Perceiving geometry. Geometrical illusions explained by natural scene statistics

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Visual perception is a daunting task for the brain, explains Purves, because light streaming into the eye carries only ambiguous information about the environment. Nevertheless, many neurobiologists have attempted to explain vision by postulating that the brain's neural wiring can definitively "calculate" the features of a visual scene, despite the visual world's inevitable ambiguity.

New Book Explains Age-Old Mystery Of Geometrical Illusions

Such "rule-based" theories, said Purves, have arisen because neurobiologists have concentrated on understanding how neurons in the brain's visual region extract and recognize specific features such as edges in a visual scene. There was no instance, even in the simplest aspects of vision, where the properties of visual neurons in the brain explain the brightness, colors or forms that we actually see.


Thus, Purves and his colleagues began exploring visual illusions -- the name given to the more obvious discrepancies between the physical world and the way people see it -- to understand the strategy the brain uses in perceiving the world. Basically, they statistically compared perceptions -- such as the apparent length of a line -- with physical measurements of what the line stimulus on the retina was most likely to represent in the real world. This sort of analysis, made by measuring a large set of geometrical images with a device called a laser range scanner, showed that the brain is not a calculating engine, cranking out stimulus features, but a "statistical engine" wired by evolution and a person's experience to make the best statistical guess about objects in a visual scene, based on how successful those guesses have been in the past.

Received 10 January ; received in revised form 12 November ; accepted 12 November Available online 25 November One of the major issues in investigations of the visual distance, direction, angle, and size.

Studies on judgments perception of space is specification of the geometrical of exocentric distance i. Both factors influenced distance b. Specification of the geometrical properties of judgments independently. A larger observation distance visual space implies determination of the relationships implied foreshortening of the perceived exocentric between the geometrical features of visual space such as distance.

The visual angle effect was not as straightforward. Matsushima, Aline M. Vaz, and Rafael A. Cazuza, that the overestimating of exocentric distances decreased Department of Psychology, Institute of Psychology, Universidade Federal Fluminense. Nilton P. Ribeiro Filho, as the visual angles increased.

Perception and the Ever-Elusive Ellipse. | Art and Articles

Correspondence regarding this article should be distance. The authors showed that spatial orientation of directed to: Elton H. Email: eh. This model established that perceived exocentric were evaluated, focusing on the potential influence of distance was determined by the two egocentric distances the former geometrical feature over the latter. Aznar- and visual angle subtended by the exocentric distance. Casanova et al. They suggested that the processing of the spatial orientation of an exocentric interval Thirty undergraduate students, aged years depends on the prior processing of exocentric distance, mean age, In another study, Aznar-Casanova to the experimental hypothesis and untrained in the et al.

Their findings suggested that the processing binocular and monocular.

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The participants provided of exocentric direction depends on the processing of informed consent before being enrolled in the study. The processing of exocentric distance did not depend on Experimental environment the processing of exocentric direction. They suggested The experiments were conducted in a visual alley that exocentric distance and direction are hierarchically 1.

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The table was located other relationships between exocentric distance and 0. The study investigated inside a dark observation cabin with a fixed chin rest and these relationships under full cue conditions in response platform 0. The large-scale environments using a task in which the observation point was 0. More specifically, the the visual alley to illuminate the experimental scene.

Then they had to turn their Stimuli and apparatus bodies to align their heading to the orientation of that The stimuli were seven blue rubber spheres 5. Their results indicated that the observers diameter with a white identifying letter approximately were accurate in this exocentric direction judgment as 1. The The present study sought to determine the stimuli were placed on the table as depicted in Figure 1 relationship between judgments of ego- and exocentric with the following Cartesian coordinates: E One may The judgments were accomplished using a compass with legs that were adjustable in length, which allowed independent judgments of exocentric direction and two egocentric directions.

Another expected result was independence between perceived egocentric and exocentric directions, in which the processing of exocentric direction depends on the coding of exocentric distance Aznar-Casanova et al. Additionally, one may suppose that exocentric direction is also independent of the processing of egocentric direction, in which the processing of exocentric direction depends on the processing of egocentric distance but not egocentric direction. This statement was based on the model of perceived exocentric distance proposed by Figure 1. Physical spatial layout of the stimuli.

Ego- and exocentric direction in visual space J A then had to adjust the length of the leg until the imaginary wooden chin rest kept a fixed observation point at a 1. In the second part of the task, the observers non-dominant eye in the monocular visual modality had to adjust the length of the compass legs so that the group. Binaural acoustic isolators minimized external orientation of the spatial interval between the endpoints noise while preserving the hearing of instructions.

This Experimental design psychophysical task can be conceived as the magnitude The experiment had a mixed between-groups and production of perceived directions. For The research assistant asked the observers to each of these spatial orientations, three measurements raise the binocular mask and adjust the opening of the were taken: the two produced egocentric directions and compass so that each leg pointed to a stimulus of the the angle of produced exocentric direction. The observers then adjusted the length of each leg to match the standard exocentric direction.

The participants were free to make corrections in their Procedures responses. There was no time constraint on the responses, As shown in Figure 2A, the participants were given but the participants took less than 10 s to make their objective instructions that asked them to adjust the response. A Figure presented to observers. Gray circles represent a pair of stimuli that would be indicated by a research assistant. The two dashed lines represent the spatial intervals of stimuli and endpoints of compass legs.

B Photograph of the actual experimental environment. Gray lines that connect a pair of stimuli and the endpoints of compass legs were digitally added to the photograph to indicate the standard and comparison exocentric directions. Measurements were taken a posteriori Analysis of egocentric direction using two points marked on a white card These points were perpendicular direction angles of each leg as a function of the standard projections of the endpoints of the compass legs.

The former in conditions, thus ruling out the hypothesis of a uniform was the angle subtended by each compass leg and the distribution of angles in our samples. Directional data are in interval level of measurement, considering that the position of zero is arbitrary. For statistical inference, when comparing two means, the Watson-Williams F test for independent samples compares means from two independent samples of angles, and the F test for related samples compares two means that originated from the same sample.

For measuring the association between two angular variables, there is the circular correlation raa. Descriptive and inferential statistics were calculated using BioEstat 5. Figure 4. Mean angles of comparison egocentric directions as a function of standard egocentric direction, in degrees. The upper panel summarizes the left leg angles. The lower panel summarizes the right leg angles.

Filled circles represent monocular group judgments, and empty circles represent binocular group judgments. Vertical bars represent angular deviations and are depicted in a single direction for better presentation in the figure. Larger caps represent monocular Figure 3. Angles extracted from the judgments. The dashed line represents accuracy. The represent the angles of the produced egocentric directions, and angle solid line represents the linear regression of the binocular group. Ego- and exocentric direction in visual space analyses.

The slopes of linear functions that fit the isosceles triangles. Binocular perception, we compared visual angles of the spatial information, such as binocular disparity and fusional intervals with similar magnitudes and that formed vergence, did not appear to provide any advantage in isosceles and scalene layouts. Although the angle angular processing. Thus, modalities and two legs of the slopes did not reveal constant errors were used in the analysis. One must conclude et al.

Perceptual similarity and the neural correlates of geometrical illusions in human brain structure

All of the angles of that the effect of the global shape of the layout should egocentric direction in the present study ranged from be restricted to angles in frontoparallel presentations 2. This Kennedy et al. This would be accomplished , 10 pairs of stimuli could be matched in pairs by the relative frequencies of origins that underlie the according to their angle magnitude in the two groups: retinal projections experienced by the observers during one with longer legs and one with shorter legs.

The their history of interactions with similar visual scenes. The former of a leg-length effect Table 2. The leg-length effect on effect states that angles of the same magnitude in angle perception appears to be restricted to angles that scalene triangles are perceived as less obtuse than in are presented in the frontoparallel plane. Table 1. Mean visual angles of spatial intervals and their constant errors CE as a function of stimulus pairs with angles of similar magnitude relative to their physical angles and a classification of their layouts as isosceles or scalene for both visual modalities. Table 2. Mean visual angles of spatial intervals and their constant errors CE as a function of stimulus pairs with angles of similar magnitude relative to their physical angles and leg length longer or shorter for both visual modalities. Mono, monocular; Bino, binocular.

One must conclude that the most adequate explanation overestimating horizontally oriented distances and for the pattern of perceived egocentric directions was the underestimating distances aligned in depth Beusmans, statistical approach of the visual system to determine the ; Foley, ; Foley et al. Figure 5 shows a trend from the overestimation of smaller exocentric direction angles toward accuracy for larger angles that were closer to a right angle. This pattern was further investigated by separating the exocentric direction angles as a function of the spatial orientation based on the criteria of Haber Figure 5.

Mean angles of comparison exocentric directions as a Furthermore, accuracy was observed for comparison function of standard exocentric directions. Larger caps represent monocular group angular deviations. The The overestimation of exocentric direction angles dashed line represents accuracy.

The continuous line represents the at radial intervals is consistent with the anisotropy of linear regression of the binocular group. The dotted line represents the perceived visual space, a phenomenon associated with linear regression of the monocular group. These two phenomena between the perceptual processing of egocentric compress the spatial layout in its depth dimension and directions and exocentric directions using a task that enlarge it in the horizontal dimension, generating effects independently provided both perceptual variables in a on the perceived exocentric directions and distances.