0042.6989192 f5.00+0.00

VisionRes.Vol.32,NO. 6,pp. 1085-1097.1992

Pergamon Press Ltd

Printed in Great Britain

The Coding of Spatial Position by the Human Visual System: Effects of Spatial Scale and Contrast ROBERT

F. HESS,* IAN E. HOLLIDAYt

Receiwd f .&gust 1991; in rwisedform

25 October 1991

In this study we investigate the nature of the computations that underlie the encoding of spatial position by the human visual system, S~ci~ea~y, we explore the relatio~jp between abler accuracy and spatial scale on the one hand, and between a~gnment accuracy and contrast on the other. We do this for stimuli where local luminance, local contrast, and o~entation cues do not underlie ~~o~a~e. The results suggest that spatial localisation is inde~nd~t of spatial seaIe and weakly dependent on contrast, We present subsequent models based on the properties of some classes of visual cortical neurones, namely multiplicative noise and contrast energy detection of complex cells, which describe the form of these relationships. Spatiai alignment

Contrast

Spatial frequency

Spatial scale

spatial mechanisms, the individua1 contributions of which are difficult to disentangle. There is now abundant evidence that the early stages Ifwe are to understand the mechanisms which underlie of visual processing involve arrays of spatial filters. the encoding of spatial localisation we need to use: (I) Psychophysical evidence for this comes from. among stimdus arrangements for which local luminance and others, studies on adaptation (Bfakemore & Campbell, contrast cues are not used and for which orientation 1969) and masking ~Stromeyer & Julesz, 1972). Electrojudgements do not determine performance; and (2) physiological evidence comes from the properties of spatially narrow-band stimuli so that the relative influsingle cortical neurones in primate and sub-primate ences of spatial scale and contrast can be assessed. Studies species (Hubel & Wiesel, 1962; De Valois, Albrecht & which have overcome these obstacles are those of Toet Thorell, 1982). This concept of pre-filtering is also seen in the recent computational models of spatial vision (1987), Toet and Koenderink (1988) and Kooi, DeValois {Watt & Morgan, 1985; Wilson, 1986; Klein & Levi, and Switkes (1991). They used stimuli that were spatialty bandpass and in arrangements where local cues could not 198.5>. One key phenomenon of spatial vision is that the be used. Toet (1987) reports that visua1 localisation accuracy with which spatial focation is encoded can accuracy scaies with Gaussian blob size and interblob separation, while Kooi et ai. (1991) report an indepenexceed the resotution limit by an order of magnitude. dence of spatial localisation on orientation and colour Formerly, this has been investigated with experiments contrast. In both studies their common conclusion on the under the general heading of Vernier acuity. While these absence of an effect of spatial frequency is not definitive studies have been operationally successful, in measuring because the dimension across which Iocalisations were performan~ for tasks where the experimental variable is made was orthogonal to the stimulus blob’s spatial spatial location, they have not provided clear insight into structure, namely vertical alignments of horizontally the underlying mechanisms. There are two reasons for orientated stimuli. Additionally neither of the two former this. The first is that with the usual stimulus arrangestudies investigated the relationship between localisation ment, performance can be determined by cues other than accuracy and contrast; Toet worked at detection those dependant on location coding per se, namely threshold while Kooi et al. (1991) worked at a constant secondary cues such as local luminance, local contrast s~pra-threshoId level. The only studies which have examand orientation (Watt, Morgan & Ward, 1983; Findlay, ined the influence of contrast are those of Watt and 1973). Secondly, the spatial frequency spectra of the Morgan (19831, Morgan and Regan (1987), Bradley and stimuli are broadband and therefore may activate many Freeman (1985) and Krauskopf and Fare11 (1991). The conclusions of these studies are opposed in that Bradley *McGill Vision Research Centre, Department of Ophthaimotogy. and Freeman (1985) find that localisation accuracy is McGill University, Montreal, Canada H3A 1Al. proportional to contrast where as other studies report SDepartment of Physiology, University of Cambridge, Cambridge CB2 3EG, England. that it depends on the square-root of contrast.

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ROBERT F. HESS and IAN E. HOLLIDAY

Here, we concentrate on these two unresolved issues, namely spatial scale and contrast, because of their importance for understanding the mechanisms underlying localisation accuracy. Specificafly, we address two questions: (1) does spatial Iocalisation improve with increasing spatial frequency as one might expect from a visual system whose initial filters have matched sampling and frequency response properties? In other words where the higher frequency filters form a finer sampling grid and thus a better representation of the stimulus contrast energy. (2) Is there a square-root relationship between localisation accuracy and contrast as one might expect if the post-filtering iocahsation process is statistical in nature? The task we employ is very important because we believe that it represents a spatial localisation task in which localisation is not derived secondarily to some local cue. Our results suggest that neither of these initial expectations are correct and we show, using a simple neurophysiologically-based model, that one would not necessarily expect them to be so. METHODS Psychophysics All the stimuli were presented on a Joyce Electronics display screen with a P40 phosphor. The display was refreshed at 99 Hz, and had a vertical 100 kHz raster. The dimensions of the display area were 30 x 20cm. The mean l~inan~ of the display was 300 cd/m2. The stimuli were generated by a Cambridge Electronic Design ~SCj2 graphics display controller (TMS34OlOflMS320C25). The host was a Compaq 386120. The display was viewed monocularly by the subjects in a room lit from above by tungsten filament bulbs. Care was taken to eliminate reflections. In all the experiments the subjects responded to the stimuli by depressing the buttons of a Logitech “mouse”. Stimuli The stimuli were all patches of sinusoidal grating enveloped in both the x - and y-dimensions by a Gaussian envelope (see Fig. 1). These stimuli are referred to commonly as ‘“Gabor” patches. The orientation of the grating component of the stimuli was typically vertical [see Fig l(A)], but horizontal gratings were used in some conditions [see Fig. l(B)]. Similarly, the envelope was typically circularly symmetric, ahhough in some conditions the effect of elongation of the envelope in one dimension was investigated [see Fig. l(C)]. The form of the Gabor functions was thus typically: G(x) = Asin(x)exI$-(x2

+ y2)/(2.r2)]

(1)

where A is the amplitude of the function, and s is the standard deviation ofthe Gaussian envelope defining the patch. The choice of sinusoidal modulation at sine phase ensures that there is no moan lumitmnce component in the stimulus. The spread and spatial frequency of the patch was manipulated by changing the viewing distance

to the screen. For viewing distances > 4 m the display was viewed using a mirror. Alignment accrrracy In the experiments we measured the accuracy with which a single Gabor patch could be localized on the horizontal bisector of the mid-point of the line joining the centres of two outer vertically aligned patqhes. Sub-pixel spatial accuracy was achieved by recomputing each newly located stimulus instead of simply repositioning the stimulus in the frame store, this results in the spatial accuracy being limited in principle to 1/2%th of a pixel; The measurements were derived either by a method of adjustment technique (unlimited viewing time) or by the method of constant stimuli in Which the temporal presentation time was limited (Gauss&r temporal window with a spread 200msec). There are advantages and disadvantages to each technique. In the case of the method of adjustment, the subj~tsdir~tly controlled the position of the central patch using the left/right mouse buttons, indicating when they had found a satisfactory alignment by pressing the central button. They quickly learn to make accurate settings, and a range of conditions can be studied in short time. The mean and standard deviation of the settings were cakulated, the standard deviation being taken as the measure of the accuracy of alignment. In the method of constant stimuli, a set of stimuli covering the range of interest is used, which in our case was the range over which the central patch wasseen to change from being to the left to being to the right of alignment with the reference patches. The stimuli were presented repeatedly in random&d order using a one interval temporal forced choice (1 IFC) technique without feedback. The observers’ task was to identify on each trial (consisting of one interval) whether the central stimulus was positioned to the right or the left of the two outside stimuli isee Fig. 1). From the resulting ps~homet~~ function the threshold was found by fitting the error function, ERF(x), of the form: Pfs) = A 10.5 + 0.5 ERF[(x - ~~~~~2~* Cl]

(2)

where A is the number of presentations per stimulus condition, B is the offset of the function relative to zero, and C is the slope parameter of the function,. which corresponds to the standard deviation in the case of a Gaussian. The slope is the measure of the accuracy of alignment.

Detection thresholds were deterniined for the central stimulus alone (central fixation) and for the two peripheral stimuli jointly (central fixation). This was done either using a method of adjacent (IO-20 ~tt~~~ with extended viewing or by a two temporal foreed choice approach (lo-20 presentations at eaeh of 10 alignment positions) using the method of Constant stimuli (in both cases the presentation time Gaussian W&S 2O@mse@. Contrast was controlled by varying a (14 bit> voltage from the digital siginal generator and mtdtipkying it with the Gabor stimuli output from the frame store, the contrast of which could also be scafed (8 bit

THE CODING OF SPATIAL POSITION

1087

FIGURE I. Illustration of the stimuli used in the present study. In (A) all stimuli are spatial Gabors of the same orientation, the horizontal position of the central one being adjustable. In (B) the influence of the spatial structure of the carrier frequency is investigated. In (C) the influence of the Gaussian envelope is investigated. In (D) the influence of cross-scale representation IS investigated.

resolution). This provided accurate estimates of contrast threshold as the Joyce display screen has a linear Z-amplifier. The resultant psychometric functions were fitted with a Weibull function of the form: Y(db) = 50 + 50{ 1 - exp[ -(10-Mdh-o’~20)]~

(3)

where b is the slope of the psychometric function and a is the threshold corresponding to 82% correct. Solutions were found with both of these parameters free to vary. RESULTS

Psychophysical results

In Fig. 2 alignment accuracy in min of arc is plotted against contrast in decibels above threshold. The par-

ameters are spatial frequency and Gaussian spread (blob spread). The task is a three Gabor alignment task in which the centre Gabor (all Gabors are vertically oriented, see Fig. l(A)] is positioned horizontally using a method of adjustment procedure to achieve vertical alignment with the other two flanking (also orientated vertically) Gabors. The inter-Gabor distance was set to 10 times the Gaussian spread which falls within the scaling region defined by Toet (1987). The results presented in Fig. 2 suggest two things. Firstly. the effect of suprathreshold contrast on alignment accuracy for any of these stimuli is small. For example (98 min blob spread) a 30 times increment in suprathreshold contrast produces only a factor of 4 improvement in alignment accuracy. The second feature of these results is that alignment accuracy depends not

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ROBERT F. HESS and IAN E. HOLLIDAY SF c/d

Blob aprasd 24.9 min

Blob spread 88 min

Blob spread 24.9 min

ii

SF cid

f Blob spread 6.2 min

cl

f

The coding of spatial position by the human visual system: effects of spatial scale and contrast.

In this study we investigate the nature of the computations that underlie the encoding of spatial position by the human visual system. Specifically, w...
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