PUBLICATIONS

The following is a list of some recent publications from the lab, along with the abstract and download links. A complete list of Purves’ publications can be found here.

The Demands of Geometry on Color Vision

Authors: Dale Purves ^1,2,3,* and Chidambaram Yegappan¹Affiliations: Neuroscience and Behavioral Disorders Program, Duke-NUS Graduate Medical School Singapore
Department of Neurobiology, Duke University Medical Center
Duke Institute for Brain Sciences

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While studies of human color vision have made enormous strides, an overarching rationale for the circular sense of color relationships generated by two classes of color opponent neurons and three cone types is still lacking. Here we suggest that color circularity, color opponency and trichromacy may have arisen, at least in part, because of the geometrical requirements needed to unambiguously distinguish all possible spectrally different regions on a plane.

Perception and Reality: Why a Wholly Empirical Paradigm is Needed to Understand Vision

Authors: Dale Purves¹, Yaniv Morgenstern² and William T. Wojtach^1,2
Affiliations: ¹Duke Institute for Brain Sciences, Duke University
²Duke-NUS Graduate Medical School, Singapore
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A central puzzle in vision science is how perceptions that are routinely at odds with physical measurements of real world properties can arise from neural responses that nonetheless lead to effective behaviors. Here we argue that the solution depends on: (1) rejecting the assumption that the goal of vision is to recover, however imperfectly, properties of the world; and (2) replacing it with a paradigm in which perceptions reflect biological utility based on past experience rather than objective features of the environment. Present evidence is consistent with the conclusion that conceiving vision in wholly empirical terms provides a plausible way to understand what we see and why.

A Biological Rationale for Musical Consonance

Authors: Daniel L. Bowling¹ and Dale Purves²
Affiliations: ¹Department of Cognitive Biology, University of Vienna
²Duke Institute for Brain Science, Duke University; Corresponding authors
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The basis of musical consonance has been debated for centuries without resolution. Three interpretations have been considered: 1) that consonance derives from the mathematical simplicity of small integer ratios; 2) that consonance derives from the physical absence of interference between harmonic spectra; and 3) that consonance derives from the advantages of recognizing biological vocalization, human vocalization in particular. Whereas the mathematical and physical explanations are at odds with the evidence that has now accumulated, biology provides a plausible explanation for this central issue in music and audition.

Will Understanding Vision Require a Wholly Empirical Paradigm?

Purves D, Morgenstern Y and Wojtach WT (2015) Will Understanding Vision Require a Wholly Empirical Paradigm? Front. Psychol. 6:1072. doi: 10.3389/fpsyg.2015.01072
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Based on electrophysiological and anatomical studies, a prevalent conception is that the visual system recovers features of the world from retinal images to generate perceptions and guide behavior. This paradigm, however, is unable to explain why visual perceptions differ from physical measurements, or how behavior could routinely succeed on this basis. An alternative is that vision does not recover features of the world, but assigns perceptual qualities empirically by associating frequently occurring stimulus patterns with useful responses on the basis of survival and reproductive success. The purpose of the present article is to briefly describe this strategy of vision and the evidence for it.

Properties of artificial networks evolved to contend with natural spectra

Morgenstern, Y, Rostami, M, Purves, D (2014) Properties of artificial networks evolved to contend with natural spectra. Proc Natl Acad Sci, 111(3): 10868-10872.
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Understanding why spectra that are physically the same appear different in different contexts (color contrast), whereas spectra that are physically different appear similar (color constancy) presents a major challenge in vision research. Here, we show that the responses of biologically inspired neural networks evolved on the basis of accumulated experience with spectral stimuli automatically generate contrast and constancy. The results imply that these phenomena are signatures of a strategy that biological vision uses to circumvent the inverse optics problem as it pertains to light spectra, and that double-opponent neurons in early-level vision evolve to serve this purpose. This strategy provides a way of understanding the peculiar relationship between the objective world and subjective color experience, as well as rationalizing the relevant visual circuitry without invoking feature detection or image representation.

How biological vision succeeds in the physical world.

Purves D, Monson BB, Sundararajan J, Wojtach WT (2014).
Proceedings of the National Academy of Sciences 111: 4750-4755
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Biological visual systems cannot measure the properties that define the physical world. Nonetheless, visually guided behaviors of humans and other animals are routinely successful. The purpose of this article is to consider how this feat is accomplished. Most concepts of vision propose, explicitly or implicitly, that visual behavior depends on recovering the sources of stimulus features either directly or by a process of statistical inference. Here we argue that, given the inability of the visual system to access the properties of the world, these conceptual frameworks cannot account for the behavioral success of biological vision. The alternative we present is that the visual system links the frequency of occurrence of biologically determined stimuli to useful perceptual and behavioral responses without recovering real-world properties. The evidence for this interpretation of vision is that the frequency of occurrence of stimulus patterns predicts many basic aspects of what we actually see. This strategy provides a different way of conceiving the relationship between objective reality and subjective experience, and offers a way to understand the operating principles of visual circuitry without invoking feature detection, representation, or probabilistic inference.

Why the Conventional Concept of “Visual Illusions” is Incorrect

Purves D, Wojtach, W T., Lotto, R B (2013). In: Oxford Compendium of Visual Illusions. Oxford University Press.

A common conception is that we see the world in accord with physical reality, but are sometimes fooled in special circumstances that give rise to discrepancies between reality and perception (“visual illusions”). Evidence accumulated over the last decade, however, indicates that all visual perceptions are at odds with the parameters revealed by physical measurements. Because retinal images cannot specify stimulus sources (the inverse problem), visual animals have evolved a strategy of vision based on the value of stimuli for reproductive success. Since this criterion is not determined by physics but by many factors, all visual perceptions are equally “illusory”.

Are Auditory Percepts Determined by Experience?

Monson B B, Han S E and Purves D (2013). PLoS ONE. doi: 10.1371/journal.pone.0063728
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Audition—what listeners hear—is generally studied in terms of the physical properties of sound stimuli and physiological properties of the auditory system. Based on recent work in vision, we here consider an alternative perspective that sensory percepts are based on past experience. In this framework, basic auditory qualities (e.g., loudness and pitch) are determined by the frequency of occurrence of stimulus patterns. To explore this concept of audition, we examined five well-documented psychophysical functions. The frequency of occurrence of acoustic patterns in a database of natural sound stimuli (speech) predicts some qualitative aspects of these functions, but with substantial quantitative discrepancies. This approach may offer a rationale for auditory phenomena that are difficult to explain in terms of the physical attributes of the stimuli as such.

Network Connections That Evolve to Circumvent the Inverse Optics Problem

Ng C, Sundararajan J, Hogan M, Purves D (2013). PLoS ONE 8(3): e60490. 1. doi:10.1371/journal.pone.0060490.
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A fundamental problem in vision science is how useful perceptions and behaviors arise in the absence of information about the physical sources of retinal stimuli (the inverse optics problem). Psychophysical studies show that human observers contend with this problem by using the frequency of occurrence of stimulus patterns in cumulative experience to generate percepts. To begin to understand the neural mechanisms underlying this strategy, we examined the connectivity of simple neural networks evolved to respond according to the cumulative rank of stimulus luminance values. Evolved similarities with the connectivity of early level visual neurons suggests that biological visual circuitry uses the same mechanisms as a means of creating useful perceptions and behaviors without information about the real world.

Expression of emotion in Eastern and Western music mirrors vocalization

Bowling DL, Sundararajan J, Han S, Purves D (2012). PLoS ONE 7(3): e31942. doi:10.1371/journal.pone.0031942.
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In Western music, the major mode is typically used to convey excited, happy, bright or martial emotions, whereas the minor mode typically conveys subdued, sad or dark emotions. Recent studies indicate that the differences between these modes parallel differences between the prosodic and spectral characteristics of voiced speech sounds uttered in corresponding emotional states. Here we ask whether tonality and emotion are similarly linked in an Eastern musical tradition. The results show that the tonal relationships used to express positive/excited and negative/subdued emotions in classical South Indian music are much the same as those used in Western music. Moreover, tonal variations in the prosody of English and Tamil speech uttered in different emotional states are parallel to the tonal trends in music. These results are consistent with the hypothesis that the association between musical tonality and emotion is based on universal vocal characteristics of different affective states.

Co-Variation of Tonality in the Music and Speech of Different Cultures

Han Se, Sundararajan J, Bowling DL, Lake J, Purves D (2011). PLoS ONE 6(5): e20160. doi:10.1371/journal.pone.0020160.
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Whereas the use of discrete pitch intervals is characteristic of most musical traditions, the size of the intervals and the way in which they are used is culturally specific. Here we examine the hypothesis that these differences arise because of a link between the tonal characteristics of a culture’s music and its speech. We tested this idea by comparing pitch intervals in the traditional music of three tone language cultures (Chinese, Thai and Vietnamese) and three non-tone language cultures (American, French and German) with pitch intervals between voiced speech segments. Changes in pitch direction occur more frequently and pitch intervals are larger in the music of tone compared to non-tone language cultures. More frequent changes in pitch direction and larger pitch intervals are also apparent in the speech of tone compared to non-tone language cultures. These observations suggest that the different tonal preferences apparent in music across cultures are closely related to the differences in the tonal characteristics of voiced speech.

Understanding vision in wholly empirical terms.

Purves, D., Wojtach, W.T., & Lotto, R.B. (2011) Proc Natl Acad Sci (doi:10.1073/pnas.1012178108, March 7).
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This article considers visual perception, the nature of the information on which perceptions seem to be based, and the implications of a wholly empirical concept of perception and sensory processing for vision science. Evidence from studies of lightness, brightness, color, form and motion all indicate that, because the visual system cannot access the physical world by means of retinal light patterns as such, what we see cannot and does not represent the actual properties of objects or images. The phenomenology of visual perceptions can be explained, however, in terms of empirical associations that link images whose meanings are inherently undetermined to their behavioral significance. Vision in these terms requires fundamentally different concepts of what we see, why, and how the visual system operates.

Major and minor music compared to excited and subdued speech.

Bowling, D.L., K.Gill, et al. (2010). J Acoust Soc Am 127 (1): 491-503.
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The affective impact of music arises from a variety of factors, including intensity, tempo, rhythm, and tonal relationships. The emotional coloring evoked by intensity, tempo, and rhythm appears to arise from association with the characteristics of human behavior in the corresponding condition; however, how and why particular tonal relationships in music convey distinct emotional effects are not clear. The hypothesis examined here is that major and minor tone collections elicit different affective reactions because their spectra are similar to the spectra of voiced speech uttered in different emotional states. To evaluate this possibility the spectra of the intervals that distinguish major and minor music were compared to the spectra of voiced segments in excited and subdued speech using fundamental frequency and frequency ratios as measures. Consistent with the hypothesis, the spectra of major intervals are more similar to spectra found in excited speech, whereas the spectra of particular minor intervals are more similar to the spectra of subdued speech. These results suggest that the characteristic affective impact of major and minor tone collections arises from associations routinely made between particular musical intervals and voiced speech.

A Biological Rationale for Musical Scales

Gill KZ and Purves D (2009). PLoS ONE 4: e8144. doi:10.1371/ journal.pone.0008144.
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Scales (some of which are also referred to as modes) are collections of tones separated by specific intervals that many cultures have used over the millennia to make music. Since humans can distinguish about 240 different pitches over an octave in the mid-range of pitch perception, in principle a very large number of tone combinations could have been used for this purpose. Nonetheless, compositions in Western classical, folk and popular music as well as in many other musical traditions are based on just a few sets of five to seven tones. Why musical scales employ only a few of the enormous number of possible tone combinations humans can discriminate is not known. Here we show that the component intervals of the most widely used scales throughout history and across cultures are those with the greatest spectral similarity to a harmonic series. These findings are consistent with the idea that humans have a bias for conspecific vocalizations.

Neuroscience

Purves D. (2009)
Scholarpedia, 4(8):7204
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Neuroscience is concerned with how the nervous systems of humans and other animals are organized and how they function. This subfield of biology has used many different methods and a wide variety of animal models to advance over the years. Among the most important questions answered during much of the last century concern how the neurons in all nervous systems convey signals from the sensory periphery to inform animals about the external and internal environment; how ensembles of then signal each other in processing this information in the central nervous system; and finally how these ensembles ultimately convey the outcome of neural processing to the body’s effectors (muscles and glands). Although understanding these signaling functions that underlie virtually all neural functions and behaviors was based on anatomical, physiological and biochemical knowledge acquired by many investigators, the pioneers in understanding how information is conveyed over long distances by action potentials were Alan Hodgkin and Andrew Huxley; Bernard Katz whose work revealed how synapses transfer information from one neuron to another and to effector cells; and Stephen Kuffler who participated in both these efforts and made fundamental contributions understanding how peripheral sensory receptors initiate action potentials by responding to energy from different sources in the environment. Biochemical and more recently molecular genetic techniques complemented these largely physiological studies, first identifying an ever increasing number of neurotransmitter agents used at chemical synapses, and ultimately the ion channels activated by these agents as well as the ion channels responsible for action potential conduction. In addition to validating and greatly extending the results of electrophysiology, this knowledge fomented a wealth of clinically oriented neuroscience aimed at better understanding and treating neurological and other diseases by means of improved molecular pharmacology.

An empirical explanation of the speed-distance effect

Wojtach W. T., Sung K, Purves D (2009)
PLoS ONE 4(8): e6771
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Understanding motion perception continues to be the subject of much debate, a central challenge being to account for why the speeds and directions seen accord with neither the physical movements of objects nor their projected movements on the retina. Here we investigate the varied perceptions of speed that occur when stimuli moving across the retina traverse different projected distances (the speed-distance effect). By analyzing a database of moving objects projected onto an image plane we show that this phenomenology can be quantitatively accounted for by the frequency of occurrence of image speeds generated by perspective transformation. These results indicate that speed-distance effects are determined empirically from accumulated past experience with the relationship between image speeds and moving objects.

Reconsidering Perceptual Content

Wojtach W.T. (2009)
Phil Science 76: 22-43
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An important class of teleological theories cannot explain the representational content of visual states because they fail to address the relationship between the world, projected retinal stimuli, and perception. A different approach for achieving a naturalized theory of visual content is offered that rejects the traditional internalism/externalism debate in favor of what is termed “empirical externalism”. This position maintains that, while teleological considerations can underwrite a broad understanding of representation, the content of visual representation can only be determined empirically according to accumulated past experience. A corollary is that a longstanding problem concerning the indeterminacy of visual content is dissolved.

An empirical explanation of aperture effects

Sung K, Wojtach W.T., Purves D (2009)
Proc Natl Acad Sci 106:298-303
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The perceived direction of a moving line changes, often markedly, when viewed through an aperture. Although several explanations of this remarkable phenomenology have been proposed, these accounts typically focus on the percepts elicited by a particular type of aperture and offer no biological rationale for these puzzling effects. Here we test the hypothesis that to contend with the inherently ambiguous nature of motion stimuli, the perceived direction of objects moving behind apertures of different shapes is determined by a wholly empirical strategy of visual processing. An analysis of moving line stimuli generated by objects projected through apertures shows that the directions of motion subjects report in psychophysical testing is accounted for by the frequency of occurrence of the 2-D directions of stimuli generated by simulated 3-D sources. The accuracy of these predictions supports the conclusion that the direction of perceived motion is determined entirely by accumulated behavioral experience with sources whose physical motions cannot be conveyed by image sequences as such.

An empirical explanation of the flash-lag effect

Wojtach W.T., Sung K, Truong S, Purves D (2008)
Proc Natl Acad Sci 105(42): 16338-16343
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When a flash of light is presented in physical alignment with a moving object, the flash is perceived to lag behind the position of the object. This phenomenon, known as the flash-lag effect, has been of particular interest to vision scientists because of the challenge it presents to understanding how the visual system generates perceptions of objects in motion. Although various explanations have been offered, the significance of this effect remains a matter of debate. Here, we show that: (i) contrary to previous reports based on limited data, the flash-lag effect is an increasing nonlinear function of image speed; and (ii) this function is accurately predicted by the frequency of occurrence of image speeds generated by the perspective transformation of moving objects. These results support the conclusion that perceptions of the relative position of a moving object are determined by accumulated experience with image speeds, in this way allowing for visual behavior in response to real-world sources whose speeds and positions cannot be perceived directly.

Perception of Surfaces and Forms

Purves D
in: Larry R. Squire, Editor-in-Chief, Encyclopedia of Neuroscience, Academic Press, Oxford 2008.

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.

Vision

Purves D
in: Handbook of Neuroscience for the Behavioral Sciences (Berntson, Gary G and Cacioppo, John T, eds). John Wiley & Sons. Chapter 11, pp. 224–250.
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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.

Experience with Natural Images as a Basis for Vision

Purves D
in: Encyclopedia of Neuroscience (M.D. Binder, N.Hirokawa, U.Windhorst, M.C. Hirsch, eds) New York: Springer-Verlag
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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.

Visual Illusions

Purves D,Wojtach W, Howe, C
Scholarpedia (2007)
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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.

Musical intervals in speech

Ross D, Choi J, Purves D
PNAS 104(23): 9852-9857. (2007)
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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.

Evolution of visually-guided behavior in artificial agents.

Boots B, Nundy S, Purves D
Network:Computation in Neural Systems 18(1): 11-34. (2007)
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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.

Comparison of Bayesian and empirical ranking approaches to visual perception

Howe CQ, Lotto RB, Purves D
J Theoretical Biol 241: 866-875. (2006)
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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.

Spectral statistics in natural scenes predict hue, saturation, and brightness

Long F, Yang Z, Purves D
Proc Natl Acad Sci 103(15): 6013-6018. (2006)
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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.

The wagon wheel illusion in continuous light

Andrew, TJ, Purves D
Trends in Cog Neurosci 9(6): 261-263. (2005)
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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.

The Poggendorff illusion explained by natural scene geometry

Howe CQ, Yang Z, Purves D
Proc Natl Acad Sci 102(21): 7707-7712. (2005)
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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.

Natural scene geometry predicts the perception of angles and line orientation

Howe CQ, Purves D
Proc Natl Acad Sci 102 (4): 1228-1233. (2005)
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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.

The Müller-Lyer illusion explained by the statistics of image-source relationships

Howe CQ, Purves D
Proc Natl Acad Sci 102(4): 1234-1239. (2005)
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The Müller-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.

Pitch is determined by naturally occurring periodic sounds

Schwartz, DA, Purves D
Hearing Research 194:31-46 (2004)
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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.

The statistical structure of natural light patterns determines perceived light intensity

Yang Z, Purves D
Proc Natl Acad Sci 101(23): 8745-8750 (2004)
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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.

Perceiving the intensity of light

Purves D, Williams SM, Nundy S, Lotto RB
Psych Rev 111(1): 142-158. (2004)
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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.

Size contrast and assimilation explained by the statistics of scene geometry

Howe CQ, Purves D
J Cog Neurosci 16(1): 90-102. (2004)
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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.

Perceiving Colour

Lotto RB, Purves D
Review of Progress in Coloration 34: 12-25. (2004)
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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.

Why we see what we do: An empirical theory of vision

Lotto RB, Purves D
Optician 225: 22-26 (2003)
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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.

Cornsweet Effect

Purves D, Lotto RB in: Encyclopedia of Neuroscience, 3rd Edition (G. Adelman, B.H. Smith, eds) Elsevier Press (2004) Read full article

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.

Natural scene statistics as the universal basis for color context effects

Long F, Purves D
Proc Natl Acad Sci 100 (25): 15190-15193. (2003)
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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.

Image/source statistics of surfaces in natural scenes

Yang, Z, Purves, D
Network: Comput. Neural Syst. 14 371-39 (2003)
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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.

The statistical structure of human speech sounds predicts musical universals

Schwartz, DA, Howe, CQ, Purves D
J Neurosci. 23(18):7160-7168 (2003)
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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.

A statistical explanation of visual space

Yang, Z, Purves, D
Nature Neurosci. 6:632-640 (2003)
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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.

Perception of objects that are translating and rotating

Yang Z, Shimpi A, Purves D
Perception 31(8): 925-942. (2002)
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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.

A probabilistic explanation of brightness scaling

Nundy S, Purves D
Proc Natl Acad Sci 99(22): 14482-14487. (2002)
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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.

The empirical basis of color perceptionaling

Lotto RB, Purves D
Consciousness and Cognition 11(4): 609-629. (2002)
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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.

Range image statistics can explain the anomalous perception of length

Howe CQ, Purves D
Proc Natl Acad Sci 99(20):13184-13188. (2002)
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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.

Why we see what we do

Purves D, Lotto RB, Nundy S
American Scientist 90(3): 236-243. (2002)
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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.

A rationale for the structure of color space

Lotto RB, Purves D
Trends Neurosci 25(2): 84-89. (2002)
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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.

An empirical explanation of the Chubb illusion

Lotto RB, Purves D
J Cog Neurosci 13(5): 547-555. (2001)
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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.

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
Philos Trans R Soc Lond B, 356:285-297. (2001)
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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.

A wholly empirical explanation of perceived motion

Yang Z, Shimpi A, Purves D
Proc Natl Acad Sci 98(9): 5252-5257. (2001)
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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.

The relevance of visual perception to cortical evolution and development

Purves D, Williams SM, Lotto RB
in: Evolutionary Developmental Biology of the Cerebral Cortex (Novartis Foundation Symposium)John Wiley & Sons, 228:240-258(2000)
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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.

An empirical explanation of color contrast

Lotto, RB, Purves D
Proc Natl Acad Sci 97(23): 12834-12839. (2000)
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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.

Why are angles misperceived?

Nundy S, Lotto B, Coppola D, Shimpi A, Purves D
Proc Natl Acad Sci. 97(10): 5592-5597. (2000)
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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.

Color vision and the four-color-map problem

Purves D, Lotto B, Polger T
J Cog Neurosci 12(2): 233-237. (2000)
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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.

Interindividual variation in human visual performance

Halpern, SD, Andrews TJ, Purves D
J Cog Neurosci 11(5): 521-534. (1999)
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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.

The effects of color on brightness

Lotto, RB, Purves D
Nature Neurosci 2: 1010-1014. (1999)
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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.

An empirical explanation of the Cornsweet effect

Purves D, Shimpi A, Lotto RB
J Neurosci 19(19): 8542-8551. (1999)
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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.

Mach bands as empirically derived associations

Lotto RB, Williams SM, Purves D
Proc Natl Acad Sci 96(9): 5245-5250. (1999)
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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.

An empirical basis for Mach bands

Lotto RB, Williams SM, Purves D
Proc Natl Acad Sci 96(9): 5239-5244. (1999)
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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.

An empirical explanation of brightness

Williams, SM, McCoy AN, Purves D
Proc Natl Acad Sci 95(22): 13301-13306. (1998)
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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.

The influence of depicted illumination on perceived brightness

Williams, SM, McCoy AN, Purves D
Proc Natl Acad Sci 95(22): 13296-13300. (1998)
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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.

The distribution of oriented contours in the real world

Coppola DM, Purves HR, McCoy AN, Purves D
Proc Natl Acad Sci 95(7): 4002-4006. (1998)
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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.

Unequal representation of cardinal and oblique contours in ferret visual cortex

Coppola DM, White LE, Fitzpatrick D, Purves D
Proc Natl Acad Sci 95(5): 2621-2623. (1998)
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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.

Similarities in normal and binocularly rivalrous viewing

Andrews TJ, Purves, D
Proc Natl Acad Sci 94: 9905-9908 (1997)
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We report here a series of observations—most of which the reader can experience directly—showing that distinct components of patterned visual stimuli (orthogonal lines of a different hue) vary in perception as sets. Although less frequent and often less complete, these perceptual fluctuations in normal viewing are otherwise similar to the binocular rivalry experienced when incompatible scenes are presented dichoptically.

The perception of transparent 3-dimensional objects

Andrews TJ, Purves, D
Proc Natl Acad Sci 94: 6517-6522 (1997)
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When the proximal and distal elements of wire-frame cubes are conflated, observers perceive illusory structures that no longer behave veridically. These phenomena suggest that what we normally see depends on visual associations generated by experience. The necessity of such learning may explain why the mammalian visual system is subject to a prolonged period of plasticity in early life, when novel circuits are made in enormous numbers.

Correlated size variations in human visual cortex, lateral geniculate nucleus and optic tract.

Andrews TJ, Halpern SD, Purves D
J Neurosci 17: 2859-2868 (1997)
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We have examined several components of the human visual system to determine how the dimensions of the optic tract, lateral geniculate nucleus (LGN), and primary visual cortex (V1) vary within the same brain. Measurements were made of the cross-sectional area of the optic tract, the volumes of the magnocellular and parvocellular layers of the LGN, and the surface area and volume of V1 in one or both cerebral hemispheres of 15 neurologically normal human brains obtained at autopsy. Consistent with previous observations, there was a two- to threefold variation in the size of each of these visual components among the individuals studied. Importantly, this variation was coordinated within the visual system of any one individual. That is, a relatively large V1 was associated with a commensurately large LGN and optic tract, whereas a relatively small V1 was associated with a commensurately smaller LGN and optic tract. This relationship among the components of the human visual system indicates that the development of its different parts is interdependent. Such coordinated variation should generate substantial differences in visual ability among humans.

Structure of the Human Sensorimotor System II. Lateral symmetry.

White LE, Andrews TJ, Hulette C, Richards A, Groelle M, Paydarfar J, Purves D
Cereb Cortex 7:31- 47 (1997)
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We have studied the morphology of the central sulcus and the cytoarchitecture of the primary sensorimotor cortex in 20 human brains obtained at autopsy. Although the surface appearance of the central sulcus varies greatly from brain to brain (and between hemispheres of individual brains), its deep structure is remarkably consistent. The fundus of the central sulcus is divided into medial and lateral limbs by a complex junction midway between the sagittal and Sylvian fissures. Based on functional imaging studies, this junction appears to be a structural hallmark of the sensorimotor representation of the distal upper extremity. We also identified and measured area 4 (primary motor cortex) and area 3 (primary somatic sensory cortex) in Nissl-stained sections cut orthogonal to the course of the central sulcus. Although the positions of the cytoarchitectonic boundaries in the paracentral lobule showed considerable interindividual variation, the locations of the borders of areas 4 and 3 along the course of the sulcus were similar among the 40 hemispheres examined. In addition to describing more thoroughly this portion of the human cerebral cortex, these observations provide a basis for evaluating lateral symmetry of the human primary sensorimotor cortex.

Structure of the human sensorimotor system I. Morphology and cytoarchitecture of the central sulcus.

White LE, Andrews TJ, Hulette C, Richards A, Groelle M, Paydarfar J, Purves D
Cereb Cortex 7: 18-30 (1997)
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Is neural development Darwinian?

Purves D, White LE, Riddle DR
TINS 19 (11): 460-464 (1996)
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Gradually, and without much debate, the idea that the developing nervous system is in some sense Darwinian has become one of the canons of neurobiology. In fact, there is little evidence to support this idea.

The extraordinarily rapid disappearance of entoptic images

Coppola D, Purves D
Proc Natl Acad Sci 93: 8001-8004 (1996)
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It has been known for more than 40 years that images fade from perception when they are kept at the same position on the retina by abrogating eye movements. Although aspects of this phenomenon were described earlier, the use of close-fitting contact lenses in the 1950s made possible a series of detailed observations on eye movements and visual continuity. In the intervening decades, many investigators have studied the role of image motion on visual perception. Although several controversies remain, it is clear that images deteriorate and in some cases disappear following stabilization; eye movements are, therefore, essential to sustained exoptic vision. The time course of image degradation has generally been reported to be a few seconds to a minute or more, depending upon the conditions. Here we show that images of entoptic vascular shadows can disappear in less than 80 msec. The rapid vanishing of these images implies an active mechanism of image erasure and creation as the basis of normal visual processing.

The wagon wheel illusion in movies and reality

Purves D, Paydarfar JA, Andrews TJ
Proc Natl Acad Sci 93: 3693-3697 (1996)
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Wheels turning in the movies or in other forms of stroboscopic presentation often appear to be rotating backward. Remarkably, a similar illusion is also seen in continuous light. The occurrence of this perception in the absence of intermittent illumination suggests that we normally see motion, as in movies, by processing a series of visual episodes.

Temporal events in cyclopean vision

Andrews TJ, White LE, Binder D, Purves D
Proc Natl Acad Sci 93: 3689-3692 (1996)
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The majority of neurons in the primary visual cortex of primates can be activated by stimulation of either eye; moreover, the monocular receptive fields of such neurons are located in about the same region of visual space. These well-known facts imply that binocular convergence in visual cortex can explain our cyclopean view of the world. To test the adequacy of this assumption, we examined how human subjects integrate binocular events in time. Light flashes presented synchronously to both eyes were compared to flashes presented alternately (asynchronously) to one eye and then the other. Subjects perceived very-low-frequency (2 Hz) asynchronous trains as equivalent to synchronous trains flashed at twice the frequency (the prediction based on binocular convergence). However, at higher frequencies of presentation (4-32 Hz), subjects perceived asynchronous and synchronous trains to be increasingly similar. Indeed, at the flicker-fusion frequency (approximately 50 Hz), the apparent difference between the two conditions was only 2%. We suggest that the explanation of these anomalous findings is that we parse visual input into sequential episodes.

Individual variation and lateral asymmetry of the rat primary somatosensory cortex.

Riddle DR, Purves D
J Neurosci 15: 4184-4195 (1995)
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We have evaluated the interindividual variability and lateral symmetry of a major cortical area by comparing the primary somatosensory cortex (S1) of adult rats. Our choice of the rat was dictated by the accuracy with which one can measure S1 and its component representations in the rodent brain; the importance of such measurements lies in understanding the rules that govern the allocation of cortical space and, ultimately, the consequences of differential allocation for behavior. With respect to interindividual differences, the major somatic representations in S1 are surprisingly variable in size. The area of the whiskerpad representation, for example, ranged from 3.72 to 6.84 mm² in a sample of 53 rats; other components of S1 showed comparable differences among animals. With respect to lateral symmetry, the average area of each major representation was similar for the right and left hemispheres; thus, we found no consistent bias in the size of S1 or its elements in the sample as a whole. Within individual animals, however, the sizes of the major somatic representations were often quite different in the two hemispheres. The magnitude of the lateral differences averaged 7.9 +/- 0.8% (mean +/- SEM) for the whisker pad representation, 11.6 +/- 1.3% for the upper lip, 15.4 +/- 1.6% for the furry buccal pad, 13.9 +/- 1.4% for the lower jaw, and 13.3 +/- 1.2% for the forepaw. These results show that the amount of cortical space allocated to corresponding functions in individual rats–or in the two hemispheres of a particular rat–are often different. Such variations are likely to be reflected in somatosensory performance.

Effects of increased neural activity on brain growth

Zheng D, Purves D
Proc Natl Acad Sci 92: 1802-1806 (1995)
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We have measured the effects of regionally increased metabolic activity–and by inference electrical activity–on cortical growth in the developing rat brain. Cortical growth is significantly and specifically greater in regions of chronically increased activity. This effect of activity on cortical growth may help explain the permanent storage of early experience in the developing nervous system.