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Journal ArticleDOI

Invariant features of spatial summation with changing locus in the visual field.

01 May 1970-The Journal of Physiology (John Wiley & Sons, Ltd)-Vol. 207, Iss: 3, pp 611-622
TL;DR: Spatial summation curves have been determined under photopic conditions for loci between 5 and 55° from fixation and the area and Weber fraction for the largest stimulus showing complete summation has been estimated.
Abstract: 1. Spatial summation curves have been determined under photopic conditions for loci between 5 and 55° from fixation. At each locus the area and Weber fraction for the largest stimulus showing complete summation (Sc) has been estimated. While the area of Sc increases progressively towards the periphery, its Weber fraction remains constant. 2. The invariance of the Weber fraction for Sc, coupled with changes in its area, have been compared with similar findings observed during changes in adaptation level, in impaired fields, and during accommodative and convergence changes. It is suggested that the Weber fraction for Sc may be an important parameter of visual function which is maintained under changing conditions by alterations in the area over which background energy is summated. 3. It has been shown that, for stimulus areas up to at least 1 log unit greater than Sc, all the summation curves from 5 to 55° from fixation can be superimposed by simple displacement along the log area axis. For loci closer together, the superimposition has been shown for larger ranges of areas beyond Sc. This suggests that, so far as spatial summation is concerned, changes in locus serve only to change the spatial scale of the visual system. 4. Comparisons have been made between the area of Sc at various loci and the sizes of the central regions of the receptive fields of retinal ganglion cells determined electrophysiologically in the primate.
Citations
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Journal ArticleDOI
TL;DR: Crowding in the fovea and peripheral vision showed that when scaled in proportion to recent estimates of the cortical magnification factor, vernier acuity is as good in the periphery as it is centrally.

638 citations

Journal ArticleDOI
TL;DR: The results indicated specificly that visual patterns can be made equally visible if they are scaled so that their calculated cortical representations become equivalent and the power law of spatial summation suggests the existence of a central integrator that pools the activity of cortical neurons.
Abstract: This study shows that photopic contrast sensitivity and resolution can be predicted by means of simple functions derived by using the cortical magnification factor M as a scale factor of mapping from the visual field into the striate cortex. We measured the minimum contrast required for discriminating the direction of movement or orientation of sinusoidal gratings, or for detecting them in central and peripheral vision. No qualitative differences were found between central and peripheral vision, and almost all quantitative differences observed could be removed by means of a size compensation derived from M. The results indicated specifically that (1) visual patterns can be made equally visible if they are scaled so that their calculated cortical representations become equivalent; (2) contrast sensitivity follows the same power function of the cortical area stimulated by a grating at any eccentricity; (3) area and squared spatial frequency are reciprocally related as determinants of contrast sensitivity; and (4) acuity and resolution are directly proportional to M, and the minimum angle of resolution is directly proportional to M-1. The power law of spatial summation expressed in (2) and (3) suggests the existence of a central integrator that pools the activity of cortical neurons. This summation mechanism makes the number of potentially activated visual cells the most important determinant of visibility and contrast sensitivity. The functional homogeneity of image processing across the visual field observed here agrees with the assumed anatomical and physiological uniformity of the visual cortex.

512 citations

Journal Article
TL;DR: The hypothesis that the target area (A) can be represented by the number of underlying ganglion cells (G) to give G(k) = C/L is tested to see if spatial summation is unchanged in glaucoma and this scale more accurately reflects the amount of neuronal damage.
Abstract: PURPOSE. Differential light sensitivity (DLS) in white-on-white perimetry is used as a measure of ganglion cell function to estimate the amount of neuronal damage in glaucoma. The physiological relationship between DLS and ganglion cell numbers is poorly understood. Within small retinal areas, brightness information is summated, so that A p L 5 C ,o rA 5 C/L, where A is target area, L is threshold luminance, and C is a constant. In larger illuminated areas, as with a Goldmann size III target in perimetry, summation is incomplete, so that A k 5 C/L, where k is the coefficient of summation, and 0 , k , 1. This study tests the hypothesis that the target area (A) can be represented by the number of underlying ganglion cells (G) to give G k 5 C/L. METHODS. Normative human data for ganglion cell density within 30° of retinal eccentricity were taken from the literature and corrected for lateral displacement of ganglion cells from the fovea to estimate ganglion cell receptive field density (g). The number of ganglion cell receptive fields within a Goldmann size III target (G) was calculated from target area (A) and receptive field density (g )[ G 5 A (g)]. Normative data for DLS in the central 30° (Humphrey 30-2) were taken from the literature. The coefficient summation (k) was measured empirically at each Humphrey 30-2 test point in 8 normal subjects. The relationship between DLS and G was investigated by plotting DLS as decibels (dB) against G and DLS as 1/L (1/Lamberts) against G k . The physiological relationship was extrapolated to glaucomatous ganglion cell loss by calculating hypothetical cell losses for 3 and 6 dB sensitivity defects at each test point. RESULTS. Spatial summation increased with eccentricity. The relationship between DLS (dB) and G was curvilinear. The relationship between DLS (1/L) and G k was linear (r 2 5 0.73). The extrapolation to glaucomatous ganglion cell loss indicated that a proportionally greater loss of ganglion cells is required in the central compared with peripheral visual field for equal losses in dB sensitivity. CONCLUSIONS. The number of underlying ganglion cells, adjusted for local spatial summation, is better reflected by the DLS scale of 1/L than by dB. If spatial summation is unchanged in glaucoma, this scale more accurately reflects the amount of neuronal damage. (Invest Ophthalmol Vis Sci. 2000;41:1774 ‐1782)

263 citations

Journal ArticleDOI
TL;DR: This article examined the contribution of optical and photoreceptor properties as well as receptor pooling to eccentricity-dependent variations in spatial vision by comparing the performance of ideal observers with that of human observers.
Abstract: We examined the contribution of optical and photoreceptor properties as well as receptor pooling to eccentricity-dependent variations in spatial vision by comparing the performance of ideal observers with that of human observers. We measured contrast sensitivity functions in human observers and calculated such functions in ideal observers for retinal eccentricities of 0-40 deg. Comparisons of human and ideal performance in a variety of tasks reveal that many aspects of the variation in spatial vision with eccentricity can be understood from an analysis of the discrimination information available at the retinal ganglion cells.

204 citations

Journal ArticleDOI
TL;DR: The current evidence for the nature of the ‘structure–function’ relationship in primary open‐angle glaucoma is outlined and the current mathematical models linking structure and function are highlighted.
Abstract: An understanding of the relationship between functional and structural measures in primary open-angle glaucoma is necessary for both grading the severity of disease and for understanding the natural history of the condition This article outlines the current evidence for the nature of this relationship and highlights the current mathematical models linking structure and function Large clinical trials demonstrate that both structural and functional change are apparent in advanced stages of disease, and at an individual level, detectable structural abnormality may precede functional abnormality in some patients, whereas the converse is true in other patients Although the exact nature of the 'structure-function' relationship in primary open-angle glaucoma is still the topic of scientific debate and the subject of continuing research, this article aims to provide the clinician with an understanding of the past concepts and contemporary thinking in relation to the structure-function relationship in primary open-angle glaucoma

185 citations


Cites background from "Invariant features of spatial summa..."

  • ...This plot bears a striking resemblance to spatial summation curves which predict a shallower slope for test locations nearer fixation and a steeper slope peripherally.(28,31,69) The change in slope can be explained by the size of the (Goldmann size III) test stimulus in relation to the critical area (Ricco’s area)....

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References
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Journal ArticleDOI
TL;DR: The present experiments show up the complicated interrelations between temporal and spatial summation and background intensity; tentative explanations of these effects, and of the failure to perform up to the quantal fluctuation limit, are put forward.
Abstract: The present experiments were undertaken as part of an investigation of the suggestion made by Rose (1942, 1948) and de Vries (1943) that human visual performance is limited by the inevitable fluctuations in the numbers of quanta absorbed in the retina. In a previous paper (Barlow, 1957) it was shown that this idea (modified by assuming that there is also a weak intrinsic source of noise) leads to theoretical curves which fit experimental determinations of increment threshold made with a short duration small area test stimulus superimposed upon a large uniform adapting field. It was also shown that big changes in the amount of temporal and spatial summation occur when the background intensity is changed, with the result that when thresholds are determined with a long duration large area test stimulus the experimental points deviate from the appropriate theoretical curve and tend to obey the Weber law instead. In following up this finding there were two objectives. The quantum fluctuation hypothesis predicts that the increment threshold intensity should be inversely proportional to the square root ofthe area and duration ofthe stimulus, and the first object was to find whether the occurrence of these laws fitted in with the hypothesis: the results show that the predicted laws of summation do hold over certain ranges, but when they hold the actual values of the thresholds are higher than the theory predicts. The second objective was to determine the parameters oc and r which were introduced in the previous paper; these are the area and time over which quanta absorbed from the background light are liable to be confused with those absorbed from a short duration small area stimulus light, and here the results obtained are disappointing, for one can only derive lower limits to these quantities. On the other hand, the results do show up the complicated interrelations between temporal and spatial summation and background intensity; tentative explanations of these effects, and of the failure to perform up to the quantal fluctuation limit, are put forward. 22 PHYSIO. CXLI

671 citations

Journal ArticleDOI
TL;DR: An attempt is made to determine the value of intrinsic retinal noise, and to test whether the idea that thresholds are efficient statistical judgements of constant fallibility can be applied to the differential threshold of the human eye at low intensities.
Abstract: It was shown by Hecht, Shlaer & Pirenne (1942) and Van der Velden (1944, 1946) that the quantal nature of light is largely responsible for the variability of response of human subjects to near-threshold visual stimuli. At about the same time Rose (1942, 1948) and de Vries (1943) suggested that the inescapable variability in the number of quanta absorbed from a constant light limits the accuracy with which its intensity can be judged, and that the differential threshold is set at as low a level as is compatible with this limit. If this suggestion is correct, one's concept of the nature of a psycho-physical threshold needs to be altered considerably; instead of recalling the all-or-nothing behaviour of a nerve fibre, one should consider the 'threshold' of sensitivity of a galvanometer which is constantly perturbed by noise, or some other example of a limit which is set in accordance with statistical criteria. It has been shown that such a view of the nature of threshold is entirely compatible with the data for the absolute sensitivity of the eye if it is assumed that there is a certain low level of intrinsic retinal noise, even in complete darkness (Barlow, 1956). In the present paper an attempt is made to determine the value of this retinal noise, and to test whether the idea that thresholds are efficient statistical judgements of constant fallibility can be applied to the differential threshold of the human eye at low intensities.

402 citations

Journal ArticleDOI
TL;DR: In this article, the receptive fields of single optic nerve fibres in the spider monkey were described, and some observations were also made on ganglion cell responses to monochromatic stimuli.
Abstract: Our present knowledge ofhow mammalian retinal ganglion-cell receptive fields are organized is based mainly on findings in the cat by Kuffler (1953). These results have since been confirmed and extended (Barlow, FitzHugh & Kuffler, 1957; Hubel, 1960; Wiesel, 1960), but up to now similar studies have not been made in primates. The retina of the monkey is of interest, since in most species, including Ateles (spider monkey) and Macaca mulatta, it is deeply pigmented and has a well defined fovea. It appears to be much closer to the human retina than to that of the cat, which has a highly reflectile tapetum and lacks a fovea. The purpose of this report is to describe the receptive fields of single optic nerve fibres in the spider monkey. In view of the monkey's ability to discriminate colours, some observations were also made on ganglion cell responses to monochromatic stimuli.

357 citations

Journal ArticleDOI
TL;DR: This hypothesis is put forward: according to which the receptive field is considered as a servo system, in which the light stimulus causes excitation and inhibition, balancing it.

160 citations