Geometric and Perceptual Effects of the Location of the Observer Vantage Point for Linear-Perspective Images

New geometric analyses are presented of three impressive examples of the effects of location of the vantage point on virtual 3-D spaces conveyed by linear-perspective images. In the ‘egocentric-road’ effect, the perceived direction of the depicted road is always pointed towards the observer, for any position of the vantage point. It is shown that perspective images of real-observer-aimed roads are characterised by a specific, simple pattern of projected side lines. Given that pattern, the position of the observer, and certain assumptions and perspective arguments, the perceived direction of the virtual road towards the observer can be predicted. In the ‘skewed balcony’ and the ‘collapsing ceiling’ effects, the position of the vantage point affects the impression of alignment of the virtual architecture conveyed by large-scale illusionistic paintings and the real architecture surrounding them. It is shown that the dislocation of the vantage point away from the viewing position prescribed by the perspective construction induces a mismatch between the painted vanishing point of elements in the picture and the real vanishing point of corresponding elements of the actual architecture. This mismatch of vanishing points provides visual information that the elements of the two architectures are not mutually parallel.

A New Set of Illusions—the Dynamic Luminance-Gradient Illusion and the Breathing Light Illusion

A novel set of illusions that break brightness constancy and size constancy at the same time is reported. The illusions occur when observers move towards or away from these patterns. Many variations of these phenomena and a possible explanation are discussed.

Effects of 3-D Complexity on the Perception of 2-D Depictions of Objects

In a recent study, Pelli (1999 Science285 844–846) performed a set of perceptual experiments using portrait paintings by Chuck Close. Close's work is similar to the ‘Lincoln’ portraits of Harmon and Julesz (1973 Science180 1194–1197) in that they are composite images consisting of coarsely sampled, individually painted, mostly homogeneous cells. Pelli showed that perceived shape was dependent on size, refuting findings that perception of this type is scale-invariant. In an attempt to broaden this finding we designed a series of experiments to investigate the interaction of 2-D scale and 3-D structure on our perception of 3-D shape. We present a series of experiments where field of view, 3-D object complexity, 2-D image resolution, viewing orientation, and subject matter of the stimulus are manipulated. On each trial, observers indicated if the depicted objects appeared to be 2-D or 3-D. Results for face stimuli are similar to Pelli's, while more geometrically complex stimuli show a further interaction of the 3-D information with distance and image information. Complex objects need more image information to be seen as 3-D when close; however, as they are moved further away from the observer, there is a bias for seeing them as 3-D objects rather than 2-D images. Finally, image orientation, relative to the observer, shows little effect, suggesting the participation of higher-level processes in the determination of the ‘solidness’ of the depicted object. Thus, we show that the critical image resolution depends systematically on the geometric complexity of the object depicted.

Errors in Judging Information about Reflections in Mirrors

We investigated people's perception and knowledge of planar mirror reflections. People were accurate at deciding when they could first see their reflection as they approached a mirror from the side, but only if their reflection was visible. Most people stopped too early if the mirror was covered up. People also overestimated the size of the reflection of their face on the surface of a mirror if they were shown a covered mirror. Their accuracy improved somewhat if their reflection was visible but, unlike the first task, they still made striking errors. Perceptual feedback thus improved performance at predicting the behaviour of mirror reflections in both tasks but failed to eliminate errors in the second task. The overestimation of reflection size was not face-specific as it generalised to novel stimuli (paper ellipses) and it was found with both a matching response and for verbal size estimations. The early error in the first task appears to be due to an inaccurate belief that can be overridden by perceptual feedback. The overestimation in the second task is primarily caused by a powerful size-constancy effect.

How Many Faces Can Be Processed during a Single Eye Fixation?

The purpose of our study was to estimate the perceptual span for facial information: how many faces can be processed during a single eye fixation. We used a visual-search task, in which the targets and distractors were facial photographs. The task of the observer was to search for and identify a target face in an array of faces. We measured the time needed for one search—threshold search time—by using a multiple-alternative staircase method. The threshold represents the duration of stimulus presentation at which the probability of correct responses was 79%. The array size was varied from 2 × 2 to 8 × 8 faces. Simultaneously with the performance measurements we measured eye movements with a video eye tracker. We found that threshold search time increased with increasing set size nearly linearly. The number of fixations also increased linearly from unity at the smallest set size to about fifteen at the largest set size. The result of 2 × 2 faces during a single fixation gave an estimate of 4 faces for the perceptual span. If, on average, only half of the elements had to be scanned for finding the target, 15 fixations at the largest set size (8 × 8) gave another estimate of 2.13 faces. The mean fixation duration was around 200 ms. Thus, the results suggest that 2–4 faces can be processed during one fixation of about 200 ms.

Jitter and Size Effects on Vection are Immune to Experimental Instructions and Demands

Both coherent perspective jitter and explicit changing-size cues have been shown to improve the vection induced by radially expanding optic flow. We examined whether these stimulus-based vection advantages could be modified by altering cognitions and/or expectations about both the likelihood of self-motion perception and the purpose of the experiment. In the main experiment, participants were randomly assigned into two groups—one where the cognitive conditions biased participants towards self-motion perception and another where the cognitive conditions biased them towards object-motion perception. Contrary to earlier findings by Lepecq et al (1995 Perception24 435–449), we found that identical visual displays were less likely to induce vection in ‘object-motion-bias’ conditions than in ‘self-motion bias’ conditions. However, significant jitter and size advantages for vection were still found in both cognitive conditions (cognitive bias effects were greatest for non-jittering same-size control displays). The current results suggest that if a sufficiently large vection advantage can be produced when participants are expecting to experience self-motion, it is likely to persist in object-motion-bias conditions.

Estimation of Lifted Weight and Produced Effort through Perception of Point-Light Display

It has been shown that human observers can estimate the weight of a box from the observation of a point-light display of a lifting motion. We asked observers to report the weight of the box and the effort produced by five lifters ranging in size and strength to determine if observers can perceive lifter size. In experiment 1, five or six weights from each of five lifters were shown to fourteen observers in a random order. Observers showed less error in estimating the amount of effort each lifter produced than in estimating the actual weight of the box. In experiment 2, the lifters were presented individually to forty observers to remove any effect observing a previous lift might have had on estimating the subsequent lift by a different lifter. The results showed an improvement in estimated weight but not in estimated effort. In experiment 3, the actual size of the lifters was given to thirty-four observers, and the estimations of both weight and effort improved. In experiment 4, observers did not improve when observing practice trials and estimating either only weight or only effort. The results from the four experiments suggest that observers are more sensitive to lifter's effort than to the weight lifted, and that observers tend to use changes in the velocity profile of the lift when making their estimates.

Effects of Motion Parallax and Perspective Cues on Perceived Size and Distance

In three experiments we examined the relative effectiveness of motion parallax and two perspective cues for the perception of size and distance. The experimental stimuli consisted of two ellipses (a standard and a comparison) and a horizontal line that indicated the horizon. The subject's task was to report the apparent size and distance of the comparison stimulus relative to the standard stimulus. Two perspective cues were given by the relative heights of the two stimuli and the absolute height of the standard stimulus below the horizon. Motion parallax was defined by both the ratio and the difference in angular velocities between the two stimuli on the display. In experiment 1 we examined the effects of the two perspective cues and the motion parallax. In experiment 2 we eliminated the horizon line, and examined the role of the horizon in size and distance perception. In experiment 3 we separately evaluated the effects of motion parallax and the relative height cues. The results from the three experiments showed that the effect of motion parallax and the two perspective cues were different in three ways. First, the relative effectiveness of motion parallax and the two perspective cues differed for size and distance estimates. For size estimates, the motion parallax was more effective than the perspective cues (experiments 1 and 3). For distance estimates, the motion parallax was as effective as the two perspective cues (experiments 1 and 3). Second, the role of the horizon differed for size and distance estimates. The size estimates were strongly affected by the horizon, while the distance estimates were not affected much by the horizon (experiment 2). Third, the effective perspective cues differed for the size estimates and the distance estimates: size estimates were affected by the perspective cues as a combination of the horizon and relative height; distance estimates were affected by the perspective cues as an interaction between the absolute and relative heights without the horizon line.

Size and distance are perceived independently in an optical tunnel: Evidence for direct perception

The historical but questionable size-distance invariance hypothesis (SDIH) features computation over geometric, oculomotor, and binocular cues and the coupling of percepts-perceived size, S', is mediated by perceived distance, D'. A contemporary non-mediational hypothesis holds that S' and D' are specific to distinct optical variables. We report two experiments with an optical tunnel, an arrangement of alternating black and white concentric rings, that allows systematic manipulation of the optic array at a point of observation while controlling a variety of size and depth cues. Participants viewed targets of different sizes at different distances monocularly, reporting S' and D' via magnitude production. In Experiment 1, the target was either placed in a continuous tunnel (extending 164cm) or in a tunnel that truncated at the target's location. Experiment 2 included a third tunnel, one that was truncated with a flat depiction of the posterior surface structure that would have been visible in the continuous tunnel. In both experiments, S' decreased with D but D' was unaffected by S. Partial correlation analyses showed that the relationship between S' and D' was not significant when the contributions of other variables were removed. Importantly, S' and D' were affected differently by manipulations of the optical tunnel's continuity while computationally obvious visual cues were controlled. These outcomes suggest that D' is not a mediator of S'. Rather S' and D' are independently determined with correlated but different optical bases, results that support the direct model.

Planning to Reach for an Object Changes How the Reacher Perceives It

Three experiments assessed the influence of the Ebbinghaus illusion on size judgments that preceded verbal, grasp, or touch responses. Prior studies have found reduced effects of the illusion for the grip-scaling component of grasping, and these findings are commonly interpreted as evidence that different visual systems are employed for perceptual judgment and visually guided action. In the current experiments, the magnitude of the illusion was reduced by comparable amounts for grasping and for judgments that preceded grasping (Experiment 1). A similar effect was obtained prior to reaching to touch the targets (Experiment 2). The effect on verbal responses was apparent even when participants were simply instructed that a target touch task would follow the verbal task. After participants had completed a grasping task, the reduction in the magnitude of the illusion remained for a subsequent verbal-response judgment task (Experiment 3). Overall, the studies demonstrate strong connections between action planning and perception.

Differing views: Can chimpanzees do Level 2 perspective-taking?

Although chimpanzees understand what others may see, it is unclear whether they understand how others see things (Level 2 perspective-taking). We investigated whether chimpanzees can predict the behavior of a conspecific which is holding a mistaken perspective that differs from their own. The subject competed with a conspecific over two food sticks. While the subject could see that both were the same size, to the competitor one appeared bigger than the other. In a previously established game, the competitor chose one stick in private first and the subject chose thereafter, without knowing which of the sticks was gone. Chimpanzees and 6-year-old children chose the ‘riskier’ stick (that looked bigger to the competitor) significantly less in the game than in a nonsocial control. Children chose randomly in the control, thus showing Level 2 perspective-taking skills; in contrast, chimpanzees had a preference for the ‘riskier’ stick here, rendering it possible that they attributed their own preference to the competitor to predict her choice. We thus run a follow-up in which chimpanzees did not have a preference in the control. Now, they also chose randomly in the game. We conclude that chimpanzees solved the task by attributing their own preference to the other, while children truly understood the other’s mistaken perspective.

Response trajectories capture the continuous dynamics of the size congruity effect

In a comparison task involving numbers, the size congruity effect refers to the general finding that responses are usually faster when there is a match between numerical size and physical size (e.g., 2-8) than when there is a mismatch (e.g., 2-8). In the present study, we used computer mouse tracking to test two competing models of the size congruity effect: an early interaction model, where interference occurs at an early representational stage, and a late interaction model, where interference occurs as dynamic competition between response options. In three experiments, we found that the curvature of responses for incongruent trials was greater than for congruent trials. In Experiment 2 we showed that this curvature effect was reliably modulated by the numerical distance between the two stimulus numbers, with large distance pairs exhibiting a larger curvature effect than small distance pairs. In Experiment 3 we demonstrated that the congruity effects persist into response execution. These findings indicate that incongruities between numerical and physical sizes are carried throughout the response process and result from competition between parallel and partially active response options, lending further support to a late interaction model of the size congruity effect.

Spatial properties of objects predict patterns of neural response in the ventral visual pathway

Neuroimaging studies have revealed topographically organised patterns of response to different objects in the ventral visual pathway. These patterns are thought to be based on the form of the object. However, it is not clear what dimensions of object form are important. Here, we determined the extent to which spatial properties (energy across the image) could explain patterns of response in these regions. We compared patterns of fMRI response to images from different object categories presented at different retinal sizes. Although distinct neural patterns were evident to different object categories, changing the size (and thus the spatial properties) of the images had a significant effect on these patterns. Next, we used a computational approach to determine whether more fine-grained differences in the spatial properties can explain the patterns of neural response to different objects. We found that the spatial properties of the image were able to predict patterns of neural response, even when categorical factors were removed from the analysis. We also found that the effect of spatial properties on the patterns of response varies across the ventral visual pathway. These results show how spatial properties can be an important organising principle in the topography of the ventral visual pathway.

Seeing the Big Picture: Size Perception Is More Context Sensitive in the Presence of Others

This paper tests the hypothesis that social presence influences size perception by increasing context sensitivity. Consistent with Allport's prediction, we expected to find greater context sensitivity in participants who perform a visual task in the presence of other people (i.e., in co-action) than in participants who perform the task in isolation. Supporting this hypothesis, participants performing an Ebbinghaus illusion-based task in co-action showed greater size illusions than those performing the task in isolation. Specifically, participants in a social context had greater difficulty perceiving the correct size of a target circle and ignoring its surroundings. Analyses of delta plot functions suggest a mechanism of interference monitoring, since that when individuals take longer to respond, they are better able to ignore the surrounding circles. However, this type of monitoring interference was not moderated by social presence. We discuss how this lack of moderation might be the reason why the impact of social presence on context sensitivity is able to be detected in tasks such as the Ebbinghaus illusion.

A horse's eye view: size and shape discrimination compared with other mammals

Mammals have adapted to a variety of natural environments from underwater to aerial and these different adaptations have affected their specific perceptive and cognitive abilities. This study used a computer-controlled touchscreen system to examine the visual discrimination abilities of horses, particularly regarding size and shape, and compared the results with those from chimpanzee, human and dolphin studies. Horses were able to discriminate a difference of 14% in circle size but showed worse discrimination thresholds than chimpanzees and humans; these differences cannot be explained by visual acuity. Furthermore, the present findings indicate that all species use length cues rather than area cues to discriminate size. In terms of shape discrimination, horses exhibited perceptual similarities among shapes with curvatures, vertical/horizontal lines and diagonal lines, and the relative contributions of each feature to perceptual similarity in horses differed from those for chimpanzees, humans and dolphins. Horses pay more attention to local components than to global shapes.

Edge Length and Surface Area of a Blank: Experimental Assessment of Measures, Size Predictions and Utility

Blank size and form represent one of the main sources of variation in lithic assemblages. They reflect economic properties of blanks and factors such as efficiency and use life. These properties require reliable measures of size, namely edge length and surface area. These measures, however, are not easily captured with calipers. Most attempts to quantify these features employ estimates; however, the efficacy of these estimations for measuring critical features such as blank surface area and edge length has never been properly evaluated. In addition, these parameters are even more difficult to acquire for retouched implements as their original size and hence indication of their previous utility have been lost. It has been suggested, in controlled experimental conditions, that two platform variables, platform thickness and exterior platform angle, are crucial in determining blank size and shape meaning that knappers can control the interaction between size and efficiency by selecting specific core angles and controlling where fracture is initiated. The robustness of these models has rarely been tested and confirmed in context other than controlled experiments. In this paper, we evaluate which currently employed caliper measurement methods result in the highest accuracy of size estimations of blanks, and we evaluate how platform variables can be used to indirectly infer aspects of size on retouched artifacts. Furthermore, we investigate measures of different platform management strategies that control the shape and size of artifacts. To investigate these questions, we created an experimental lithic assemblage, we digitized images to calculate 2D surface area and edge length, which are used as a point of comparison for the caliper measurements and additional analyses. The analysis of aspects of size determinations and the utility of blanks contributes to our understanding of the technological strategies of prehistoric knappers and what economic decisions they made during process of blank production.

Ensemble perception of size in 4-5-year-old children

Groups of objects are nearly everywhere we look. Adults can perceive and understand the 'gist' of multiple objects at once, engaging ensemble-coding mechanisms that summarize a group's overall appearance. Are these group-perception mechanisms in place early in childhood? Here, we provide the first evidence that 4-5-year-old children use ensemble coding to perceive the average size of a group of objects. Children viewed a pair of trees, with each containing a group of differently sized oranges. We found that, in order to determine which tree had the larger oranges overall, children integrated the sizes of multiple oranges into ensemble representations. This pooling occurred rapidly, and it occurred despite conflicting information from numerosity, continuous extent, density, and contrast. An ideal observer analysis showed that although children's integration mechanisms are sensitive, they are not yet as efficient as adults'. Overall, our results provide a new insight into the way children see and understand the environment, and they illustrate the fundamental nature of ensemble coding in visual perception.

Object visibility alters the relative contribution of ventral visual stream and mirror neuron system to goal anticipation during action observation

We used fMRI to study the effect of hiding the target of a grasping action on the cerebral activity of an observer whose task was to anticipate the size of the object being grasped. Activity in the putative mirror neuron system (pMNS) was higher when the target was concealed from the view of the observer and anticipating the size of the object being grasped requested paying attention to the hand kinematics. In contrast, activity in ventral visual areas outside the pMNS increased when the target was fully visible, and the performance improved in this condition. A repetition suppression analysis demonstrated that in full view, the size of the object being grasped by the actor was encoded in the ventral visual stream. Dynamic causal modeling showed that monitoring a grasping action increased the coupling between the parietal and ventral premotor nodes of the pMNS. The modulation of the functional connectivity between these nodes was correlated with the subject's capability to detect the size of hidden objects. In full view, synaptic activity increased within the ventral visual stream, and the connectivity with the pMNS was diminished. The re-enactment of observed actions in the pMNS is crucial when interpreting others' actions requires paying attention to the body kinematics. However, when the context permits, visual-spatial information processing may complement pMNS computations for improved action anticipation accuracy.

Properties of the size-weight illusion as shown by lines of subjective equality

We studied the size-weight illusion through comparative judgments. The experiment had two direct aims: to verify whether the relative contribution of size to apparent heaviness can differ for different stimulus sets, and to verify whether that contribution can differ for different methods of comparing two objects (consecutive vs. simultaneous weighing). Thirty university students participated. Results show that the relative contribution of size depends on stimulus set, but is independent of the method used for comparing objects. The first finding implies that a linear model cannot describe the integration of size and weight information in the illusion; the second finding is evidence for the low-level character of the integration process.

A geometric and dynamic affordance model of reaches-to-grasp: Men take greater risks than women

Mon-Williams and Bingham (2011) developed an affordance model of the spatial structure of reaches-to-grasp. With a single free parameter (P), the model predicted the safety margins (SMs) exhibited in maximum grasp apertures (MGAs), during the approach of a hand to a target object, as a function of an affordance measure of object size and a functional measure of hand size. An affordance analysis revealed that object size is determined by a diagonal through the object, called the maximum object extent. Mon-Williams and Bingham provided no theoretical account for the empirically determined values of P. We now address this question. Snapp-Childs and Bingham (2009) augmented Warren's (1984) geometric affordance scaling model with a dynamical component determined by the stability of the motor performance. Because P was found to vary with the speeds of reaches, we incorporated a measure of the variability of performance into the model to yield predictions of P. We also found that P varied with gender. In respect to the size of safety margins, women were more conservative in taking risks then men. Finally, following Warren (1984), the classic paradigm for testing affordance models is to test the scaling relations with both small and large participants. We tested small- and large-handed men and small- and large-handed women and found that the new parameter free model successfully accounted for the spatial structure of reaches-to-grasp.

Getting a grip on heaviness perception: a review of weight illusions and their probable causes

Weight illusions--where one object feels heavier than an identically weighted counterpart--have been the focus of many recent scientific investigations. The most famous of these illusions is the 'size-weight illusion', where a small object feels heavier than an identically weighted, but otherwise similar-looking, larger object. There are, however, a variety of similar illusions which can be induced by varying other stimulus properties, such as surface material, temperature, colour, and even shape. Despite well over 100 years of research, there is little consensus about the mechanisms underpinning these illusions. In this review, I will first provide an overview of the weight illusions that have been described. I will then outline the dominant theories that have emerged over the past decade for why we consistently misperceive the weights of objects which vary in size, with a particular focus on the role of lifters' expectations of heaviness. Finally, I will discuss the magnitude of the various weight illusions and suggest how this largely overlooked facet of the topic might resolve some of the debates surrounding the cause of these misperceptions of heaviness.

Measuring psychometric functions with the diffusion model

The diffusion decision model (Ratcliff, 1978) was used to examine discrimination for a range of perceptual tasks: numerosity discrimination, number discrimination, brightness discrimination, motion discrimination, speed discrimination, and length discrimination. The model produces a measure of the quality of the information that drives decision processes, a measure termed drift rate in the model. As drift rate varies across experimental conditions that differ in difficulty, a psychometric function that plots drift rate against difficulty can be constructed. Psychometric functions for the tasks in this article usually plot accuracy against difficulty, but for some levels of difficulty, accuracy can be at ceiling. The diffusion model extends the range of difficulty that can be evaluated because drift rates depend on response times (RTs) as well as accuracy, and when RTs decrease across conditions that are all at ceiling in accuracy, then drift rates will distinguish among the conditions. Signal detection theory assumes that the variable driving performance is the z-transform of the accuracy value, and, somewhat surprisingly, this closely matches drift rate extracted from the diffusion model when accuracy is not at ceiling, but not sometimes when accuracy is high. Even though the functions are similar in the middle of the range, the interpretations of the variability in the models (e.g., perceptual variability, decision process variability) are incompatible.

Enlargement of perceived target size: intentional or natural?

This study used a soccer context to examine the relations between scores and judgments of goal sizes. In Experiment 1, 18 participants (4 women, 14 men; M age = 21.9 yr., SD = 0.9) kicked balls into 5 goals of different sizes. Participants' estimates of the goal size correlated positively with their scores. In Experiment 2, 17 participants (3 women, 14 men; M age = 22.1 yr., SD = 1.0) kicked the balls either from a standing position or while running. Participants' estimates of the goal sizes were higher when they were running. The enlargement of perceived goal size was seemingly related to scoring, and was scaled by the running action. Experiments reinforced the notion of affordance-based control. Differing views from Oriental philosophy and psychology were discussed.

Decimals are not processed automatically, not even as being smaller than one

Common fractions have been found to be processed intentionally but not automatically, which led to the conclusion that they are not represented holistically in long-term memory. However, decimals are more similar to natural numbers in their form and thus might be better candidates to be holistically represented by educated adults. To test this hypothesis, we investigated the automatic processing of decimals by college students in 4 experiments. When decimals were presented in a familiar form (e.g., 0.3, 0.05) the length of the stimuli (i.e., the number of digits) dominated performance rather than the decimal value. When controlling for the number of digits and their location within the digit string, using the place-value task, decimals were not processed automatically in either a numerical comparison task or a physical comparison task. Under the same conditions, natural numbers were processed automatically. We conclude that decimals are not represented holistically. Results of mixed pairs of a decimal and a natural number suggest that, unlike common fractions, decimals are not automatically perceived as smaller than natural numbers. We conclude that decimal place-values (e.g., tenths, hundredths) are not represented well enough to be automatically activated, and we discuss possible explanations.