the classic size illusions. These are followed by descriptions of dynamic versions of these illusions. The next section reviews observations from our empirical studies, revealing the strong influence of motion on perceived size, and our interpretation of these findings. Following is a discussion of related illusions and how this concept more broadly applies to perception beyond size illusions, and finally we propose future directions and open questions.

Principles Revealed by Classic Size Illusions

Much of what we know about size perception has been discovered through the study of size illusions. In this section, we will discuss various classical illusions that reveal the main principle discussed in this paper: the perception of an object’s size is influenced by its surrounding context.

Size-contrast illusions

One of the most famous and well studied of the classic size illusions is the Ebbinghaus figure (Burton, 2001; Thiery, 1896), discovered in the 1890s by German psychologist Hermann Ebbinghaus. The illusion is also sometimes referred to as the Titchener Circles, as it was popularized in the 3 English-speaking world by Edward B. Titchener in a 1901 textbook of experimental psychology (Harris & Yates, 2005). The simple yet fascinating image clearly demonstrates that context influences our perception of an object’s size. In the best known version of the (Figure 1), the perceived size of the center circle is influenced by the size of the circles surrounding it. The center target circles are identical in size, but are typically perceived as different. It is commonly explained as a “size contrast” effect, where objects of the same size are positioned next to comparator objects that are either much smaller or much larger than the target stimuli, causing the objects to appear more different than they actually are. As the size of the surrounding circles increases, the perceived size of the target circle decreases, consistent with the concept of size contrast (Roberts, Harris, & Yates, 2005). However, the illusion is not that simple. Other effects have also been shown to predict some variants of the illusion better than a size contrast account, such as contour interactions, distance-dependent attractive and repulsive interactions between neural representations of contours (Todorović & Jovanović, 2018). Such contour interaction effects are more readily observed in the Delboeuf illusion (Figure 1b), which was first presented in 1865 (Delboeuf, 1865). In this illusion the perceived size of a circle is affected by the size of a surrounding circle. If the outer circle is much larger than the inner circle, the target will be seen as smaller, another example of a size contrast effect. However, when the outer circle is only slightly larger, the inner circle will be seen as larger. This is an example of another observed effect- size assimilation, where objects appear to be more similar in size than they actually are. The Binding Ring Illusion (McCarth, Kupitz, & Caplovitz, 2013) is a novel variant of the of the Delboeuf and Ebbinghaus illusions in which the perceived size of a circular arrangement of objects is underestimated when superimposed by a binding ring and overestimated when the binding ring is slightly larger than the overall size of the arrangement. This illusion shows that size contrast and assimilation can affect both singular objects as well as groups of objects.

Size-distance illusions

Another category of size illusions are caused by the interaction between size and distance. A key piece of information when estimating the size of an object is the relationship between retinal size and viewing distance. As objects move farther away from us, their size projected onto our retinas gets smaller and smaller. If the same retinal image is produced by two objects that appear to be at different distances, then the farther object must be physically larger. This is a simple explanation of the size constancy effect. In 1881, Emil Emmert described the phenomenon of appearing to increase in size when 4 projected to a greater distance (Emmert, 1881). “Emmert’s law” states that retinal images of the same size will look larger if they appear to be located farther away. The following illusions are thought to be due to this size constancy effect with perspective or other depth cues inappropriately setting the image’s scaling (Gregory, 1997). The (Figure 1d) is an example of contextual distance cues affecting scaling. In this illusion, lines appear to be receding in the distance. The upper line looks longer because distance cues make it seem farther away. The Corridor Illusion is a version of the Ponzo illusion in which two objects of the same size are placed in a context resembling a corridor. The object that appears to be closer in the corridor also appears smaller. The Ponzo and Corridor illusions are typically thought to be caused by the effects of apparent depth induced by the perspective cues (Gregory, 1966). These size-constancy illusions continue to provide more information about the brain’s underlying processes of size perception. More recent studies have investigated the neural correlates of this effect and implicate the primary (V1) in the representation of an object’s perceived size. Sperandio, Chouinard, & Goodale’s (2012) study of the retinotopic activity in V1 suggests that V1 plays an important role in size constancy. It is thought that in the Corridor illusion, the integration of contextual cues which are represented across multiple regions of the visual cortex occurs via feedback to V1 (Chen, Sperandio, et al., 2019; Fang, Boyaci, Kersten, & Murray, 2008; Liu et al., 2009). Further investigation of these illusions can continue to inform more biologically accurate neural models of size perception.

The Müller-Lyer illusion (Figure 1d) is an interesting case- it has also been attributed by some to be caused by a size-constancy effect, however that explanation does not seem to adequately explain all its observations. Another illusion with a long history of study, it was first discovered by German psychologist Franz Carl Müller-Lyer in 1889. Two line segments of equal length are surrounded by fins pointing either inward or outward. Depending on the direction of the fins, the lines are perceived as either shorter or longer (Judd, 1905). According to a theory put forth by R.L. Gregory (1963), the outgoing fins are seen in perspective as representing an inside corner. As represented in Figure 2, he describes the lines as flat projections of typical views of objects in three dimensional space (Gregory, 1963). According to this account, the line from which the fins extend outward is perceived as longer due to misplaced size constancy. However, in Irwin Rock’s influential criticism of this size-constancy theory, he points out that the Müller-Lyer illusion is generally not seen as three dimensional, and even if we perceptually interpret the fins as a concave and 5 convex corner, there is no evidence that we would perceive the convex corner to be closer (Rock, 1975). This was one of the first criticisms in a series of arguments against using a size-constancy effect to explain the Müller-Lyer illusion. Rock offered the ‘incorrect comparison theory’ as an alternative explanation, arguing that viewers of the Müller-Lyer compare the size of the whole figure (including the fins) rather than just the size of the two vertical lines (Rock, 1975). This hypothesis is supported by observations that the illusion magnitude is weakened if the shaft is a different color (Coren & Gingus, 1972). The size-constancy explanation relies on higher-order cognitive processes such as recognition of three dimensional cues, but many of the subsequent alternative theories examined lower order processes, such as (Festinger et al., 1968) or low pass spatial filtering (Ginsburg, 1984; Coren & Girgus, 1978). Like all illusions, a number of factors contribute to the Müller-Lyer, but it now seems evident that a basic size-constancy explanation cannot account for all observations. It is a compelling example of the complexity of size perception and how simple size illusions can inspire many different angles of ongoing inquiry into the underlying neural processes.

These classic size illusions all clearly show that contextual cues influence the process of size perception. A rich history of perceptual research shows that many different contextual cues can be taken into account, such as the relative size of different objects in the scene (Cormack, Coren, & Girgus, 1979; Kunnapas, 1955; Mruczek, Blair, Strother, & Caplovitz, 2017b; Roberts, Harris, & Yates, 2005; Rock & Ebenholtz, 1959), an object’s shape and texture (Lotze, 1852; Kundt, 1863; Helmholtz, 1867; Murray et al., 2006; Westheimer, 2008; Giora and Gori, 2010), our previous knowledge about an object’s typical size (Konkle and Oliva, 2012), and the frame around an object (Kunnapas, 1955; Rock and Ebenholtz, 1959; Robinson, 1972; Brigell et al., 1977). While these and other size illusions have informed our understanding of size perception, the number of contributing factors they reveal has made it challenging to develop a unified, biologically-accurate model of size perception. As we will discuss in the subsequent sections, the matter is made only more complicated when we take into consideration motion’s effects on the perception of size. However, our visual environment is constantly in motion and these static illusions ignore motion’s role in size perception. Only by incorporating motion dynamics can a more complete theory of size perception be formed. 6 A) B)

C) D)

Figure 1 - Classic Size Illusions A) The classic Ebbinghaus illusion The best known version of the Ebbinghaus illusion. Two circles of identical size are surrounded by circles, one by large and the other by small. As a result of the surrounding context, the central circle surrounded by large circles appears smaller than the other central circle. B) The Delboeuf Illusion The two circles discs are surrounded by rings. One surrounding ring is small, and close to the target circle, while the other surrounding ring is large and farther away from the target circle. The target circle inside the small (close) ring appears larger. C) The Ponzo Illusion The upper line looks longer because the converging sides provide distance cues, looking like parallel lines receding into the distance. In this context, the viewer interprets the upper line as being farther away, and thus longer, because a father object would have to be longer than a near object to project a retinal image of the same size. D) The Müller-Lyer Illusion Straight line segments of equal length are surrounded by “fins”, one set angled inwards and one set angled outwards. The line segment surrounded by inward fins (top) is perceived to be shorter. 7

Figure 2 - “Fins” of the Müller-Lyer illusion Representation of how the fins, as in the Müller-Lyer illusion, can either be representing an “inside corner” (Wall A) or an outgoing corner (Wall B). When viewing this scene, the viewer would know that the wall is the same height in both places, although the lines are different sizes.

Dynamic Size Illusions

We addressed the lack of motion in the study of size perception by creating novel variants of the classic size illusions that include dynamic motion. We found adding motion can have a profound influence- our novel dynamic versions of the Ebbinghaus (example in Figure 3) can create an illusion almost twice as strong as the classic Ebbinghaus illusion. Not only can motion modulate the strength of illusions observed in static configurations, but it can also lead to the experience of an object dynamically changing its size (Mruczek et al., 2014; Mruczek et al., 2015; Mruczek et al., 2017). 8

Figure 3 - Dynamic Moving Ebbinghaus In the Dynamic-Moving Ebbinghaus, the inducers continuously modulate their size and eccentricity between small-and-near and large-and-far and there is a translation of the entire stimulus across the screen.

The study of these dynamic illusions highlights the role of motion and dynamic visual information in regulating how different contextual cues are used in the perception of size (Mruczek, Blair, Strother, & Caplovitz, 2017). For example, when an object is surrounded by an expanding context and other dynamics, such as eye movements, are also present, a viewer will perceive the object to be dramatically shrinking (Mruczek, Blair, & Caplovitz, 2014). Not only is there a much greater change in perceived size when motion is present (Mruczek et al., 2015), but if the inducers expand and contract, the change in size is directly experienced as the target appears to continuously grow and shrink. This effect is perhaps best illustrated by the Dynamic Ebbinghaus illusion (Mruczek, Blair, Strother, & Caplovitz, 2015). Observation of these dynamic size illusions led to the formation of the Precision Uncertainty Hypothesis.

The Precision Uncertainty Hypothesis

In a series of empirical experiments, we explored the stimulus factors that contribute to the effects of motion on size perception. These experiments led to the formation of the Precision Uncertainty Hypothesis, arguing that the precision of an object’s size represented on the retina will influence how contextual cues are used in size perception. More noise in the retinal signal, caused by eye movements or a moving target, will create less precision in the object’s retinal size representation over time and thus greater weight will be given to contextual cues. In other words, the Precision Uncertainty hypothesis 9 argues that each visual cue is not automatically integrated but instead reweighted depending on the quality of the signal, which is greatly affected by motion. When a target is in motion, the brain’s ability to precisely represent the size of the object is impaired, so contextual cues make stronger contributions to the target’s perceived size. We can see this in action by studying dynamic illusions.

Observed Effects of Motion on Size Perception

The observed effects of motion on size perception, coupled with the inherently dynamic nature of our visual environment, highlights the fact that motion dynamics play a crucial and under-studied role in size perception. Biologically plausible models of size perception need to be able to account for the following observations. The Dynamic Ebbinghaus illusion includes expanding circles surrounding the target while also adding motion to the target itself, creating an illusion much stronger than the classic version. Interestingly however, expanding the inducers alone, in the absence of target motion, yields an illusion much weaker than the classic Ebbinghaus. The strengthening of the illusion requires both target motion on the retina and a relative size change. Relative size change without target motion leads to a very weak effect and therefore the effect cannot be explained as just size contrast played out over time. The reason the magnitude of the illusion is diminished when the inducers are moving but the target is stationary may be because the neural representation of a stationary object is more precise over time, and with less uncertainty in the size information provided by the retinal image, less weight is given to the information provided by the context. The strengthened effect depends critically on the interaction between a size-contrast effect (the root of the classical illusion) and other dynamic components, such as eye movements or changes in the position of the target object. These two factors combined lead to changes in the relative contribution of different cues to perceived size. Changes in relative size of the contextual elements are also necessary. When the size of the context is held constant, subjects do not observe an illusion at all, even in the presence of other stimulus motion and eye movements (Mruczek, Blair, & Caplovitz, 2014). These results suggest that motion alone is not enough to induce an illusion. Manipulations that require the observer to move their eyes significantly strengthen the magnitude of size contrast illusions like the Ebbinghaus (Mruczek et al. 2015). Eye movements degrade the precision of the signal as to the exact size of the retinal image. When participants are asked to visually track a 10 moving object, the retinal input from eye movements smears the projected image. This lessens the precision at which the size of the target can be represented by neurons over time. Less precision leads to larger illusion magnitudes, again in agreement with the Precision Uncertainty hypothesis. By comparing largely matched conditions, we find more supporting evidence. Stronger illusory effects are found across matched retinal conditions when the stimulus moves compared to when the eyes moves (Mruczek et al., 2014). Both involve motion of the eyes and target, but differ in what caused the motion. Motion caused by movement of the eyes can be partially accounted for by the brain using an efference copy of the eye movement command (Bridgeman, 1995; Wurtz and Sommer, 2004). In contrast, motion caused by movement of the stimulus may be more challenging to predict and would therefore lead to a higher level of noise in the image size representation. Stronger illusion magnitudes created by stimulus movement versus eye movement may be due to the higher level of uncertainty produced in that condition. Different dynamic effects such as eye movement and stimulus motion were tested in isolation and also combined. Combining dynamic manipulations, discussed in more detail below, created the highest level of uncertainty and led to the largest illusion of all. The additive effect of reducing the precision of the retinal input through combined manipulations is consistent with the Precision/Uncertainty hypothesis.

Manipulations that create more retinal uncertainty create a stronger illusion

A variety of dynamic manipulations were used to create different versions of the Dynamic Ebbinghaus illusion. Individual manipulations such as peripheral fixation, eye movements, and retinal motion were tested. For example, “target jittering,” a shaking of the target object, was used as a direct manipulation of the retinal image, degrading its precision without eye movement or target motion. The addition of more manipulations led to increasing illusion magnitudes. (Mruczek et al. 2015). Using a set of matched parameters, each manipulation was compared to the classic stationary illusion. Each new condition tested added a dynamic element that further increased the retinal noise, thus adding uncertainty. The most powerful condition combined peripheral viewing, changes in target eccentricity, smooth pursuit eye movements, and target jittering. This final condition led to an illusion four times stronger than the other conditions. 11 Quantitative behavioral metric of precision shows precision is reduced under dynamic conditions

To verify these dynamic manipulations did in fact lower precision, a quantitative behavioral measure of precision was extracted from the data. This revealed a significant main effect of context, motion, and a significant interaction between context and motion (Mruczek, Blair, & Caplovitz, 2020). Steep slopes in the psychometric curves indicated a more precise representation of the target. Consistent with the expected effects of motion on precision, slopes were lower for the dynamic compared with the static conditions. These results provide behavioral evidence that the representational precision of the target is reduced under the dynamic conditions.

Not all size illusions are increased by motion

It is important to note that not all classic size illusions are increased by the addition of target motion. The Dynamic Corridor illusion, a size constancy illusion, is actually reduced when motion is added. When target motion is added to the Corridor illusion (Figure 4) and an object appears to move up and down the corridor, effects are only half as large as the static Corridor illusion (Mruczek, Blair, & Caplovitz, 2020). This is in stark contrast to the Ebbinghaus, where the dynamic version yields an illusion twice as strong as the static. These results indicate that more research is needed to uncover what kinds of motion dynamics affect perceived size and under what conditions. 12

Figure 4: Static vs. Dynamic Corridor Illusion Comparing the Static (left) and the Dynamic (right) corridor illusion. White arrows indicate the direction of motion.

How exactly representations of perceived size are formed (e.g. lateral connectivity, cortical magnification, or feed-back from high visual areas) remains largely unknown. These observations provide a valuable contribution in the quest to discover more about the neural mechanisms of size perception as they place constraints on neural and computational models of contextual influences. The observed effects show that contextual information is not integrated automatically, but rather is reweighted based on the quality of the cues. One of the main takeaways from these observations is that individual contextual cues do not have a constant or obligatory effect in the mechanisms of size perception. Instead, they suggest that an initial cortical representation of angular size is subsequently integrated with contextual cues prior to the representation of perceived size in V1 and elsewhere.

Bayesian Modeling and Multisensory Integration The Precision Uncertainty hypothesis is also in line with models proposed for multisensory integration. As we have discussed, sensory information is noisy. To help paint a clearer picture, 13 information from different is combined in a probabilistic Bayseian process; the reliability of each sensory cue is taken into account and prior experience is also combined with the available sensory information (Laurens, J., & Angelaki, D. E., 2011; Laurens et. al 2013a, Laurens et. al 2013b). In Bayesian models of cue integration, the reliability of individual cues is proportional to their weight during the integration process at the behavioral level (Angelaki, Gu, & Deangelis, 2011; Kersten, Mamassian, & Yuille, 2004; Knill & Pouget, 2004). How this relates to our current observations is demonstrated in Figure 5. As shown, the precision of the target object is more reliable in the static illusion and thus the less weight is given to the contextual cues when the information is integrated. In contrast, in the dynamic illusion the precision of the target is less precise, and thus contextual cues have a greater influence, consistent with our argument in the Precision Uncertainty hypothesis.

Figure 5 - Bayesian Cue Integration Equation= Perceived Target Size = weight of context (sigma_target) * context + weight of target * target In the static condition (top), precision of the representation of the size of the target is higher, demonstrated in blue. The representation of size in the dynamic condition (bottom) is lower, represented in red. The weight given to contextual cues is dependent on the precision of the target (σ) , and when the precision of the target is higher, it has more influence on the final size representation. The final perception of size, represented in purple, is more heavily influenced by the target when precision is high (static, top), and is more heavily influenced by the context when precision is low (bottom). 14 Related Illusions

Although we’ve focused primarily on the Dynamic Ebbinghaus illusion and other size-contrast illusions, these effects are not limited to one illusion or a particular stimulus configuration. Similar effects have been found in other illusions as well and the principles of the Precision Uncertainty hypothesis can be generalized beyond size perception. The visual artist and writer Gianni A. Sarcone demonstrates a compelling effect using a dynamic variant of the Müller-Lyer Illusion which can be viewed online at this link: . This version of the illusion further supports the argument that the Müller-Lyer illusion is caused by more than just size-constancy effects. The context in this illusion is not changing size, however the magnitude of the illusion is enhanced with the addition of dynamic motion. It also demonstrates that a stable retinal position lessens the strength of the illusion as would be predicted by the Precision Uncertainty Hypothesis. The Duncker Illusion (Wallach, 1959) shows a moving background that alters the perceived direction of target motion. Wallach observed that if the target is stationary, the effect is weak, but a moving target enhances the influence of the background motion. Within the framework of the Precision Uncertainty Hypothesis, we would argue that the moving background creates more noise in the positional signal of the target, reweighting the positional cues and creating the illusion. Another compelling example can be observed in the Double Drift illusion. When the internal texture of a Gabor patch drifts in the orthogonal direction of the path itself, observers see a remarkable shift in its perceived direction (Zhang & De Valois, 1993; Tse & Hsieh, 2006; Shapiro et al., 2010; Lisi & Cavanagh, 2015, Shapiro et al., 2010;). The illusion demonstrates that moving stimuli containing internal motion create large shifts in perceived location. The dynamics of the stimulus could potentially be adding to positional uncertainty, thus reweighting other contextual factors in determining position, as would be predicted by the Precision Uncertainty hypothesis. In relation to Bayesian integration, various illusions have been found in which one sensory modality affects what is experienced in another. The Sound-Induced Flash illusion (Shams et al. 2000) is an example in which what you visually experience is affected by what you hear. In one version of this illusion, one flash appears on the screen and either one or two beeps are sounded. When there are two beeps, people frequently experience seeing two flashes when in reality there is always only one flash. This is the result of asynchronous visual and auditory stimulus. This discrepancy in signals could be 15 interpreted by the brain as the visual stimulus being more unreliable or less precise, and therefore more weight is given to the auditory cue. A complimentary example is the ventriloquism effect, exemplified when it appears as if a voice is coming from the mouth of a puppet rather than from the mouth of the puppeteer. Here, sound location is given less weight than visual cues due to the fact that vision has better spatial resolution. Both of the illusions are caused by reweighting of cues consistent with the Precision Uncertainty Hypothesis. In summary, these observations highlight the role of motion and dynamic visual information in regulating how different contextual cues are used in the perception of size and how dynamic multisensory integration informs the reweighting of other sensory cues. These observations and the Precision Uncertainty hypothesis they inspired can inform more biologically accurate models of the underlying neural mechanisms of size perception and perception more generally.

Future Directions

Future neuroscientific and behavioral studies that take into account the many observations of the effects of motion dynamics are needed to further explore human size perception. The Bayesian formula presented in Figure 5 presents many opportunities to further the research. A more developed and accurate measure for precision (or the target sigma) is needed. Testing measuring precision in the absence of an illusion would be one possible way to better develop a definition and measure. Another issue that needs to be addressed is the fact that in the current formula, context and target size are ostensibly in different units. To make meaningful models and to make this formula more useful mathematically, they would have to be converted into the same units, and the simple addition sign adding their two influences together would have to be further developed into a more complex function based on known neurophysiology.

Stepping back from this specific project and taking a long-term, more bird’s eye view, an intriguing idea is using the Precision Uncertainty hypothesis to understand human behavior and cognition more generally. One of the exciting things about studying more basic mechanisms like size perception is that these processes may relate to higher level human behavior and cognition. Precision is something that not only affects things like vision, but also is significant when we are talking about all kinds of information we receive from our environments. When information is uncertain, people may integrate cues like 16 emotion, gut feelings, false information they read on the internet, etc., and their final representation of reality can end up heavily affected or warped. Concepts like the precision uncertainty hypothesis might inform us about human behavior and society at large, and that is one of the reasons why studying the mechanisms of the brain is so important.

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