Graham, N. (1989a)
New York: Oxford University Press.
From the preface. This book deals with many of the parts into which visual information is initially analyzed. The parts that are the topic of this book are those relevant for patterns in space and time; that is, for discussions of shape and motion. Color and three-dimensionality are not discussed. Our knowledge of these parts has come both from psychophysics and neurophysiology. This book's major topic is the psychophysical evidence--particularly that from experiments measuring human observers' ability to detect and identify near-threshold spatiotemporal patterns. Over the last quarter-century or so of such research an enormous amount has been learned. . . . Organizing this material within a framework and making it part of a coherent story is the major aim of this book. This book is primarily for readers with a very serious interest in visual perception or closely related fields. Much of the book (parts II through V on models of four kinds of psychophysical experiments) is just as applicable to people working in the psychophysics of audition, taste, or smell as it is to people working in vision. On the other hand, the book does include a good deal of background material since people entering the field of pattern vision can come from medicine (ophthalmology), from biology (neuroscience, physiology), from engineering and physics (especially electrical and optical), from computer science, from experimental psychology, or from the arts (fine arts, film). No PDF available. (Erratum)
Notes: A short summary of much of the content of this book can be found in Graham (1992) (HTML text plus figs.) PDF (484K).
A central limit theorem for families of stochastic processes indexed by a small average step size parameter, and some applications to learning models
Norman, M. F. and Graham, N. (1968)
Psychometrika, 33, 441-449
Abstract. Let theta > 0 be a measure of the average step size of a stochastic process. Conditions are given under which Pn(theta) is approximately normally distributed when n is large and theta is small. This result is applied to a number of learning models where theta is a learning rate parameter and Pn(theta) is the probability that the subject makes a certain response on the nth experimental trial. Both linear and stimulus sampling models are considered. PDF (324K)
On tuning and amplification by lateral inhibition
Ratliff, F., Knight, B. W. and Graham, N. (1969)
Proceedings of National Academy of Sciences, 62, 733-740.
Abstract. Lateral inhibition in a neural network generally attenuates the amplitudes of the responses to sinusoidal stimuli-both spatial and temporal. For an inhibitory influence with an abrupt onset and an exponential decay in time, and with a Gaussian distribution in space (the forms often assumed in theoretical calculations), the attenuation is greatest at low temporal and spatial frequencies. The attenuation diminishes with increasing frequencies until ultimately the amplitudes of inhibited responses become equal to, but never exceed, the amplitudes of the uninhibited.
For an inhibitory influence with a delay to the maximum in time or with eccentric maxima in space, however, the amplitudes of inhibited responses to certain intermediate frequencies may be greater than those of the uninhibited responses. This "amplification" results because of the delay and the spatial separation "tune" the network to particular temporal and spatial frequencies; the inhibition is turned on at the trough of the response and off at the crest, thus tending to produce the greatest possible amplitude. The amplification has been observed in one neural network, the retina of the lateral eye of Limulus. The basic principles are general, and the effects may be expected in any system with negative feedback. PDF (872K)
Detection of grating patterns containing two spatial frequencies: A test of single-channel and multiple-channels models
Graham, N. and Nachmias, J. (1971)
Vision Research, 11, 251-259.
Abstract. Contrast thresholds were measured for gratings containing two superimposed sinusoidal components. The frequency of one component was always three times that of the other, but the phase between components and the ratio of their contrasts took on several values. Two models of pattern vision were tested (1) a single-channel model in which pattern vision is a function of a single neural network and (2) a multiple-channels model in which the stimulus information is processed by many channels, each sensitive to a narrow range of spatial frequencies. Results support the multiple-channels and reject the single-channel model. PDF (544K) (Erratum)
Influence of values in risky decision making: A formalization
McCauley, C. R. and Graham, N.(1971)
Representative Research in Social Psychology, 2, 3-11.
Abstract. Hypothetical life-situation problems used to compare individual with group risk taking share a common decision structure, which is here abstracted and formalized in decision-theory terms. By means of this formalization, risk decisions and risk shifts on life-situation problems are placed within the older, larger, and more formal literature on choice behavior. Two decision-making strategies from this literature, expected utility and minimax regret (Savage, 1951), are shown to be consistent with the relation of values (utilities) to individual risk taking found by Stoner (1968). Anomalous results for one of Stoner's 12 situations can be understood in terms of either strategy, within the context of a structural anomaly identified in that situation. The two strategies show promise for understanding the risk shift phenomenon by suggesting decision-relevant variables that may change under group discussion. PDF (1 MB)
Spatial-frequency channels in the human visual system:Effects of luminance and pattern drift rate
Graham, N. (1972)
Vision Research, 12, 53-68
Abstract. Recent evidence indicates that the human visual system contains multiple channels, with each channel sensitive to a different narrow range of spatial frequency. In this study the sensitivity of these channels for patterns at a low mean luminance or high drift rate is measured by the effect of adaptation to sinusoidal gratings on the contrast thresholds for sinusoidal gratings. The channels do not behave in the way expected from retinal ganglion cell physiology; rather, they remain selectively sensitive to narrow ranges of spatial frequency even when the luminance is low or the drift rate is high. PDF (808K)
Early light and dark adaptation in frog on-off retinal ganglion cells
Gordon, J. and Graham, N (1973)
Vision Research, 13, 647-659.
Abstract. Transient on-off cells in the frog eyecup preparation were studied. Short test flashes were presented at various times with respect to a ten second adapting flash. Total number of impulses in the response was least when the test flash was near the onset or offset of the adapting flash as a result of "postexcitation inhibition"-the decrease or inhibition of a response whenever it closely follows another response. Some modification of existing models for on-off cells is required to explain this inhibition. Postexcitation inhibition also provides a possible model for psychophysical effects. (French, German, & Russian abstracts) PDF (652K)
Facilitation of inhibition in the compound lateral eye of Limulus
Graham, N., Ratliff, F. and Hartline, H. K (1973)
Proceedings of National Academy of Sciences, 70, 894-898.
Abstract. In the compound eye of Limulus the inhibitory effect of a burst of impulses from one group of ommatidia on the response of a neighboring ommatidium is greater when that burst is preceded by another burst of impulses. This facilitation of inhibition decays slowly, with a time constant of several seconds. Facilitation of inhibition accumulates as the number of impulses in the first burst increases, but there is a maximum that it cannot exceed. The facilitation is localized; one group of ommatidia does not facilitate the inhibition exerted by another group. The mechanism of this facilitation may be similar to that which has been postulated for facilitation of excitatory influences at the neuromuscular junction. PDF (400K)
Quantitative theories of the integrative
action of the retina
Graham, N. and Ratliff, F. (1974)
In Contemporary Developments in Mathematical Psychology, R. C. Atkinson, D.H. Krantz, R. D. Luce, and P. Suppes, eds. pp. 306-371. San Francisco, W. H. Freeman Co.
Abstract. The major purpose of this survey of quantitative
studies of the neurophysiology of vision is to illustrate how
easy transitions from empirical data to abstract ideas and back
again, via mathematics, provides a most important tool for the
investigator. This survey focuses on the integrative action of
the retina, in particular, the retinas of the Limulus,
the cat, and the goldfish. PDF
(300dpi version 6.8MB)
PDF (150dpi
verson 2.2MB)
Spatial-pooling properties deduced from the detectability of FM and Quasi-AM gratings: A reanalysis
Graham, N. and Rogowitz, B. E. (1976)
Vision Research, 16, 1021-1026.
Abstract. In a thought-provoking paper, Stormeyer and Klein (1975) study several models of spatial pattern detection. The class of models they consider (Campbell and Robson, 1968; Thomas, 1970; Kulikowski and King-Smith, 1973) postulates the existence, at some stage in the visual system, of many different sizes of receptive field centered on every retinal point. Within this "multiple channels" context the questions they address directly are: (1) What is the bandwidth, or range of spatial frequencies, to which these receptive fields respond? and (2) What kind of pooling, if any, exists among receptive fields located at different spatial positions across the visual field? As Granger (1973) pointed out in a somewhat different context, bandwidth estimates in many situations depend on the spatial pooling mechanism assumed. As a tool to disentangle these two factors, Stromeyer and Klein propose the use of three different types of grating: sinusoidal, frequency-modulated, and quasi-amplitude modulated. There are several points, both about the theory and the data, which Stromeyer and Klein have overlooked. When these points are taken into account, the conclusions that can be drawn from their study are substantially unchanged, especially those about spatial pooling. Because both the questions asked by this study and the method used are interesting, it seemed worthwhile to consider these points in detail. PDF (432K)
Visual detection of aperiodic spatial stimuli by probability summation among narrowband channels
Graham, N. (1977a)
Vision Research, 17, 637-652.
Abstract. Recent psychophysical results of Shapley and Tolhurst and of Kulikowski and King-Smith have suggested that the visual system contains broadband channels like "edge detectors" and "line detectors" as well as relatively narrowband "spatial frequency" channels. These recent results (including thresholds for aperiodic stimuli) can be completely explained using only relatively narrowband channels with probability summation among them. This explanation requires many fewer free parameters than the original explanation based on both broadband and narrowband channels. The bandwidths of the individual narrowband channels can be estimated and are similar to those previously estimated from sine-wave summation experiments. PDF (1.2MB)
Spatial frequency
Graham, N. (1977b)
In International Encyclopedia of Neurology, Psychiatry, Psychoanalysis, and Psychology, B.Wolman, ed. Van Nostrand Reinhold. PDF (856K)
Grating summation in fovea and periphery
Graham, N., Robson, J. G., and Nachmias, J. (1978)
Vision Research, 18, 816-825.
Abstract. Results from previous studies measuring the detectability of sinusoidal gratings have been interpreted by models postulating several sizes of receptive fields. It has not been clear, however, whether or not these several sizes coexist at a single position in the visual field. Perhaps there is only one size centered at each position, but the size varies as a function of eccentricity.
In this study, the detectability of compound gratings containing two sinusoidal components was compared to that of each component alone. Measurements were made in the fovea and 7.5ß into the periphery. Stimuli were localized in a small region of the visual field and sharp spatial and temporal transients eliminated by weighting grating contrast with Gaussian functions of space and time. To reduce possible effects of expectation, bias and frequency uncertainty, a temporal, forced-choice, interlaced staircase procedure was used. The results are consistent with models postulating several sizes of receptive fields at each position in the visual field but not with models postulating only one size at each position, even when the size varies as a function of eccentricity to account for the differences in spatial interaction characteristic of different parts of the visual field. PDF (812K)
Does the brain perform a Fourier analysis of the visual scene?
Graham, N. (1979)
Trends in Neurosciences, August, 1979, pp 207-208.
Abstract. The decomposition of a complex auditory sound into its constituent simple harmonic variations (pure tones) is an example of Fourier analysis. Does the brain do something like this to visual scenes, decomposing a visual pattern into some simpler representation to help ease the information-processing load? As Norma Graham explains below, the answer to this question is both yes and no. But, yes or no, the idea that the brain might do a Fourier analysis of the visual scene has been a powerful impetus to much exciting visual research in the last decade. PDF (420K)
Spatial frequency channels in human vision: Detecting edges without edge detectors
Graham, N. (1980)
In Visual Coding and Adaptability, C. Harris, ed. pp. 215-262. Hillsdale, New Jersey: Lawrence Erlbaum Assocs.
Extracts from first section of chapter. One early approach to the study of vision was to investigate the appearance of small patches of light and to try to explain the appearance of the whole visual field as the juxtaposition of the appearances of many small patches. A theoretical model that can be viewed as a natural descendant of this early approach, made appropriately more rigorous for the case of threshold experiments, is what I will call a single-channel model. In the first section I will review early experiments on the detection of compound patterns made up only of sinusoidal components. These early experiments produced strong evidence against the single-channel model for threshold vision. The findings can instead be interpreted as evidence for the existence of a rather odd type of feature detector -- a detector or channel which responds only to patterns containing spatial frequencies within a limited range. Very roughly, being sensitive to a limited range of spatial frequencies means responding best to a particular size of element in the pattern (e.g. width of stripe). I'll refer to this kind of channel as a spatial frequency channel.. In the second section I will discuss some recent experiments by Shapley and Tolhurst and by Kulikowski and King-Smith. These elegant experiments used patterns made up of sinusoids plus aperiodic stimuli (for example, sinusoids plus lines, sinusoids plus edges) as well as various combinations of aperiodic stimuli. These authors interpreted their results as evidence for the existence of several additional kinds of feature detectors -- things like edge detectors and line detectors. The crucial distinction between these new feature detectors and the spatial frequency channels is that each of these new feature detectors is supposed to respond to a broader range of spatial frequencies than does any spatial frequency channel. I will argue, however, that these experiments do not actually provide persuasive evidence for the existence of additional feature detectors. On the contrary, these new findings can probably be explained in terms of the same spatial frequency channels that were inferred from the earlier sinusoid-plus-sinusoid experiments. To reach that conclusion, I will reexamine the newer data in the light of a model that allows for probability summation among spatial frequency channels. PDF (1.7MB)
Spatial frequency uncertainty effects in the detection of sinusoidal gratings
Davis, E. T. and Graham, N. (1981)
Vision Research, 21, 705-712.
Abstract. A sinusoidal grating is less detectable when it is randomly intermixed in a block of trials with gratings of other spatial frequencies than when it is the only grating presented in a block of trials. This spatial-frequency uncertainty effect is expected if observers have attentional control over multiple spatial-frequency channels. When intermixed blocks contain a preponderance of one spatial frequency, the primary, the uncertainty effect is smaller for frequencies near the primary than for frequencies further away. Both the tuning of the uncertainty effect and the analysis of sequential conditional probabilities suggest that observers can employ different attention strategies. PDF (516K)
Psychophysics of spatial-frequency channels
Graham, N. (1981)
In Perceptual Organization, M. Kubovy and J. Pomerantz, eds. pp. 1-26. Hillsdale, New Jersey, Lawrence Erlbaum Assocs.
Abstract. The concepts of spatial-frequency analysis (Fourier analysis) and of spatial-frequency channels are briefly introduced. The various kinds of psychophysical experiments providing evidence for spatial-frequency channels are discussed at some length. Tentative conclusions from these experiments about properties of the spatial-frequency channels are then described. Finally, several ways in which spatial-frequency analyses might be useful in explaining perceptual phenomena are mentioned. PDF (1.0MB)
The visual system does a crude Fourier analysis of patterns
Graham, N. (1981)
In S. Grossberg, ed.Mathematical Psychology and Psychophysiology, SIAM-AMS Proceedings, Volume 13, pp. 1-16. Providence, Rhode Island, American Mathematical Society.
From introduction to chapter. About a dozen years ago in the Journal of Physiology, John Robson and Fergus Campbell introduced the notion that the human visual system contains multiple spatial-frequency channels -- that is, multiple subsystems working in parallel, each of which is sensitive to a different range of spatial frequencies in visual patterns. At about the same time in Psychological Review, Jim Thomas made the closely related point that the existence of visual neurons with different sizes of receptive fields has important implications for pattern vision, and, in Science, Allan Pantle and Bob Sekuler suggested the existence of multiple size-selective channels. Since that time, a tremendous amount of psychophysical and physiological work has been inspired by this theoretical notion that there are multiple channels working in parallel to process visual patterns and that each of these channels is sensitive to a different, narrow band of spatial frequencies. Some people have gone so far as to say that the human visual system does a Fourier analysis of the visual scene. What I do here is review the history of this multiple-channels model of pattern vision and comment on its current status. Some referneces will be given here, and the reader can find a more extensive bibliography in Graham, 1981. Some of the material here is explained more fully at an intuitive level in Graham, 1980. First, let me point out that in discussing pattern vision, we ignore many dimensions important to vision -- color, time, depth -- discussing only monochromatic, unmoving, unchanging, flat patterns. We discuss only the initial visual processing, ignoring the higher-order perceptual or cognitive processes that occur, for example, in reading a pattern of letters on a page. In spite of this extreme limitation, there would still be too much to cover, so I will further limit it by concentrating on places where mathematics has entered into the development of the multiple-channels model of pattern vision and on places where more mathematics might be useful. PDF (820K)
Probability summation and regional variations in sensitivity across the visual field
Robson, J. G. and Graham, N. (1981)
Vision Research, 21, 409-418.
Abstract. Contrast sensitivity at different positions in the visual field has been measured at various spatial frequencies using a patch of grating suitably vignetted to give a stimulus localized in both space and spatial frequency. While contrast sensitivity along a vertical line through the fixation point falls off steadily from a maximum at the centre, sensitivity along a horizontal line displaced 42 periods of the grating above the fixation point is approximately constant, at least out to 32 periods from the midline. The way in which detectability increases with increasing number of cycles (2 up to 64) has been measured for gratings with short horizontal bars centred on the fixation point and for gratings with short vertical bars centred on the midline 42 periods above it. The relation between sensitivity and number of cycles can in each case be explained exactly assuming probability summation across space, as long as the variation in sensitivity across the visual field is taken into account. PDF (620K)
Simultaneous recognition of two spatial-frequency components
Hirsch, J., Hylton, R and Graham, N. (1982)
Vision Research, 22, 365-375.
Abstract. A two-frequency two-response paradigm was employed. The stimulus on any trial was a compound grating containing two sinusoidal components of different spatial frequencies where the contrast in one or both components could be zero. The observer gave two responses each indicating confidence that one of the two components had been presented with contrast greater than zero. If these responses are assumed to be related to outputs of spatial-frequency channels according to specified recognition linking hypotheses, then channel properties such as bandwidth, negative influences, correlation of noise, and additivity can be inferred. Possible modifications of spatial frequency channel models are discussed. PDF (708K)
Uncertainty about spatial frequency, spatial position, or contrast of visual patterns
Davis, E T., Kramer, P., and Graham, N. (1983)
Perception and Psychophysics, 33, 20-28.
Abstract. Prevalent theories of pattern vision postulate mechanisms selectively sensitive to spatial frequency and position but not to contrast. Decreased performance in the detection of visual stimuli was found when the observer was uncertain about the spatial frequency or spatial position of a patch of sinusoidal grating but not when he was uncertain about contrast. The uncertainty effects were consistent with multiple-band models in which the observer is able to monitor perfectly all relevant mechanisms. Performance deteriorates when the observer must monitor more mechanisms, because these mechanisms are noisy and give rise to false alarms. This consistency is further evidence that the spatial-frequency and spatial-position mechanisms are noisy, a conclusion previously suggested by the "probability summation" demonstrated in the thresholds for compound stimuli. Somewhat paradoxically, the Quick pooling model, which quantitatively accounts for the amount of probability summation in pattern thresholds, predicts no effects of uncertainty. It cannot, therefore, be strictly correct. PDF (776K)
Detection and identification of spatial frequency
Yager, D., Kramer, P., Shaw, M., and Graham, N. (1984)
Vision Research, 24, 9, 1021-1035
Abstract. Detection and identification of up to four simple sinusoidal gratings were studied. The experimental results were quantitatively compared to predictions from several models. The models all assumed probabilistically independent channels sensitive to different ranges of spatial frequency. The models differed in the shapes of their underlying distributions and, for detection, their decision rule. Detection and identification of far-apart spatial frequencies were consistent with these models. Thus, uncertainty effects for both detection and identification (the decrease in performance with an increase in the number of possible spatial frequencies) can be explained without assuming that attention capacity is limited. PDF (1.0MB)
Detection and identification of near-threshold visual patterns
Graham, N. (1985)
J. Optical Society of America A, 2, 1468-1482
Abstract. For a number of visual dimensions-spatial frequency, orientation, spatial position, and direction of motion (at velocities higher than 1 or 2 deg/sec)-experimental results at near-threshold contrasts can be explained by assuming that multiple mechanisms selectively sensitive along that dimension exist and have labeled outputs. For the temporal-position dimension, analogous experimental results can be explained by assuming that each mechanism's output at a particular time depends only on the recent past and is labeled. For the eye-of-origin dimension, however, although the evidence suggests selectively sensitive mechanisms (at least at some spatial and temporal frequencies), these mechanisms seem not to have labeled outputs. For the temporal-frequency dimension (at any fixed spatial frequency), evidence suggests that there are not narrowly tuned mechanisms although there may be very broadly tuned ones. PDF (1.3MB)
Attending to the spatial frequency and spatial position of near-threshold visual patterns
Graham, N., Kramer, P. and Haber, N. (1985)
In Posner, M.I. and Marin, O.S.M. (eds.) Mechanisms of Attention: Attention and Performance XI pp. 269-283. Hillsdale, N.J.; Erlbaum
Abstract. Results from extrinsic-uncertainty, primary-with-probes, and concurrent experiments using near-threshold visual patterns differing in spatial frequency or spatial position suggest: (a) Typical observers can attend to and give direct reports from selected ranges of spatial frequency and spatial position in the sense of basing their responses on appropriate subsets of visual mechanisms. (b) This selective attention may sometimes occur early enough to block the unmonitored mechanisms' outputs from influencing conscious perception. (c) Observers in these near-threshold tasks can also attend to the whole range without losing any information from any subpart of the range. (The largest number of far-apart spatial frequencies or spatial positions used was five or three, respectively, however.) PDF (732K)
Simultaneous measurement of uncertainty and summation effects: Data and theory
Kramer, P., Graham, N. and Yager, D. (1985)
Journal of Optical Society of America A, 2, 1533-1542
Abstract. The predictions for summation and uncertainty effects from several multiple-spatial-frequency-channels models were calculated. The models differed in their assumptions about the shape of the channels' underlying probability-density functions and in the decision rule used to combine the channels' outputs. Varying these assumptions resulted in different predictions about the magnitudes of these effects. Simultaneous summation and uncertainty experiments measured the detectability of gratings containing one (simple) or two (compound) spatial frequencies. Performance was assessed in two types of blocks of trials: either each stimulus was in a separate block or three stimuli (two simple gratings and their compound) were randomly intermixed in one block. Quantitative comparisons of the models with the data showed that the increasing-variance Gaussian models (in which the decision variable is the sum of the monitored channels' outputs) provided the best overall fit. PDF (768K)
Summation of very close spatial frequencies
Graham, N. and Robson, J.G. (1987)
Vision Research. 27, 1997-2007
Abstract. In accounting for pattern thresholds it is necessary to consider probability summation (or equivalent nonlinear pooling) not only across detectors selective for different spatial frequencies but across detectors in different spatial positions. Interestingly, calculation on this basis shows that the amount of summation between components of closely similar spatial frequency in a large grating is primarily determined by the variation in sensitivity of detectors at different spatial locations and is little affected by the spatial-frequency bandwidths of the detectors. To test this conclusion, we have measured the amount of summation between two components with spatial frequencies very close to 6 c/deg in two regions of the visual field: in the fovea (a region where sensitivity is very non-uniform) and in the periphery where sensitivity is nearly uniform). As predicted, there was less summation between components of very closely similar frequencies in the nearly uniform peripheral region than in the non-uniform foveal region. Measurements in the fovea of the summation of two components with spatial frequencies very near to either 1.5, 6, or 24c/deg showed, as expected, that the amount of summation depends upon the ratio of the frequencies rather than their absolute difference, indicating that probability summation takes place over an area related to spatial frequency rather than over a fixed area. PDF (688K)
Signal-Detection Models for multidimensional stimuli: Probability distributions and combination rules
Graham, N., Kramer, P. and Yager, D. (1987)
J. Mathematical Psychology, 31, 366-409
Abstract. Probablistic independence among multiple random variables (e.g., among the outputs of multiple spatial-frequency channels) has been invoked to explain two effects found with many kinds of stimuli: increments in detection performance due to "probability summation" and decrements in detection and identification performance due to "extrinsic uncertainty." Quantitative predictions of such effects, however, depend on precise assumptions. Here we calculate predictions from multidimensional signal-detection theory assuming any of several different probability distributions characterizing the random variables (including two-state, Gaussian, exponential, and double-exponential distributions) and either of the two rules for combining the multiple random variables into a single decision variable (taking the maximum or summing them). In general, the probability distributions predicting shallower ROC curves to actually predict greater increments due to summation but smaller decrements due to extrinsic uncertainty. some probability distributions yield steep-enough ROC curves to actually predict decrements due to summation in blocked-summation experiments. Probability distribution matters much less for intermixed-summation than for blocked-summation predictions. Of the two combination rules, the sum-of-outputs rule usually predicts both greater increments due to summation and greater decrements due to extrinsic uncertainty. Put another way, of the two combination rules, the sum-of-outputs rule usually predicts better performance on the compound stimulus under any condition but worse performance on simple stimuli under intermixed conditions. PDF (1.9MB)
Visual Pattern Analyzers (Book)
Graham, N. (1989a)
New York: Oxford University Press.
See Book subsection at the beginning of this list for more information. See Graham 1992 below for a summary.
Low-level visual processes and texture segregation
Graham, N. (1989b)
Physica Scripta, 39, 147-152
Abstract. Parallel processing by a set of multiple mechanisms selectively sensitive along various dimensions of visual patterns - e.g., spatial frequency, orientation, direction-of-motion, - seems to be one of the earlier states in the perception of forms and objects. The evidence for these mechanisms - which comes primarily from neurophysiology and psychophysics using near-threshold patterns (patterns of such low contrast that they are imperfectly discriminable from a blank field of the same mean luminance) - and the properties of these mechanisms are briefly reviewed. The responses of these mechanisms to some texture patterns used to investigate the segmentation of the visual field into separate region is illustrated. PDF (1.3MB) (erratum)
Sensory and Perceptual Processes
Graham, N., Bartoshuk, L., Bregman, A., Hochberg, J., Rosenfeld, A., and Studdert-Kennedy, M. (1989)
In Leading Edges in Social and Behavioral Science, edited by R. D. Luce, N. J. Smelser, and D. R. Gerstein. New York: Russell Sage Foundation.
Abstracted from preface of book and introduction to chapter. This book is a collection of the working papers on from the ten-year outlook on research opportunities, a project of the Committee on Basic Research in the Behavioral and Social Sciences, Commission on Behavioral and Social Sciences and Education, National Research Council. Each working paper was written by an interdisciplinary committee attempting to reach concensus on the most promising areas of research in their fields. The working paper on Sensory and Perceptual Processes contains a number of recent developments that are to be considered examples only, as they were chosen as much for what was hoped to be their easy describability to persons outside the field as for their intrinsic scientific merit. PDF (720K)
Contrast and spatial variables in texture segregation: Testing a simple spatial-frequency channels model
Sutter, A., Beck, J. and Graham, N. (1989)
Perception and Psychophysics, 46, 312-332
Abstract. Observers were shown patterns composed of two textures in which each texture contained two types of elements. The elements were arranged in a striped pattern in the top and bottom regions and in a checked pattern in the center region. Observers rated the degree to which the three regions were seen as distinct. When the elements were squares or lines, perceived segregation resulting from differences in element size could be canceled by differences in element contrast. Minimal perceived segregation occurred when the products of the area and the contrast (areal contrasts) of the elements were equal. This dependence of perceived segregation on the areal contrasts of the elements is consistent with a simple model based on the hypothesis that the perceived segregation of the regions is a function of their differential stimulation of spatial-frequency channels. Two aspects of the data were not consistent with quantitative predictions of the model. First, as the size difference between the large and small elements increased, the ratings at the point of minimum perceived segregation increased. Second, some effects of changing the fundamental frequency of the textures were not predicted by the model. These discrepancies may be explained by a more complex model in which a retification or similar nonlinearity occurs between two stages of orientation- and spatial-frequency-selective linear filters. PDF (1.3MB) (erratum)
Lightness Differences and the Perceived Segregation of Regions and Populations
Beck, J., Graham, N., and Sutter, A. (1991)
Perception and Psychophysics, 257-269
Abstract. A striking finding reported by Beck, Sutter, and Ivry (1987) was that, in textures composed of regions differentiated by the arrangement (checks and stripes) of two texture elements (light and dark squares), a large lightness difference between the squares could fail to yield segregation between the regions, whereas a smaller lightness difference could sometimes yield strong segregation. In the experiments reported here, we compared the segregation of striped and checked arrangements of light and dark squares into regions with the segregation of two randomly interspersed populations of light and dark squares into subpopulations. Perceived lightnesses are the same for a given set of squares, whether they are arranged in regions or in intermixed populations. Perceived population segregation is approximately a single-valued function of the lightness differences of the squares, but perceived region segregation is not. The reason for the difference between population segregation and region segregation may be that region segregation is mediated by detectors' having large oriented receptive fields (large bar detectors) that are sensitive to the fundamental spatial frequency and orientation of the texture region as defined by the arrangement of the squares (Beck et al., 1987;Sutter, Beck, & Graham, 1989). These detectors cannot be responsible for population segregation, because the light and dark squares are distributed randomly throughout these patterns and therefore do not define a consistent arrangement of any particular spatial frequency or orientation. The light and dark squares in the population patterns fall equally on excitatory and inhibitory regions of large bar detectors. A plausible explanation for population segregation is to suppose that the segregation is the result of similarity grouping of the light and dark squares. PDF (744K)
Complex Channels, Early Local Nonlinearities, and Normalization in Texture Segregation
Graham, N. (1991)
In Computational Models of Visual Processing, edited by M. L. Landy and J. A. Movshon, Cambridge, MA: MIT Press
From the chapter. The aim was to find out what such
a simple [spatial-frequency analyzers] model could do and, on
the basis of systematic discrepancies between it and the data,
to add further visual processes (either low- or higher-level)
to the model and then again test . The enhanced model describes
these hypothesized nonlinear processes and presents some preliminary
predictions from the enhanced model for one kind of experiment
(a kind for which calculating predictions is easy if one is willing
to make some reasonable simplifying assumptions). The nonlinear
behavior exhibited in these experiments can probably all be accounted
for by two different nonlinearities that exist at relatively low
levels in the visual pathways:
(1) A retification-type (spatial) nonlinearity quite like that
used to describe complex cortical cell behavior;
(2) a very dramatic compressive nonlinearity, occurring at contrasts
far less than 25 percent, which can be quantitatively predicted
either by an early local nonlinearity occurring before the channels
or by normalization among the channels (perhaps intracortical
inhibition).
Perhaps after all, higher-level processes may not play a substantial role in region segregation if region segregation is a quick and easy computation done early in visual processing in order to ease the overload on higher processes by delimiting regions beyond which a given computation need not be done. PDF (1.5MB)
Breaking the visual stimulus into parts
Graham, N.(1992)
Current Directions in Psychological Science, 1, 55-61
Abstract. Reviews the elementary parts into which visual information is initially analyzed, in particular, the elementary parts that are relevant for seeing patterns in space and time. Near-threshold psychophysical studies of pattern vision give evidence for a model in which a fundamental process is the breaking down of the visual stimulus by a set of multiple analyzers, acting in parallel with different ranges of sensitivity along different dimensions. Research also suggests that the physiological substrate of the multiple analyzers is area V1 (the lowest level of cortical visual processing) and perhaps area V2. Although much is known about how the visual systems analyze the proximal visual stimulus into parts, how the parts are put back together into a perception that corresponds to the distal stimulus is still not known. (HTML text plus figs.) PDF (484K)
Nonlinear processes in spatial-frequency channel models of perceived texture segregation: Effects of sign and amount of contrast
Graham, N., Beck, J. and Sutter, A. (1992)
Vision Research, 32, 719-743
Abstract. Observers rated the degree of segregation between two textures, each composed of the same two element types but in differing arrangements (a checkerboard arrangement in the middle region of the pattern and a striped arrangement in the top and bottom regions). The two element types in a given pattern were either both solid squares or both center-surround elements. The two element types were identical in size but differed in sign and/or amount of contrast. Discrepancies between the observers' ratings of perceived segregation and the predictions of simple (linear) spatial-frequency and orientation channels models of texture segregation suggested adding nonlinear processes to the model. Complex channels (a retification-type nonlinearity between two linear-filtering stages) can explain why some patterns made of center-surround elements segregate even though there is little energy at the spatial frequencies that differentiate the two textures. Complex channels cannot, however, explain the poor segregation of "same-sign-of-contrast" patterns (Where the luminances of the two element types were both far above or far below the background). This second result might arise from a local nonlinearity preceding the channels and might be ascribed to retinal light adaptation except that it occurs at contrasts Û25%! Alternatively, it might arise from normalization, which may result from intracortical inhibition. Some preliminary quantitative predictions were computed from two models, one incorporating complex channels and an early local nonlinearity, the other complex channels normalization. With suitable choices of parameters, either model could account for the results. PDF (1.8MB)
Quantal noise and decision rules in dynamic models of light adaptation
Graham, N. and Hood, D. (1992)
Vision Research, 32, 779-787
Abstract. To evaluate some of the consequences of including probabilistic processes (e.g. quantal noise) in a computable model of light-adaptation dynamics, we considered the behavior of a general class of models. These models contain four stages: (1) early noise; (2) a deterministic filtering and gain-changing stage; (3) late noise; (4) a decision rule that is either an ideal (signal-known-exactly) detector or a peak-trough detector. With the ideal detector and without late noise, the observer's sensitivity as a function of mean luminance and temporal frequency is not affected by the filtering and gain-changing stage. Consequently, if the early noise is entirely quantal fluctuations, sensitivity will always be a square-root function of mean luminance and a uniform (flat) function of temporal frequency. This latter prediction is contradicted by all known data; either the ideal-detector is the wrong decision rule or sensitivity is almost always limited by sources of noise other than quantal fluctuations. With the peak-trough detector, however, with or without late noise, the observer's sensitivity as a function of temporal frequency does reflect the sensitivity of the low-level filtering and gain-changing stage. Late noise is needed, however, if the observer's sensitivity as a function of mean luminance is to go through both a square-root and a Weber region. Comparing these conclusions to similar work on the spatial frequency dimension highlights differences between the spatial and temporal frequency domains. Finally, on the basis of these analyses and evidence from the literature, we question whether quantal fluctuations limit visual sensitivity under any condition. PDF (580K)
Modeling the dynamics of light adaptation: The merging of two traditions
Graham, N. and Hood, D. (1992)
Vision Research, 32, 1373-1393
Abstract. Light adaptation has been studied using aperiodic and periodic stimuli. Two well-documented phenomena are described: the background-onset effect (from an aperiodic-stimulus tradition) and high-temporal-frequency linearity (from the periodic-stimulus tradition). These phenomena have been explained within two different theoretical frameworks. Here we briefly review those frameworks. We then show that the models developed to predict the phenomenon from one tradition cannot predict the phenomenon from the other tradition, but that the models from the two traditions can be merged into a class of models that predicts both phenomena. PDF (1.5MB)
Nonlinear processes in perceived region segregation: Orientation selectivity of complex channels
Graham, N., Sutter, A., Venkatesan, C., and Humaran, M. (1992)
Opthalmic and Physiological Optics, 12, 142-146.
Abstract. Models incorporating linear spatial-frequency and orientation-selective channels explain many aspects of visual texture segregation. The inability of such models to fully explain texture segregation results indicates that non-linear processes are also involved. One non-linearity that has been suggested is complex channels consisting of two stages of linear filtering separated by a retification-type non-linearity (much like cortical complex cells). Here we further demonstrate the usefulness of complex channels in explaining texture segregation results and investigate the orientation-selectivity of the first stage of such complex channels. Our results suggest that the first stage is much more selective for orientation than are lateral geniculate nucleus cells, but that the first-stage orientation bandwidth is rather wide with some interaction occurring between perpendicular orientations. PDF (1.8MB) (Erratum)
Spatial-frequency- and orientation-selectivity of simple and complex channels in region segregation
Graham, N., Sutter, A., Venkatesan, C. (1993)
Vision Research , 33, 14, 1893-1911
Abstract. Models incorporating spatial-frequency- and orientation-selective channels explain many texture segregation results, particularly when known nonlinearities are included. One such nonlinearity is complex channels. A complex channel consists of two stages of linear filtering separated by a retification-type nonlinearity. Here we investigate the spatial-frequency- and orientation-selectivity of simple (linear) channels and of the complex channels' first stage. Observers rated the degree of segregation between two "textures" both composed of elements which were Gabor patches. When the textures differed in type of element (e.g. one composed of vertical and the other of horizontal Gabor patches), the segregation results yield bandwidth estimates for simple channels of approx. 0.5-1.0 octave on the spatial-frequency dimension and 5-20 deg of rotation on the orientation dimension. When the textures differ in the arrangement of elements (e.g. striped vs checkerboard arrangements, both of vertical and horizontal patches), the segregation results yield bandwidth estimates for the first stage of complex channels. These estimates, while differing substantially from one observer to another, were always substantially wider than those for simple channels (by at least a factor of two) but narrower than bandwidths of LGN cells (particularly on the orientation dimension where LGN cells show little selectivity at all). PDF (1.8MB) (Erratum)
Nonlinearities in texture segregation
Graham, N. (1994)
Higher-order Processing in the Visual System (Ciba Foundation Symposium No. 184) , pp. 309-329, Chichester:Wiley
Abstract. The existence of complex (non-Fourier, second-order) channels is suggested by some characteristics of segregation perceived between regions distinguished by visual texture. These complex channels consist of two linear-filtering stages separated by a rectification-type non-linearity. We have investigated (i) the spatial frequency selectivity and orientation selectivity of their first-stage filters; (ii) the relationship between the preferred values of orientation and spatial frequency at the first and second filters; (iii) spatial pooling and its implications for the non-linearity at the middle of the complex channel; and (iv) the dynamics of complex and simple linear channels. An intensive non-linearity is also necessary to explain perceived region segregation. This intensive non-linearity might arise from an early local non-linearity preceding the channels (perhaps retinal light adaptation) or from normalization among the channels themselves (perhaps due to intracortical inhibition). Deciding between these two candidates has been more difficult than we had hoped. It appears that : (I) this intensive non-linearity operates for both simple and complex channels; (ii) the effects on it of changing mean luminanceor spatial scale may be accounted for by a sensitivity parameter; (iii) it can be dramatically compressive even at contrasts less than 25% for high mean luminances and large scales; and (iv) at even lower contrasts there is an accelerating non-linearity that acts before the second filter of the complex channels. PDF (1.2MB)
Investigating simple and complex mechanisms in texture segregation using the speed-accuracy tradeoff method
Sutter, A. and Graham, N. (1995)
Vision Research., 35, 20, 2825-2843
Abstract. Several recent models of texture segregation have proposed two mechanisms: simple, linear channels (first-order, Fourier mechanisms) and complex channels (second-order, non-Fourier mechanisms). We used the speed-accuracy tradeoff (SAT) method to examine the time course of texture segregation processing in simple and complex channels. The stimuli were texture patterns designed to segregate primarily as a result of activity in one set of channels or the other. We presented subjects with channels that were checked or striped arrangements of either Gaussian-blob or Gabor-patch elements. Subjects were required to identify the orientation of a rectangular texture region embedded in a background field of a different texture. A range of contrasts and a control task were used to equate visibility of the Gabor and Gaussian textures. SAT functions were obtained by requiring subjects to respond within 200 msec after an auditory cue. We found that when segregation depended primarily on simple channels, performance was faster than when it depended primarily on complex channels: the 75% correct level was reached 100-200 msec sooner and this extra speed was reflected both in smaller delay and higher rate parameters. PDF (2.4MB)
Testing a computational model of light-adaptation dynamics
Wiegand, T.E., Hood, D.C., and Graham, N. (1995)
Vision Research., 35, 21, 3037-3051
Abstract. Experiments from the periodic and aperiodic traditions were used to guide the development of a quantitatively valid model of light adaptation dynamics. Temporal contrast sensitivity data were collected over a range of three log units of mean luminance for sinusoids of 2 to 50 Hz. Probe thresholds on flashed backgrounds were collected over a range of stimulus-onset asynchronies and background intensities from 0.1 to 1000 td. All experiments were performed foveally in the photopic range and used a consistent stimulus paradigm and psychophysical method. The resulting model represents a merging of elements from both traditions, and consists of a frequency-dependent front-end followed by a subtractive process and static nonlinearity. PDF (1.2MB)
Effect of spatial scale and background luminance on the spatial and intensive nonlinearities in texture segregation
Graham, N. and Sutter, A. (1996)
Vision Research, 36, 10, 1371-1390
Abstract. Perceived segregation between element-arrangement textures is affected both by spatial scale and background luminance. the effects of the spatial nonlinearity are consistent with the proposed structure for complex (second-order) channels. The effects on the intensive nonlinearity are not consistent with an early, local nonlinearity but are consistent with either (I) a relatively early, local, nonlinearity occurring before the spatial frequency channels but after a sensitivity-setting stage, or (ii) inhibitory interaction among channels modeled as a normalization network. Thus the texture intensive nonlinearity comes after sensitivity to spatial frequency and background luminance has been determined. For six of seven observers, the texture intensive nonlinearity was compressive by 10% contrast for both increments and decrements ( at high background luminance, large spatial scale). PDF (1.9MB)
Probed-sinewave paradigm: A test of models of light-adaptation dynamics
Hood, D.C., Graham, N., Wiegand, T.E, and Chase, V. M. (1997)
Vision Research, 37, 9, 1177-1191
Abstract. Studies of light adaptation have, in general, employed either aperiodic or periodic stimuli. In earlier work, models originally developed to predict the results from one tradition failed to predict results from the other but the models from the two traditions could be merged to predict phenomena from both. To further test these merged models, a paradigm combining both types of stimuli was used. The threshold for a brief flash (the probe) was measured at various phases on a background that was varied sinusoidally in time. The probe threshold depends upon the phase at which it is presented for all background frequencies used, 0-16 Hz. These threshold variations are not well described by a sinewave; the peak threshold is >180 deg out of phase with the trough threshold. Further, the positions of the peaks and troughs shift fairly abruptly at background modulations of 4-8Hz. The difference between the peak and trough thresholds varies as a function of temporal frequency in a manner approximating the temporal contrast sensitivity function. The dc level (mean threshold) does not. The peak-trough difference dominates at low frequencies of background modulation, while the dc level dominates for higher frequencies. Existing models of light adaptation do not predict the key features of the data. PDF (1.6MB
Spatial summation in simple (Fourier) and complex (non-Fourier) channels in texture segregation
Graham, N., and Sutter, A. (1998)
Vision Research, 38, 231-257
Abstract. Complex (non-Fourier, second-order) channels have been proposed to explain aspects of texture-based region segregation and related perceptual tasks. Complex channels contain two stages of linear filtering with an intermediate pointwise nonlinearity. The intermediate nonlinearity is crucial. Without it, a complex channel is equivalent to a single linear filter (a simple channel). Here, we asked whether the intermediate nonlinearity is piecewise-linear (an ordinary rectifier), or compressive, or expansive. We measured the perceptual segregation between element-arrangement textures where the contrast and area of the individual elements were systematically varied. For solid-square elements, the tradeoff between contrast and area was approximately linear, consistent with simple linear channels. For Gabor-patch elements, the tradeoff was highly nonlinear, consistent with complex channels in which the intermediate nonlinearity is expansive (with an exponent somewhat higher than 2). Also, substantial individual differences in certain details were explainable by differential intrusion from "off-frequency" complex channels. Lastly, the results suggest that the strongly compressive intensive nonlinearity previously known to act in texture segregation cannot be attributed to a compressive nonlinearity acting locally and relatively early (before the spatial-frequency and orientation-selective channels) but could result from inhibition among the channels (as in a normalization network). PDF (2.0MB)
Threshold fluctuations on temporally modulated backgrounds: A possible physiological explanation based upon a recent computational model
Hood, D.C. and Graham, N.G. (1998)
Visual Neuroscience, 15, 957-967
Abstract. When a temporally fluctuating background is rapidly modulated (e.g. 30Hz), the threshold variation of a superimposed flash (the probe) is approximately sinusoidal and in phase with the stimulus. But, with low rates of sinusoidal modulation (e.g. 1Hz), the threshold variation is distinctly nonsinusoidal in shape. The bases of these aspects of the data, as well as unmodulated, dc, threshold elevation, are poorly understood. Here 30-Hz and 1-Hz conditions are simulated using a new model of light adaptation (Wilson, 1997). By assuming that the OFF pathway is twice as sensitive as the ON pathway, the model correctly captured the key aspects of both conditions. The results suggest that the 1-Hz data are mediated by a mixture of ON and OFF pathways while the 30-Hz data are largely mediated by the OFF pathway. The probe thresholds on the 30-Hz background appear approximately sinusoidal and approximately in phase with the background stimulus. A number of factors contribute to this deceptively simple observation. PDF (424K)
Texture segregation shows only a very small lower-hemifield advantage
Graham, N., Rico, M., Offen, S. and Scott, W. (1999)
Vision Research, 39, 1171-1175
Abstract. Possible hemifield differences in texture segregation were investigated for both simple (Fourier, linear) and complex (non-Fourier, 2nd-order) texture channels. There was only a very small lower-field advantage for texture segregation, consistent with the notion that the major processing in texture segregation is quite low level, perhaps area V1. Complex-channel tasks do not show larger hemifield asymmetries than do simple-channel tasks, which suggests that the processes in complex texture channels are not higher level than those in simple ones. PDF (180K)
Exploring the dynamics of light adaptation: The effects varying the flickering background's duration in the probed-sinewave paradigm.
Wolfson, S. and Graham, N. (2000)
Vision Research, 40, 2277-2289.
Abstract. In the probed-sinewave paradigm, threshold for detecting a probe is measured at various phases with respect to a sinusoidally-flickering background. Here we vary the duration of the flickering background before (and after) the test probe is presented. The adaptation is rapid; after approximately 10-30 msec of the flickering background, probe threshold is the same as that on a continually-flickering background. It is interesting that this result holds at both low (1.2 Hz) and middle (9.4 Hz) frequencies because at middle frequencies (but not at low) there is a dc-shift, i.e. probe threshold is elevated at all phases relative to that on a steady background (of the same mean luminance). We compare our results to predictions from Wilson's model [Wilson (1997), Vis. Neurosci., 14, 403-423; Hood & Graham (1998), Vis. Neurosci., 15, 957-967] of light adaptation. The model predicts the rapid adaptation, and the dc-shift, but not the detailed shape of the probe-threshold-versus-phase curve at middle frequencies. PDF (536K)
Normalization: Contrast-gain control in simple (Fourier) and complex (non-Fourier) pathways of pattern vision.
Graham, N. and Sutter, A. (2000)
Vision Research, 40, 2737-2761.
Abstract. Results from two types of texture-segregation experiments considered jointly demonstrate that the heavily-compressive intensive nonlinearity acting in static pattern vision is not a relatively early, local gain control like light adaptation in the retina or LGN. Nor can it be a late, within-channel contrast-gain control. All the results suggest that it is inhibition among channels as in a normalization network. The normalization pool affects the complex-channel (second-order, non-Fourier) pathway in the same manner in which it affects the simple-channel (first-order, Fourier) pathway, but it is not yet known whether complex channels' outputs are part of the normalization pool. PDF (732K)
Errata to Graham & Sutter (2000)
Comparing increment and decrement probes in the probed-sinewave paradigm.
Wolfson, S. and Graham, N. (2001a)
Vision Research, 41, 1119-1131
Abstract. Using the probed-sinewave paradigm, we explore the differences between increment and decrement probes across a range of frequencies (approx. 1-19 Hz). In this paradigm, detection threshold is measured for a small test probe presented on a large sinusoidally flickering background (at eight different phases). Probe thresholds are very similar for increment and decrement probes, but there is a very small (and systematic) difference: increment thresholds are usually slightly higher relative to decrement thresholds during the part of the cycle when the background's intensity is increasing. Although Wilson's (1997, Vis. Neuro., 14, 403-423) model substantially underestimates the size of this difference, it predicts some phase dependency. However, the existence of On- and Off- pathways in Wilson's model is not important for these predictions. A recent model by Snippe, Poot, and van Hateren (2000, Vis. Neuro., 17, 449-462) may be able to predict this result by using explicit contrast-gain control rather than separate On- and Off- pathways. Auxiliary experiments measuring the perceived polarity of the probes provide a further argument suggesting that separate On- and Off- pathways are not useful in explaining increment and decrement probe thresholds. PDF (444K)
A note about preferred orientations at the first and second stages of complex (second-order) texture channels
Graham, N. and Wolfson, S. (2001)
Journal of the Optical Society of America A, 18, 2273-2281.
Abstract. Complex (second-order) channels have been useful in explaining many of the phenomena of perceived texture segregation. These channels contain two stages of linear filtering with an intermediate pointwise nonlinearity. One unanswered question about these hypothetical channels is that of the relationship between the preferred orientations of the two stages of filtering. Is a particular orientation at the second stage equally likely to occur with all orientations at the first stage, or is there a bias in the "mapping" between the two stages' preferred orientations? In this study we consider two possible mappings: that where the orientations at the two stages are identical (called "consistent" here) and that where the orientations at the two stages are perpendicular ("inconsistent"). We explore these mappings using a texture-segregation task with textures composed of arrangements of grating-patch elements. The results imply that, to explain perceived texture segregation, complex channels with a consistent orientation mapping must be either somewhat more prevalent or more effective than those with an inconsistent mapping. PDF (448K)
The processing in the probed-sinewave paradigm is likely retinal.
Wolfson, S. and Graham, N, (2001b)
Visual Neuroscience. 18, 1003-1010
In the probed-sinewave paradigm - used to study the dynamics of light adaptation - a small probe of light is superimposed on a sinusoidally flickering background. Detection threshold for the probe is measured at various times with respect to the flickering background. Here we present such stimuli using three methods: monoptic (the probe and the flickering background are presented to the same eye), dichoptic (the probe is presented to one eye and the flickering background is presented to the other eye), and binocular (the probe and the flickering background are both presented to both eyes). The results suggest that the processing associated with detecting the probe is primarily in the retina (or any place with monocular input). However, the results also suggest a slight amount of processing in the cortex (or any place with binocular input), particularly at the higher frequency of flickering background used here (9.4 Hz versus 1.2 Hz). A simple schematic model with three ocular dominance channels is consistent with the results. PDF (1.8MB)
Visual Perception of Texture
Landy, M. and Graham, N. (2003)
In The Visual Neurosciences, Eds. L. M. Chalupa and J.S. Werner, MIT press. Vol. 2, pp. 1106-1118.
(No abstract. These are the first paragraphs from: 1. Introduction
and the one paragraph of 6. Conclusions)
1. Introduction
What is visual texture, and how might a study of the visual perception
of texture help us to better understand human vision? In this
chapter we will attempt to give the reader a feel for how the
study of texture perception is useful both in understanding the
impact of texture itself, as well as in providing a better understanding
of basic visual mechanisms that respond not only to texture but
to all visual stimuli. This review will be relatively brief and,
of necessity, incomplete. We hope to give an overview of the different
research areas concerned with texture perception and of the current
issues.
6. Conclusions
The perception of texture is a rich and varied area of study.
In the early coding of texture borders, there is some common ground
between current psychophysical data and models and the physiology
of primary visual cortex, such as the suggestion that texture
border coding involves a succession of linear spatial filters
and nonlinearities that include both static nonlinearities as
well as contrast gain control mechanisms. Less well understood,
however are such higher-level computations involving texture as
the calculation of figure-ground, the coding of texture appearance,
and the determination of depth and 3-D shape from texture cues.
PDF (2.8MB)
For publications since 2004, see Research AFTER mid-2004.