Here you will find a list of some selected publications, along with their abstract and links to their downloads. The complete list can be found here.
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Perceptions of Surfaces and Forms
Purves D
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The purpose of this article is to consider the strategy that vision uses to generate perceptions of surface qualities such as brightness and color, as well as perceptions of surface form. The basic challenge that vision must contend with in elaborating these subjective experiences is linking inherently ambiguous retinal stimuli to their real-world sources in a manner that leads to successful visually guided behavior. The evidence derived from what people actually see indicates that this problem is solved in a fundamentally empirical manner - that is, by the accumulation of past experience rather than by analytical operations on visual stimulus features. |
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Visual Perception
Purves D
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The purpose of visual percepts is to generate successful behavior based on the information in retinal stimuli. When photoreceptors capture a sufficient number of photons, a series of processing steps is initiated in retinal circuitry; the outcome is then carried centrally by action potentials in the optic nerve to further processing stations in the thalamus and primary visual cortex, eventually reaching the visual association cortices. Perception - defined as what we actually see - is the result of this processing. Despite enormous progress in understanding the organization of visual circuitry over the last 50 years, how this circuitry generates percepts is not yet understood. The focus of this chapter is thus on perception as such, with the expectation that what we see can tell us much about what the underlying cicuitry is seeking to accomplish. |
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Vision and Natural Images
Purves D
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Understanding vision in terms of features detection has until recently been based on the presentation of simple stimuli to animals in the laboratory; understanding visual percepts in empirical terms has depended an analysis of natural images as a means of predicting what people actually see. The purpose of this article is to compare and contrast these approaches to explaining vision, which must eventually be brought together if vision is to be understood. |
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Visual Illusions.
Purves D,Wojtach W, Howe, C
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The evolution of biological systems that generate behaviorally useful visual percepts has inevitably been guided by many demands. Among these are: 1) the limited resolution of photoreceptor mosaics (thus the input signal is inherently noisy); 2) the limited number of neurons available at higher processing levels (thus the information in retinal images must be abstracted in some way); and 3) the demands of metabolic efficiency (thus both wiring and signaling strategies are sharply constrained). The overarching obstacle in the evolution of vision, however, was recognized several centuries ago by George Berkeley, who pointed out that the information in images cannot be mapped unambiguously back onto real-world sources (Berkeley, 1975). In contemporary terms, information about the size, distance and orientation of objects in space are inevitably conflated in the retinal image (Figure 1; the same conflation obtains for illumination, reflectance and transmittance; see ref. 2). In consequence, the patterns of light in retinal stimuli cannot be related to their generative sources in the world by any logical operation on images as such. Nonetheless, to be successful, visually guided behavior must deal appropriately with the physical sources of light stimuli, a quandary referred to as the "inverse optics problem". As briefly explained here, visual illusions appear to arise primarily from the way the visual system solves this problem. |
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Musical intervals in speech.
Ross D, Choi J, Purves D
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Throughout history and across cultures, humans have created music using pitch intervals that divide octaves into the 12 tones of the chromatic scale. Why these specific intervals in music are preferred, however, is not known. In the present study we analyzed a database of individually spoken English vowel phones to examine the hypothesis that musical intervals arise from the relationships of the formants in speech spectra that determine the perceptions of distinct vowels. Expressed as ratios, the frequency relationships of the first two formants in vowel phones represent all 12 intervals of the chromatic scale. Were the formants to fall outside the ranges found in the human voice, their relationships would generate either a less complete or a more dilute representation of these specific intervals. These results imply that human preference for the intervals of the chromatic scale arises from experience with the way speech formants modulate laryngeal harmonics to create different phonemes. |
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Evolution of visually-guided behavior in artificial agents.
Boots B, Nundy S, Purves D
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Recent work on brightness, color and form has suggested that human visual percepts represent the probable sources of retinal images rather than stimulus features as such. Here we investigate the plausibility of this empirical concept of vision by allowing autonomous agents to evolve in virtual environments based solely on the relative success of their behavior. The responses of evolved agents to visual stimuli indicate that fitness improves as the neural network control systems gradually incorporate the statistical relationship between projected images and behavior appropriate to the sources of the inherently ambiguous images. These results: 1) demonstrate the merits of a wholly empirical strategy of animal vision as a means of contending with the inverse optics problem; 2) argue that the information incorporated into biological visual processing circuitry is the relationship between images and their probable sources; and 3) suggest why human percepts do not map neatly onto physical reality. |
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Comparison of Bayesian and empirical ranking approaches to visual perception
Howe CQ, Lotto RB, Purves D
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Much current vision research is predicated on the ideaand a rapidly growing body of evidencethat visual percepts are generated according to the empirical significance of light stimuli rather than their physical characteristics. As a result, an increasing number of investigators have asked how visual perception can be rationalized in these terms. Here, we compare two different theoretical frameworks for predicting what observers actually see in response to visual stimuli: Bayesian decision theory and empirical ranking theory. Deciding which of these approaches has greater merit is likely to determine how the statistical operations that apparently underlie visual perception are eventually understood. |
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Spectral statistics in natural scenes predict hue, saturation, and brightness
Long F, Yang Z, Purves D
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The perceptual color qualities of hue, saturation, and brightness do not correspond in any simple way to the physical characteristics of retinal stimuli, a fact that poses a major obstacle for any explanation of color vision. Here we test the hypothesis that these basic color attributes are determined by the statistical covariations in the spectral stimuli that humans have always experienced in typical visual environments. Using a database of 1,600 natural images, we analyzed the joint probability distributions of the physical variables most relevant to each of these perceptual qualities. The cumulative density functions derived from these distributions predict the major colorimetric functions that have been reported in psychophysical experiments over the last century. |
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The wagon wheel illusion in continuous light
Andrew, TJ, Purves D
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The fact that a perceptual experience akin to the familiar wagon-wheel illusion in movies and on TV can occur in the absence of stroboscopic presentation is intriguing because of its relevance to visuo-temporal parsing. The wagon-wheel effect in continuous light has also been the source of considerable misunderstanding and dispute, as is apparent in a series of recent papers. Here we review this potentially confusing evidence and suggest how it should be interpreted. |
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The Poggendorff illusion explained by natural scene geometry
Howe CQ, Yang Z, Purves D
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One of the most intriguing of the many discrepancies between perceived spatial relationships and the physical structure of visual stimuli is the Poggendorff illusion, when an obliquely oriented line that is interrupted no longer appears collinear. Although many different theories have been proposed to explain this effect, there has been no consensus about its cause. Here, we use a database of range images (i.e., images that include the distance from the image plane of every pixel in the scene) to show that the probability distribution of the possible locations of line segments across an interval in natural environments can fully account for all of the behavior of this otherwise puzzling phenomenon. |
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Natural scene geometry predicts the perception of angles and line orientation
Howe CQ, Purves D
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Visual stimuli that entail the intersection of two or more straight lines elicit a variety of well known perceptual anomalies. Preeminent among these anomalies are the systematic overestimation of acute angles, the underestimation of obtuse angles, and the misperceptions of line orientation exemplified in the classical tilt, Zllner, and Hering illusions. Here we show that the probability distributions of the possible real-world sources of projected lines and angles derived from a range-image database of natural scenes accurately predict each of these perceptual peculiarities. These findings imply that the perception of angles and oriented lines is determined by the statistical relationship between geometrical stimuli and their physical sources in typical visual environments.
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The Mller-Lyer illusion explained by the statistics of image-source relationships
Howe CQ, Purves D
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The Mller-Lyer effect, the apparent difference in the length of a line as the result of its adornment with arrowheads or arrow tails, is the best known and most controversial of the classical geometrical illusions. By sampling a range-image database of natural scenes, we show that the perceptual effects elicited by the Mller-Lyer stimulus and its major variants are correctly predicted by the probability distributions of the possible physical sources underlying the relevant retinal images. These results support the conclusion that the Mller-Lyer illusion is a manifestation of the probabilistic strategy of visual processing that has evolved to contend with the uncertain provenance of retinal stimuli.
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Pitch is determined by naturally occurring periodic sounds
Schwartz, DA, Purves D
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The phenomenology of pitch has been difficult to rationalize and remains the subject of much debate. Here we test the hypothesis that audition generates pitch percepts by relating inherently ambiguous sound stimuli to their probable sources in the human auditory environment. A database of speech sounds, the principal source of periodic sound energy for human listeners, was compiled and the dominant periodicity of each speech sound determined. A set of synthetic test stimuli were used to assess whether the major pitch phenomena described in the literature could be explained by the probabilistic relationship between the stimuli and their probable sources (i.e., speech sounds). The phenomena tested included the perception of the missing fundamental, the pitch-shift of the residue, spectral dominance and the perception of pitch strength. In each case, the conditional probability distribution of speech sound periodicities accurately predicted the pitches normally heard in response to the test stimuli. We conclude from these findings that pitch entails an auditory process that relates inevitably ambiguous sound stimuli to their probable natural sources.
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The statistical structure of natural light patterns determines perceived light intensity
Yang Z, Purves D
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The same target luminance in different contexts can elicit markedly different perceptions of brightness, a fact that has long puzzled vision scientists. Here we test the proposal that the visual system encodes not luminance as such but rather the statistical relationship of a particular luminance to all possible luminance values experienced in natural contexts during evolution. This statistical conception of vision was validated by using a database of natural scenes in which we could determine the probability distribution functions of co-occurring target and contextual luminance values. The distribution functions obtained in this way predict target brightness in response to a variety of challenging stimuli, thus explaining these otherwise puzzling percepts. That brightness is determined by the statistics of natural light patterns implies that the relevant neural circuitry is specifically organized to generate these probabilistic responses.
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Perceiving the intensity of light
Purves D, Williams SM, Nundy S, Lotto RB
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The relationship between luminance (i.e., the photometric intensity of light) and its perception (i.e., sensations of lightness or brightness) has long been a puzzle. In addition to the mystery of why these perceptual qualities do not scale with luminance in any simple way, "illusions" such as simultaneous brightness contrast, Mach bands, Craik-O'Brien-Cornsweet edge effects, and the Chubb-Sperling-Solomon illusion have all generated much interest but no generally accepted explanation. The authors review evidence that the full range of this perceptual phenomenology can be rationalized in terms of an empirical theory of vision. The implication of these observations is that perceptions of lightness and brightness are generated according to the probability distributions of the possible sources of luminance values in stimuli that are inevitably ambiguous.
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Size contrast and assimilation explained by the statistics of scene geometry
Howe CQ, Purves D
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The term "size contrast and assimilation" refers to a large class of geometrical illusions in which the apparent sizes of identical visual targets in various contexts are different. Here we have examined whether these intriguing discrepancies between physical and perceived size can be explained by a visual process in which percepts are determined by the probability distribution of the possible real-world sources of retinal stimuli. To test this idea, we acquired a range image database of natural scenes that specified the location of every image point in 3-D space. By sampling the possible physical sources of various size contrast or assimilation stimuli in the database, we determined the probability distributions of the size of the target in the images generated by these sources. For each of the various stimuli tested, these probability distributions of target size in different contexts accurately predicted the perceptual effects reported in psychophysical studies. We conclude that size contrast and assimilation effects are a further manifestation of a fundamentally probabilistic process of visual perception.
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Perceiving Colour
Lotto RB, Purves D
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Understanding the percepts elicited by spectral distributions in visual stimuli (i.e. understanding the perception of colour) is made especially challenging by the peculiar phenomenology of colour contrast and constancy effects. Interestingly, the first systematic account of colour contrast was published in 1839 by the French chemist Michel Chevreul based on work done while serving as the director of dyes for the Royal Manufacturers. In this current paper we review the nature of colour vision, the problems that the observations of Chevreul and others present for colour science, and recent work that suggests a solution.
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Why we see what we do: An empirical theory of vision
Lotto RB, Purves D
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Beau Lotto and Dale Purves discuss the mechanisms by which we see what we do, and explain that we tend to see what a visual scene hsa typically signified in the past, rather than what it actually is in the present.
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Cornsweet Effect
Purves D, Lotto RB
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The Cornsweet stimulus is a specific instance of a broad class of edge effects first described by Kenneth Craik in the 1940s. Like standard stimuli used to elicit simultaneous brightness contrast, the stimulus generates a perception of brightness (or lightness) that fails to tally with photometric measurements; the Cornsweet stimulus, however, is quite different in structure from standard brightness contrast stimuli, depending on opposing light gradients that meet at an edge.
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Natural scene statistics as the universal basis for color context effects
Long F, Purves D
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The color context effects referred to as color contrast, constancy, and assimilation underscore the fact that color percepts do not correspond to the spectral characteristics of the generative stimuli. Despite a variety of proposed theories, these phenomena have resisted explanation in a single principled framework. Using a hyperspectral image database of natural scenes, we here show that color contrast, constancy, and assimilation are all predicted by the statistical organization of spectral returns from natural visual environments.
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Image/source statistics of surfaces in natural scenes
Yang, Z, Purves, D
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Perceiving surfaces in a manner that accords with their physical properties is essential for successful behaviour. Since, however, a given retinal image can have been generated by an infinite variety of natural surfaces with different geometrical and/or physical qualities, the corresponding percepts cannot be determined by the stimulus per se. Rather, resolution of this quandary requires a strategy of vision that incorporates the statistical relationship of the information in retinal images to its sources in representative environments. To examine this probabilistic relationship with respect to the features of object surfaces, we analysed a database of range images in which the distances of all the objects in a series of natural scenes were measured with respect to the image plane by a laser range scanner. By taking any particular scene obtained in this way to be made up of a set of concatenated surface patches, we were able to explore the statistics of scene roughness, sizedistance relationships, surface orientation and local curvature, as well as the independent components of natural surfaces. The relevance of these statistics to both perception and the neuronal organization of the underlying visual circuitry is discussed.
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The statistical structure of human speech sounds predicts musical universals
Schwartz, DA, Howe, CQ, Purves D
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The similarity of musical scales and consonance judgments across human populations has no generally accepted explanation. Here we present evidence that these aspects of auditory perception arise from the statistical structure of naturally occurring periodic sound stimuli. An analysis of speech sounds, the principal source of periodic sound stimuli in the human acoustical environment, shows that the probability distribution of amplitude-frequency combinations in human utterances predicts both the structure of the chromatic scale and consonance ordering. These observations suggest that what we hear is determined by the statistical relationship between acoustical stimuli and their naturally occurring sources, rather than by the physical parameters of the stimulus per se.
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A statistical explanation of visual space
Yang, Z, Purves, D
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The subjective visual space perceived by humans does not reflect a simple transformation of objective physical space; rather, perceived space has an idiosyncratic relationship with the real world. To date, there is no consensus about either the genesis of perceived visual space or the implications of its peculiar characteristics for visually guided behavior. Here we used laser range scanning to measure the actual distances from the image plane of all unoccluded points in a series of natural scenes. We then asked whether the differences between real and apparent distances could be explained by the statistical relationship of scene geometry and the observer. We were able to predict perceived distances in a variety of circumstances from the probability distribution of physical distances. This finding lends support to the idea that the characteristics of human visual space are determined probabilistically.
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Perception of objects that are translating and rotating
Yang Z, Shimpi A, Purves D
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The motion of objects that are both translating and rotating can be decomposed into an infinite number of translational and rotational combinations. How, then, do such stimuli routinely elicit specific percepts and behavioral responses that are usually appropriate? A possible answer is that motion percepts are fully determined by the probability distributions of all the possible correspondences and differences in the stimulus sequence. To test the merits of this conceptual framework, we investigated the perceived motion elicited by a line that is both translating and rotating behind an aperture. When stimuli are presented such that a particular sequence of appearance and disappearance occurs at the aperture boundary, subjects report that the line is rotating only; furthermore, the perceived centers of rotation appear to describe a cycloidal trajectory, even when one aperture shape is replaced by another. These and other perceptual effects elicited by translating and rotating stimuli are all accurately predicted by the probability distribution of the possible sources of the physical movements, supporting the conclusion that motion perception is indeed generated by a wholly probabilistic strategy.
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A probabilistic explanation of brightness scaling
Nundy S, Purves D
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The perceptions of lightness or brightness elicited by a visual target are linked to its luminance by a nonlinear function that varies according to the physical characteristics of the target and the background on which it is presented. Although no generally accepted explanation of this scaling relationship exists, it has long been considered a byproduct of low- or mid-level visual processing. Here we examine the possibility that brightness scaling is actually the signature of a biological strategy for dealing with inevitably ambiguous visual stimuli, in which percepts of lightness/brightness are determined by the probabilistic relationship between luminances in the image plane and their possible real-world sources.
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The empirical basis of color perception
Lotto RB, Purves D
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Rationalizing the perceptual effects of spectral stimuli has been a major challenge in vision science for at least the last 200 years. Here we review evidence that this otherwise puzzling body of phenomenology is generated by an empirical strategy of perception in which the color an observer sees is entirely determined by the probability distribution of the possible sources of the stimulus. The rationale for this strategy in color vision, as in other visual perceptual domains, is the inherent ambiguity of the real-world origins of any spectral stimulus.
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Range image statistics can explain the anomalous perception of length
Howe CQ, Purves D
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A long-standing puzzle in visual perception is that the apparent extent of a spatial interval (e.g., the distance between two points or the length of a line) does not simply accord with the length of the stimulus but varies as a function of orientation in the retinal image. Here, we show that this anomaly can be explained by the statistical relationship between the length of retinal projections and the length of their real-world sources. Using a laser range scanner, we acquired a database of natural images that included the three-dimensional location of every point in the scenes. An analysis of these range images showed that the average length of a physical interval in three-dimensional space changes systematically as a function of the orientation of the corresponding interval in the projected image, the variation being in good agreement with perceived length. This evidence implies that the perception of visual space is determined by the probability distribution of the possible real-world sources of retinal images.
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Why we see what we do
Purves D, Lotto RB, Nundy S
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The visual information that reaches the eye cannot uniquely describe the physical world. Because light arising from different physical objects can stimulate the retina in the same way, the source of a light stimulus is inevitably ambiguous. For example, a large object far away and a small one closer by can generate exactly the same retinal image. The visual port of the brain resolves this ambiguity by assigning appropriate values of brightness, color and geometry to the things we see. Purves, Lotto and Nundy argue that this assignment is made on a wholly probabilistic basis: What observers see in any circumstance is simply what the stimulus has typically signified in the past, indicated by behavioral success or failure.
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A rationale for the structure of color space
Lotto RB, Purves D
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The colors perceived by humans in response to light stimuli are generally described in terms of four color categories (reds, greens, blues and yellows), the members of which are systematically arrayed around gray. This broadly accepted description of color sensation differs fundamentally from the light that induces it, which is neither circular nor categorical. What, then, accounts for these discrepancies between the structure of color experience and the physical reality that underlies it? We suggest that these differences are based on two related requirements for successful color vision: (1) that spectra be ordered according to their physical similarities and differences; and (2) that this ordering be constrained by the four-color map problem.
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An empirical explanation of the Chubb illusion
Lotto RB, Purves D
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The perceived difference in brightness between elements of a patterned target is diminished when the target is embedded in a similar surround of higher luminance contrast (the Chubb illusion). Here we show that this puzzling effect can be explained by the degree to which imperfect transmittance is likely to have affected the light that reaches the eye. These observations indicate that this illusion is yet another signature of the fundamentally empirical strategy of visual perception, in this case generated by the typical influence of transmittance on inherently ambiguous stimuli.
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Why we see things the way we do: Evidence for a wholly empirical strategy of vision
Purves D, Lotto RB, Williams SM, Nundy S, Yang, Z
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Many otherwise puzzling aspects of the way we see brightness, colour, orientation and motion can be understood in wholly empirical terms. The evidence reviewed here leads to the conclusion that visual percepts are based on patterns of reflex neural activity shaped entirely by the past success (or failure) of visually guided behaviour in response to the same or a similar retinal stimulus. As a result, the images we see accord with what the sources of the stimuli have typically turned out to be, rather than with the physical properties of the relevant objects. If vision does indeed depend upon this operational strategy to generate optimally useful perceptions of inevitably ambiguous stimuli, then the underlying neurobiological processes will eventually need to be understood within this conceptual framework.
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A wholly empirical explanation of perceived motion
Yang Z, Shimpi A, Purves D
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Because the retinal activity generated by a moving object cannot specify which of an infinite number of possible physical displacements underlies the stimulus, its real-world cause is necessarily uncertain. How, then, do observers respond successfully to sequences of images whose provenance is ambiguous? Here we explore the hypothesis that the visual system solves this problem by a probabilistic strategy in which perceived motion is generated entirely according to the relative frequency of occurrence of the physical sources of the stimulus. The merits of this concept were tested by comparing the directions and speeds of moving lines reported by subjects to the values determined by the probability distribution of all the possible physical displacements underlying the stimulus. The velocities reported by observers in a variety of stimulus contexts can be accounted for in this way.
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The relevance of visual perception to cortical evolution and development
Purves D, Williams SM, Lotto RB
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The quality of brightness - perhaps the simplest visual attribute we perceive - appears to be determined probabilistically. In this empirical conception of the perception of light, the stimulus-induced activity of visual cortical neurons does not encode the retinal image or the properties of the stimulus per se, but associations (percepts) determined by the relative probabilities of the possible sources of the stimulus. If this theory is correct, the rationale for the prolonged postnatal construction of visual circuitry - and the evolution of this visual scheme - is to strengthen and/or create by activity-dependent feedback the empirically determined associations on which vision depends.
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An empirical explanation of color contrast
Lotto, RB, Purves D
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For reasons not well understood, the color of a surface can appear quite different when placed in different chromatic surrounds. Here we explore the possibility that these color contrast effects are generated according to what the same or similar stimuli have turned out to signify in the past about the physical relationships between reflectance, illumination, and the spectral returns they produce. This hypothesis was evaluated by (i) comparing the physical relationships of reflectances, illuminants, and spectral returns with the perceptual phenomenology of color contrast and (ii) testing whether perceptions of color contrast are predictably changed by altering the probabilities of the possible sources of the stimulus. The results we describe are consistent with a wholly empirical explanation of color contrast effects.
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Why are angles misperceived?
Nundy S, Lotto B, Coppola D, Shimpi A, Purves D
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Although it has long been apparent that observers tend to overestimate the magnitude of acute angles and underestimate obtuse ones, there is no consensus about why such distortions are seen. Geometrical modeling combined with psychophysical testing of human subjects indicates that these misperceptions are the result of an empirical strategy that resolves the inherent ambiguity of angular stimuli by generating percepts of the past significance of the stimulus rather than the geometry of its retinal projection.
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Color vision and the four-color-map problem
Purves D, Lotto B, Polger T
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Four different colors are needed to make maps that avoid adjacent countries of the same color. Because the retinal image is two dimensional, like a map, four dimensions of chromatic experience would also be needed to optimally distinguish regions returning spectrally different light to the eye. We therefore suggest that the organization of human color vision according to four-color classes (reds, greens, blues, and yellows) has arisen as a solution to this logical requirement in topology.
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Interindividual variation in human visual performance
Halpern, SD, Andrews TJ, Purves D
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The responses of 20 young adult emmetropes with normal color vision were measured on a battery of visual performance tasks. Using previously documented tests of known reliability, we evaluated orientation discrimination, contrast sensitivity, wavelength sensitivity, vernier acuity, direction-of-motion detection, velocity discrimination, and complex form identification. Performance varied markedly between individuals, both on a given test and when the scores from all tests were combined to give an overall indication of visual performance. Moreover, individual performances on tests of contrast sensitivity, orientation discrimination, wavelength discrimination, and vernier acuity covaried, such that proficiency on one test predicted proficiency on the others. These results indicate a wide range of visual abilities among normal subjects and provide the basis for an overall index of visual proficiency that can be used to determine whether the surprisingly large and coordinated size differences of the components of the human visual system (Andrews, Halpern, & Purves, 1997) are reflected in corresponding variations in visual performance.
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The effects of color on brightness
Lotto, RB, Purves D
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Observation of human subjects shows that the spectral returns of equiluminant colored surrounds govern the apparent brightness of achromatic test targets. The influence of color on brightness provides further evidence that perceptions of luminance are generated according to the empirical frequency of the possible sources of visual stimuli, and suggests a novel way of understanding color contrast and constancy.
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An empirical explanation of the Cornsweet effect
Purves D, Shimpi A, Lotto RB
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A long-standing puzzle in vision is the assignment of illusory brightness values to visual territories based on the characteristics of their edges (the Craik-O'Brien-Cornsweet effect). Here we show that the perception of the equiluminant territories flanking the Cornsweet edge varies according to whether these regions are more likely to be similarly illuminated surfaces having the same material properties or unequally illuminated surfaces with different properties. Thus, if the likelihood is increased that these territories are surfaces with similar reflectance properties under the same illuminant, the Craik-O'Brien-Cornsweet effect is diminished; conversely, if the likelihood is increased that the adjoining territories are differently reflective surfaces receiving different amounts of illumination, the effect is enhanced. These findings indicate that the Craik-O'Brien-Cornsweet effect is determined by the relative probabilities of the possible sources of the luminance profiles in the stimulus.
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Mach bands as empirically derived associations
Lotto RB, Williams SM, Purves D
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If Mach bands arise as an empirical consequence of real-world luminance profiles, several predictions follow. First, the appearance of Mach bands should accord with the appearance of naturally occurring highlights and lowlights. Second, altering the slope of an ambiguous luminance gradient so that it corresponds more closely to gradients that are typically adorned with luminance maxima and minima in the position of Mach bands should enhance the illusion. Third, altering a luminance gradient so that it corresponds more closely to gradients that normally lack luminance maxima and minima in the position of Mach bands should diminish the salience of the illusion. Fourth, the perception of Mach bands elicited by the same luminance gradient should be changed by contextual cues that indicate whether the gradient is more or less likely to signify a curved or a flat surface. Because each of these predictions is met, we conclude that Mach bands arise because the association elicited by the stimulus (the percept) incorporates these features as a result of past experience.
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An empirical basis for Mach bands
Lotto RB, Williams SM, Purves D
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Mach bands, the illusory brightness maxima and minima perceived at the initiation and termination of luminance gradients, respectively, are generally considered a direct perceptual manifestation of lateral inhibitory interactions among retinal or other lower order visual neurons. Here we examine an alternative explanation, namely that Mach bands arise as a consequence of real-world luminance gradients. In this first of two companion papers, we analyze the natural sources of luminance gradients, demonstrating that real-world gradients arising from curved surfaces are ordinarily adorned by photometric highlights and lowlights in the position of the illusory bands. The prevalence of such gradients provides an empirical basis for the generation of this perceptual phenomenon.
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An empirical explanation of brightness
Williams, SM, McCoy AN, Purves D
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In this second part of our study on the mechanism of perceived brightness, we explore the effects of manipulating three-dimensional geometry. The additional scenes portrayed here demonstrate that the same luminance profile can elicit different sensations of brightness as a function of how the objects in the scene are arranged in space. This further evidence confirms the implication of the scenes presented in the accompanying paper, namely that sensations of relative brightness - including standard demonstrations of simultaneous brightness contrast - cannot arise by computations of local contrast. The most plausible explanation of the full range of perceptual phenomena we have described is an empirical strategy that links the luminance profile in a visual stimulus with an association (the percept) that represents the profile's most probable real-world source.
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The influence of depicted illumination on perceived brightness
Williams, SM, McCoy AN, Purves D
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The striking illusions produced by simultaneous brightness contrast generally are attributed to the center-surround receptive field organization of lower order neurons in the primary visual pathway. Here we show that the apparent brightness of test objects can be either increased or decreased in a predictable manner depending on how light and shadow are portrayed in the scene. This evidence suggests that perceptions of brightness are generated empirically by experience with luminance relationships, an idea whose implications we pursue in the accompanying paper.
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The distribution of oriented contours in the real world
Coppola DM, Purves HR, McCoy AN, Purves D
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In both humans and experimental animals, the ability to perceive contours that are vertically or horizontally oriented is superior to the perception of oblique angles. There is, however, no consensus about the developmental origins or functional basis of this phenomenon. Here, we report the analysis of a large library of digitized scenes using image processing with orientation-sensitive filters. Our results show a prevalence of vertical and horizontal orientations in indoor, outdoor, and even entirely natural settings. Because visual experience is known to influence the development of visual cortical circuitry, we suggest that this real world anisotropy is related to the enhanced ability of humans and other animals to process contours in the cardinal axes, perhaps by stimulating the development of a greater amount of visual circuitry devoted to processing vertical and horizontal contours.
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Unequal representation of cardinal and oblique contours in ferret visual cortex
Coppola DM, White LE, Fitzpatrick D, Purves D
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We have measured the amount of cortical space activated by differently oriented gratings in 25 adult ferrets by optical imaging of intrinsic signal. On average, 7% more area of the exposed visual cortex was preferentially activated by vertical and horizontal contours than by contours at oblique angles. This anisotropy may reflect the real-world prevalence of contours in the cardinal axes and could explain the greater sensitivity of many animals to vertical and horizontal stimuli.
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