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The effects of large orientation and spatial frequency differences on spatial discriminations
Vision Res. Vol. 24, No. I?. pp. 188’&1896. 1984 Printed in Great Britain. All rights reserved
0042-6989.84 53.00 + 0.00 Copyright i_” 1984 Pergamon Press Ltd
THE EFFECTS OF LARGE ORIENTATION AND SPATIAL FREQUENCY DIFFERENCES ON SPATIAL DISCRIMINATIONS ARTHUR
BRADLEY
and
BERNT
C.
SKOITUN
School of Optometry, University of California, Berkeley, CA 94720, U.S.A. (Receiced 24 February 1984; in revisedform 29 May 1984) Abstract-We have examined two questions: (I) can the finest orientation discrimination be achieved only between stimuli with similar spatial frequency content? and likewise, (2) can the lowest spatial frequency discrimination thresholds be achieved only with parallel gratings? In 2 AFC tests we found that neither type of discrimination was affected by stimulus differences along the other dimension. However, some small decreases in method of adjustment matching accuracy were associated with large differences along the secondary dimensions. Considering the neurophysiological implications, these data suggest that fine orientation and spatial frequency discrimination can occur even though separate populations of neurones in the primary visual cortex may be activated by the two stimuli to be discriminated. Orientation
Spatial frequency
INTRODUCTION Human observers two suprathreshold
Psychophysics
Discrimination
are able to discriminate between stimuli that differ only slightly in
either orientation (Andrews, 1967) or spatial frequency (Campbell et al., 1970). Indeed, the accuracy of these discriminations is sufficient to qualify them as instances of hyperacuity (Westheimer et al., 1976; Hirsch and Hylton, 1982). Currently, the physiological substrates for orientation and spatial frequency discrimination are not known, but several authors have implicated the orientation and spatial frequency selective neurones of the visual cortex (Andrews, 1967; Bouma and Andriessen, 1968; Campbell er al., 1970; Regan et al., 1982; Regan and Beverly, 1983). Typically, spatial frequency discrimination has been determined using stimuli of the same orientation (Campbell ef al., 1970; Hirsch and Hylton, 1982). Likewise, orientation discrimination has been measured with stimuli containing similar spatial frequencies (Andrews, 1967; Westheimer et af., 1976). Also, most other spatial and temporal parameters of the stimuli to be discriminated were similar, and consequently each stimulus would have activated almost identical populations of neurones in the visual cortex. In this report we ask if this is a necessary condition to achieve the finest discriminations, or whether comparable performance can be achieved when the two stimuli to be discriminated activate neurones. separate populations of cortical Specifically, is spatial frequency discrimination between orthogonal stimuli equal in accuracy to discrimination between parallel gratings? And, conversely, is orientation discrimination between stimuli that differ in spatial frequency as accurate as discrimination where the stimuli are of equal frequencies?
Our data show that orientation and spatial frequency discrimination thresholds are essentially unaffected by large differences in spatial frequency and orientation, respectively. While preparing this manuscript we learned of another investigation (Burbeck and Regan, 1983) that, using different methods, obtained similar results. METHODS
Apparatus
A microprocessor controlled grating generator (Milkman et al., 1978) was used to display sinusoidal luminance gratings (mean luminance 50 cd/m*) on an oscilloscope (Tektronix 606). The display was masked down to an 8 cm (4 deg) diameter circular field and was viewed binocularly from 114 cm. Stimuli were presented in pairs with each presentation lasting 500 msec. The presentations were separated by 500 msec during which the screen luminance was uniform (luminance equal to the space average of the grating). The onset of each stimulus was signalled by a tone. Rotation of the grating through 90deg, required to perform spatial frequency discrimination between orthogonal stimuli, was achieved by passing the X and Y signals through a coordinate rotator consisting of analog multipliers (Milkman et al., 1978). Spatial frequencies of horizontal and vertical gratings were calibrated to within 0.5% of each other. Fine control of grating orientation, needed to assess orientation discrimination thresholds, was achieved by adding to the X axis half a cycle of a triangular wave form synchronized to the Y axis sweep. Experimental rationale At first these experiments
orientation
1889
discrimination
seem straightforward: simply requires a com-
IS90
ARTHURBRADLEY and BERNTC. Scorns
parison of stimulus pairs of the same or different spatial frequencies. Likewise, spatial frequency discrimination requires a comparison of stimulus pairs containing either parallel or orthogonal orientations. However, with the 2 AFC method several problems arise when one tries to ensure that the only cues to correct identification are differences along the dimension of interest and not along the secondary dimension. To prevent the secondary dimension from being used as a cue, the reference or test stimulus must be randomly associated with the secondary variable. For example, in spatial frequency discrimination, while keeping the stimuli within each pair orthogonal, one would randomly make the reference stimulus vertical in 50% of the presentations and horizontal in the other 50%. With such a procedure it might appear at first that, (I) the only cue to discrimination is the difference along the dimension of interest and, (2) that discriminations will be made between stimuli that differ substantially along some secondary dimension. However, the randomization necessary to fulfill the first goal may compromise the second. Because the stimuli are presented sequentially, it would be possible, for example, in the case of spatial frequency discrimination, that the horizontal test stimulus in one pair was not compared to a vertical grating within the same pair but rather to a horizontal stimulus in some previous stimulus pair. Hence, identical discrimination thresholds for pairs of parallel and orthogonal stimuli may simply reflect an ability to compare stimuli over time. This problem is not easily avoided with a 2 AFC method, but can be circumvented with a method of adjustment procedure that requires the subject to match a variable test stimulus to a predefined reference. The reference and test stimuli can be uniquely related to a given secondary variable. For example, one can have the subject match the orientation of a 8 c/deg test stimulus to a I c/deg reference. Accuracy of the matches (SD of the settings) provides a measure of discrimination. This method has a limitation: in order for an observer to match stimuli he must apply a subjective criterion of equality. Consequently, an increase in SD for stimuli that are dissimiiar along a secondary dimension may reflect an inability to transfer the criterion. The problems discussed above apply equally to both orientation and spatial frequency discrimination experiments. In addition to these problems there is one complication associated only with spatial frequency discrimination between orthogonal gratings. It has been shown that vertical and horizontal gratings of equal objective spatial frequency appear different: horizontal gratings are perceived to have lower frequencies (Georgeson, 1980). This raises the problem of how to determine the just noticable difference (j.n.d.) for spatial frequency when zero physical difference may be perfectly discriminable. We have solved this problem by measuring the range of spatial frequencies for both orthogonal and paral-
lel stimuli that cannot be discriminated from a given reference. Although this range may not be centered on an objective match. its extent provides a measure of the j.n.d. not confounded by perceptual shifts. Because of the necessity to assign the reference and test frequency randomly to vertical and horizontal orientations (see above), a second problem arises. The spatial frequency range of horizontal stimuli that cannot be discriminated from that of a vertical reference frequency will be shifted to higher frequencies. The corresponding range of frequencies of a vertica1 test stimulus will be centered below the objective frequency of a horizontal reference. Therefore, if one performed the 2 AFC experiment with reference and test stimuli randomly assigned to vertical and horizontal orientations, these two ranges would merge into a single expanded range. Consequently, a false appearance that spatial frequency discrimination is poorer for orthogonal than for parallel stimuli would ensue. To avoid this problem we measured separately the ranges for each of the four combinations of reference/test pairs: V/V, H/H, V/H and H/V. Stimulus pairs from these four combinations were randomly interleaved and presented within the same series. Also, the order of test and reference stimuli was randomized within each pair. To prevent bar position from being a useful cue, grating phase was randomized between all presentations. Also, in the spatial frequency discrimination experiment, grating contrast of each presentation was randomly assigned within a + 2 dB range around a SO”%mean. In the orientation discrimination experiments, grating contrast was maintained at 50%. Procedure ~rje~~~fj~n d~~crj~~~ur~~~.(If Orientation discrimination thresholds were determined with a temporal 2 AFC staircase procedure (three correct step down. one error step up; step size was 2dB) that asymptotes at the 79% correct level (Levitt, 1971). For each stimulus pair, the subject was required to identify, by pressing one of two buttons, which presentation contained the grating tilted most clockwise. The means of the last five out of seven reversals of each staircase were used as threshold estimates. Thresholds were determined for all ten combinations of 1, 2, 4 and 8 c/deg gratings and all ten staircases were randomly interleaved during the experiment. This entire series was repeated four times for observers AB and BCS and twice for TO. The reference orientation (vertical or oblique) was kept constant during a series. (2) Method of adjustment orientation matches were made for all possible combinations of the four spatial frequencies but they were not interleaved: ten matches were made for one combination, followed by ten matches for a second combination, etc. The reference stimulus was presented for l/2 sec. This was followed by a 1/2sec interval in which the screen was uniformly illuminated after which the
Spatial discrimination variable grating was presented for i/2 sec. The variable stimulus was followed by a I see period during which its orientation could be adjusted clockwise or countercIockwise by pressing the right or left button. This sequence was repeated until an acceptable match was reached which the observer signalled by pressing both buttons. In both experiments care was taken to shield any extraneous straight contours from view. Spatial ~eq~ency d~~ri~i~ati~n. (If Thresholds were determined with a 2 AFC method of fixed stimuli. A series of (10-14) test stimuli spanning the range from 3.4 to 4.6 c/deg in equal logarithmic steps were paired with a 4c/deg reference stimulus. The task of the subject was to indicate, by pressing one of two buttons, which stimulus was higher in frequency. Each of the four psychometric functions (VV, HH, VH and HV) spanned the range from where the test stimulus was always identified as having higher frequency (100%) to where it was almost never (0%) identified as such. For each of the four stimulus combinations we determined the range of spatial frequencies that were identified to have a higher frequency than the 4 c/deg reference on less than 15% but more than 25% of the trials. (2) Method of adjustment matches were also obtained for the four combinations or orientations, but as in the orientation matching experiment each condition was run sequentially and the standard deviations of the matches were used to estimate discrimination performance. Unlike the orientation matching experiment, subjects adjusted the frequency by manipulating a ten-turn potentiometer.
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To evaluate quantitatively the effect of spatial frequency differences we compared the orientation di~~mination thresholds obtained with grating pairs containing either equal or different frequencies. We calculated the ratio between the threshold for each different frequency pair (e.g. 1 & 2 cideg) with the mean threshold for the two associated samefrequency pairs (e.g. 1 & 1, and 2 & 2 cideg). A ratio of one indicates that the thresholds obtained with dissimilar frequencies are equal to the average threshold of the component frequencies. We have averaged the ratios across subjects and frequencies. For one.
RESULTS Orientation discrimination
Our goal was to evaluate the effect of spatial frequency d,&rences on orientation discrimination. We first examined the effect of spatial frequency per se, i.e. with grating pairs of I & 1, 2 & 2, 4 & 4 and 8 & 8 cycles per degree. The results, shown in Fig. 1 (filled symbols), indicate that, for vertical reference stimuli, orientation discrimination thresholds do not change substantially with spatial frequency. For the purpose of comparison these data are repeated in each of the four panels for each observer (AB, BCS and TO). Orientation discrimination thresholds for stimulus pairs containing gratings of different frequencies are plotted as open symbols. Each panel contains data obtained with stimulus pairs that have one frequency in common. This frequency is indicated by the vertical bars (5 1 SD). Data points are plotted along the abscissae according to the frequency of the second stimulus in each pair, For example, all orientation discrimination results involving the 1cfdeg grating, i.e. 1 & 2, 1 & 4 and 1 & 8 are plotted in the top left panels at 2,4 and 8 c/deg, respectively. All three subjects show similar thresholds for same- and different-frequency pairs. V.R.z+,‘--L
OLLL_-L-t
1.5
1.0 Z\”
0--+--.-e
1
2
05 ; 01 4
8
Fig. I. Orientation discrimination thresholds (deg) obtained with vertical reference stimuli are plotted against spatial frequency (c/deg) for three observers (AB, BCS and TO). Data for each observer are given in four panels. Filled symbols show orientation di~~mination between grating pairs containing the same spatial frequencies (1 & I, 2 & 2, 4 &t 4 and 8 & 8 c/deg). Open symbols show data obtained with pairs containing different spatial frequencies (e.g. 1 & 2, 1 & 4, 1 & 8, etc). Plotted in each of the four panels are data obtained with stimulus pairs containing one common frequency (identified by the vertical bars; &I SD of the staircase reversal values). For example, the upper left hand panels contain data for the frequency pairs t & 2, 1& 4 and 1 & 8 c/deg, and the upper right hand panels show data obtained with 2 & I, 2 & 4 and 2 & 8 c/deg. etc.
1892
ARIHLIR
BRADLEY
and BERST
two and three octaves difference, these ratios were 1.054. 1.014 and 0.990, respectively. If spatial frequency differences had impaired orientation discrimination, we would have expected the ratios to be greater than t.0, and to increase with spatial frequency difference. Neither of these trends are evident. Interpretation of these data is not altogether straightforward. Literature on the “oblique effect” suggests that observers are able to utilize an internal, vertical reference (Bouma and Andriessen, 1968) in visual tasks involving vertical stimuii. Since the subjects were required to detect a titt from vertical, it could be argued that the observer compares the tilt of the stimulus to such an internal reference. If so, the vertical reference stimulus, its spatial frequency, and consequently the frequency difference might have been irrelevant. This may account for the results. In an attempt to circumvent this problem we repeated the same experiment with oblique reference gratings tilted 45 deg clockwise from vertical. Orientation discrimination data with the oblique reference are plotted in Fig. 2 for three observers. AB 4
0
I
/o
.-.
3L-
2 .-0
C. SKOTTC’N
Results obtained with pairs of equal frequencies (filled symbols) reflect elevated orientation discrimination thresholds for oblique gratings (Caelli el al., 1983). Also. thresholds increase with spatial frequency confirming Caelli er al. (1983). Increased va~ability is aiso apparent. However, there are no large additional increases in orientation discrimination thresholds for stimulus pairs containing different frequencies. Again. we calculated ratios of the thresholds for different frequencies versus the average of the thresholds for the component frequencies. Averaged across three observers. these ratios were I. 116, 1.033 and 1.027 for differences of one, two and three octaves, respectively. As outlined in the experimental rationale, a failure to find any effect of frequency differences with the 2 AFC method may be attributable to an artifact of interleaving the stimuli, i.e. of the subject utilizing information other than that contained within each stimulus pair. To control for this possibility we performed a method of adjustment matching experiment using the same four spatial frequencies. In this experiment the subject was asked to adjust the orientation of a test stimulus until it matched that of a fixed vertical reference. The results for two observers (AB and BCS) are presented in Fig. 3. Standard
1i
AB 0
lOI t
o .-•-•-. 0
05 0’ i
Spotiol
?
24
B
Spotiol
frequency
(c/degJ
Fig. 2. Orientation discrimination thresholds for oblique stimuli are plotted against spatial frequency. Axes, symbols and graph format are the same as in Fig. I.
frequency
(C/&g
1
Fig. 3. Standard deviations (in deg) of orientation matches are plotted against spatial frequency (cjdeg) for two observers (AB and KS). Data obtained with stimuli of similar and dissimilar frequencies are given with filled and open symbols, respectively. Each of the four panels shows results for one reference frequency (indicated by an arrow). Abscissae and graph format are the same as in Figs I and 2.
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Spatial discrimination
/& .*
25 I-
c
Spatial
frequency
(c/deg 1
Fig. 4. Percentage of presentations in which the variable spatial frequency was identified as higher than the reference is plotted as a function of the spatial frequency of the variable grating. The figure gives the results for observer AB. Each panel shows results obtained with one combination of grating orientations (indicated by the insets). R and Vdenote reference and variable (= test) stimulus, respectively. Solid curves represent least-squares fits to the data (see text).
deviations of the matches are plotted against spatial frequency. Filled and open symbols represent data obtained with equal and different frequencies, respectively. Each panel shows data obtained with a given reference frequency (cf. Figs 1 and 2) indicated by an arrow. Although AB generally showed larger variability than did BCS, there are no large increases in standard deviations when reference and test stimuli had different spatial frequencies. However, quantitative comparisons between sameand different-frequency pairs do show slightly larger standard deviations when frequency differences of two
and three octaves were present. Ratios of the standard deviations for stimuli of unequal frequencies to the mean standard deviations for the component frequencies were 0.936, 1.192 and 1.362 for one, two and three octaves difference, respectively. we found that introducing To summarize, differences in spatial frequency had no effect on orientation discrimination when the test was performed with a 2 AFC method. However, when using a matching paradigm we found a slight decrease in the accuracy of the matches when the gratings differed in frequency.
,I, 3.4
4.0
4.4
Spatial
4.8
4.0
34
frequency
(c/deg)
Fig. 5. Same as Fig. 4 but for observer BCS.
4.4
4.8
~~~THUR BRADLEY and BERNTC. SKOIXX
I s9.4
40
44 Spot101
48
34
frequency
discrimination
Using a 2 AFC method of constant stimuli we determined the per cent of trials on which the test stimulus was identified as higher in frequency than a 4 c/deg reference stimulus. As the actual frequency of the test dropped from 4.6 to 3.4 c/deg the percentage of trials in which it was identified as higher dropped from 100% to almost 0%. This can be seen for each of the three observers in Figs 4, 5 and 6. Each figure consists of four panels, one for each combination of orientations (shown by the insets). Each data set has been fit by least squares to the function: exp( - (~1.4)~) (Quick, 1974; Tolhurst et al., y=l-1983). Two features of these data are of interest. First, the ranges of test frequencies that were identified to be higher in spatial frequency than the reference on more than 25% or less than 75% of the trials provide a measure of discrimination. These ranges are given in Table I for all three observers and all four conditions. Although there are substantial differences between subjects (e.g. BCS exhibits frequency ranges nearly double those of AB and TO), all three subjects
,
,
40
44
48
(c/degi
Fig. 6. Same as Fig. 4 but for observer
Spatial frequency
,
TO.
exhibit very similar ranges for parallel vertical, parallel horizontal and orthogonal gratings. Frequency ranges averaged across all three observers for parallel and orthogonal stimuli are essentially identical: 0.1172 and 0.1170 octaves, respectively. Since these values correspond to the range between the 25 to 75% points on the psychometric function, the discrimination threshold for a 75% correct criterion would correspond to half this range. The average discrimination thresholds are 0.0586 and 0.0585 octaves, for parallel and orthogonal stimuli, respectively, which are comparable to thresholds previously obtained with parallel gratings (Campbell ef al., 1970; Hirsch and Hylton, 1982; Burbeck and Regan, 1983). These data also reflect the “vertical-horizontal illusion” (see experimental rationale). If there were no shifts in perceived spatial frequency with orientation, the psychometric functions should cross the 50% level (i.e. chance performance) at the frequency of the reference stimulus (i.e. 4c/deg). This position
Table 2. Spatial frequency matching data for four subjects (AB. BCS, TO, AR) are shown for all four combinations of reference and test (=variable) stimulus orientations (VV, HH, VH. HV) Orientation combinations
Table 1. The range of spatial frequencies, in octaves, identified as higher than a 4cideg reference on not less than 2S or more than 75:: of the presentations
AB BCS TO
vv
HH
HV
0.0924 0.1870 0.08 11
0.0777 0. I684 0.0957
0.0935 0. I838 0.0788
AB BCS
Orientation combinations Subjects
Subjects
VH
_.-__T 0.0976 _ 0.1584 ‘I 0.0900
Ranges are given for all three observers and ail four combinations of orientations. H = horizontal and V = vertical. The first and second character in each pair denote the orientation of the reference and variable gratings, respectively.
TO AR
w
S.Oll io.12 3.95: iO.17 4.011 10.08 4.021 /0.19
HH
3.991 io.09 4.Ol/ IO.13 4.031 /0.08 4.10/ 10.35
HV
3.991 ;o.i4 3.82' IO.19 4.01,' ;0.10 3.90 ,025
VH
--
4.071 10.19 4.03: IO.17 4.14: /0.13 4.17/ IO.23
For each combination both the mean tabove) and the standard deviations (below) of the matches are given in c’deg. Datafrom AB and KS are the result of 20 matches and data from TO and AR the values are the result of ten matches.
Spatial discrimination has been indicated by a cross in each panel. Spatial frequency discrimination functions for parallel orientations cross the SOT/, level close to this position. However, for AB and TO there are horizontal displacements of the functions to higher and lower frequencies for the vertical reference/horizontal test and horizontal reference/vertical test pairs, respectively. Although slightly displaced, a similar trend can be seen for BCS. These shifts corroborate the results from Georgeson’s (1980) method of adjustment experiment which showed that horizontal sinusoidal gratings appear lower in frequency than vertical gratings of the same physical frequency. The magnitude of this perceptual shift can be estimated by comparing the frequencies corresponding to the 50% crossings for the functions obtained with a vertical reference and horizontal test on the one hand and a horizontal reference and vertical test stimulus on the other. The shift in perceived frequency corresponds to half the difference between these points. For observers AB, BCS and TO these shifts were 0.038 ( = 2.7%) 0.032 (= 2.2%) and 0.05 1 (= 3.7%) octaves, respectively. We performed a method of adjustment frequency matching experiment similar to that described for orientation. Results from this experiment are given in Table 2 for four observers. For each observer four sets of data are given: the mean and standard deviations for the four combinations of stimulus orientations. As with the 2 AFC method the data show evidence of a perceived frequency difference between horizontal and vertical gratings. For the four reference/test pairs, the average of the matches are 3.93,4.03,4.00 and 4.1 I for H/V, H/H, V/V and V/H, respectively. On average, matches performed between orthogonal stimuli are slightly less accurate. Standard deviations, averaged for four observers were 0.175 c/deg for orthogonal stimuli and 0. I5 I c/deg for parallel gratings, a difference of 16%. In summary, differences in orientation have little or no effect on spatial frequency discrimination when tested with either a two AFC or method of adjustment technique. DISCUSSlON
Our data show that, around vertical, the detection of small orientation differences between two stimuli is largely unaffected by spatial frequency over a three octave range (l-8 c/deg). This is not the case at obliques, where orientation discrimination thresholds show a consistent increase with spatial frequency. In neither case are thresholds elevated when the spatial frequency content of the two stimuli differ. Likewise, spatial frequency discrimination thresholds are essentially identical for horizontal and vertical gratings, and are not different for orthogonal or parallel stimuli. Our results are in good agreement withThose of Burbeck and Regan (1983). who, using a somewhat different forced choice procedure, also find that spatial frequency differences do not affect orientation
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discrimination about a vertical reference. Also, they show that 90 deg orientation differences do not affect spatial frequency discrimination when vertical and horizontal gratings were used. Burbeck and Regan concluded from their data that orientation discrimination is independent of spatial frequency, and spatial frequency discrimination is independent of orientation. Our data support this conclusion but only for vertical and horizontal stimuli. Although we find no effect of spatial frequency differences on orientation discrimination at an oblique orientation, our data, and those of Caelli et al. (1983) show that orientation discrimination is clearly affected by spatial frequency at oblique orientations. Also, recent data by Hirsch and Hylton (1984) suggest that spatial frequency discrimination is not independent of orientation. Therefore, although orientation and spatial frequency may not be completely independent of each other, we confirm Burbeck and Regan’s observation that differences along one of these dimensions do not affect discrimination along the other. The slightly elevated thresholds observed with the method of adjustment matching procedure may reflect a genuine resolution difference, which we fail to detect in the discrimination (2 AFC) experiment because the subject utilizes information from previous stimuli (see Experimental rationale). Alternatively, a failure to transfer the subjective criterion between different stimuli may be the cause. Our experiments cannot distinguish between these two possibilities (see Experimental rationale), but, irrespective of the cause, the effects are small (0. I3 and 0.06 log units for orientation and spatial frequency discrimination, respectively). Although our experiments were psychophysical, one of our primary motivations arose from neurophysiological considerations. We chose the complementary variables of orientation and spatial frequency because primary cortical neurones respond to select ranges along both of these dimensions (Hubel and Wiesel, 1962, 1968; Campbell et al., 1969; Schiller ef al., 1976). Consequently large differences along either dimension will activate largely nonoverlapping sets of neurones in the primary visual cortex. Therefore, in our experiments, we were able to test the hypothesis that fine behavioural discrimination relies on the comparison of neural responses in the same population of primary cortical neurones. Our data do not support this hypothesis. Drawing this conclusion assumes that there are no cortical neurones that are finely tuned along one of these dimensions but broadly tuned along the other. In area 17 of primates there are some neurones that are non-selective for orientation (Hubel and Wiesel, 1968). However, it has been shown that neurones broadly tuned for orientation also tend to be broadly tuned for spatial frequency (DeValois er al., 1982). Such neurones would be less suited to transmit subtle differences in stimulus orientation or spatial frequency (Skottun et al., 1983).
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ARTHUR BRADLEY and BERNT C. S~omx
.-lcX-no~~ledgemenr-This work was supported by the Norwegian Research Council for Science and Humanities (NXVF). REFERENCES Andrews D. P. (1967) Perception of contour orientation in the central fovea. Part I: Short lines. Vision Res. 7, 975-997. Bouma H. and Andriessen J. J. (1968) Perceived orientation of isolated line segments. Vision Res. 8, 493-507. Burbeck C. A. and Regan D. (1983) Independence of orientation and size in spatial discriminations. J. opr. Sot. Am. 73, 1691-1694. Campbell F. W.. Cooper G. F. and Enroth-Cugell C. (1969) The spatial selectivity of the visual cells of the cat. J. Ph.vsiol. 203, 223-235. Campbell F. W., Nachmias J. and Jukes J. (1970) Spatialfrequency discrimination in human vision. J. opt. Sot. Am. 60, 555-559. Caelli T., Brettel H., Rentschler I. and Hilz R. (1983) Discrimination thresholds in the two-dimensional spatial frequency domain. Vision Res. 23, 129-133. DeValois R. L., Albrecht D. G. and Thorell L. G. (1982) Spatial frequency selectivity of cells in macaque visual cortex. Vision Res. 22, 545-559. Georgeson M. A. (1980) Spatial frequency analysis in early visual processing. Phil. Trans. R. $0~. Lbnd. 8290, I l-22. Hirsch J. and Hylton R. (1982) Limits of spatial-frequency discrimination as evidence of neural interpolation. J. opt. Sot. Am. 72, 1367-1374. Hirsch J. and Hylton R. (1984) Orientation dependence of visual hyperacuity contains a component with hexagonal symmetry. J. opr. Sot. Am. A 1, 30&308.
Hubel D. H. and Wiesel T. N. (1962) Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physioi. 160, 106-154. Hubel D. H. and Wiesel T. N. (1968) Receptive fields and functional architecture of monkey striate cortex. J. Physiol. 195, 2 15-243. Levitt H. (1971) Transformed up-down methods in psychoacoustics. J. acoust. Sac. Am. 49, 467177. Milkman N.. Shapley R. and Schick G. (1978) Experimental applications. A microcomputer-based visual stimulator. iehao. Res. Merh. lnstrumtwt. 10, 539-545. Quick R. F. (1974) A vector-magnitude model of contrast detection. Kvbernetik 16, 65-67. Regan D., Bartol S.. Murray T. J. and Beverley K. I. (1982) Spatial frequency discrimination in normal vision and in patients with multiple sclerosis. Brain 105, 735-754. Regan D. and Beverley K. I. (1983) Spatial-frequency discrimination and detection: comparison of postadaptation thresholds. J. opt. Sot. Am. 73, 1684-1690. Schiller P. H.. Finlay B. L. and Volman S. F. (1976) Quantitative studies of single-cell properties in monkey striate cortex. III. Spatial frequency. J. Neurophysiol. 39, 1334-1351. Skottun B. C.. Bradley A. and Ohzawa 1. (1983) Orientation and spatial frequency discrimination: cat single cells and human psychophysics. Sot. Neurosci. Absrr. 9, 822. Tolhurst D. J.. Movshon J. A. and Dean A. F. (1983) The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vision res. 23, 775-785. Westheimer G.. Shimamura K. and McKee S. P. (1976) Interference with line-orientation sensitivity. J. opr. Sot. Am. 66. 332-338.
0042-6989.84 53.00 + 0.00 Copyright i_” 1984 Pergamon Press Ltd
THE EFFECTS OF LARGE ORIENTATION AND SPATIAL FREQUENCY DIFFERENCES ON SPATIAL DISCRIMINATIONS ARTHUR
BRADLEY
and
BERNT
C.
SKOITUN
School of Optometry, University of California, Berkeley, CA 94720, U.S.A. (Receiced 24 February 1984; in revisedform 29 May 1984) Abstract-We have examined two questions: (I) can the finest orientation discrimination be achieved only between stimuli with similar spatial frequency content? and likewise, (2) can the lowest spatial frequency discrimination thresholds be achieved only with parallel gratings? In 2 AFC tests we found that neither type of discrimination was affected by stimulus differences along the other dimension. However, some small decreases in method of adjustment matching accuracy were associated with large differences along the secondary dimensions. Considering the neurophysiological implications, these data suggest that fine orientation and spatial frequency discrimination can occur even though separate populations of neurones in the primary visual cortex may be activated by the two stimuli to be discriminated. Orientation
Spatial frequency
INTRODUCTION Human observers two suprathreshold
Psychophysics
Discrimination
are able to discriminate between stimuli that differ only slightly in
either orientation (Andrews, 1967) or spatial frequency (Campbell et al., 1970). Indeed, the accuracy of these discriminations is sufficient to qualify them as instances of hyperacuity (Westheimer et al., 1976; Hirsch and Hylton, 1982). Currently, the physiological substrates for orientation and spatial frequency discrimination are not known, but several authors have implicated the orientation and spatial frequency selective neurones of the visual cortex (Andrews, 1967; Bouma and Andriessen, 1968; Campbell er al., 1970; Regan et al., 1982; Regan and Beverly, 1983). Typically, spatial frequency discrimination has been determined using stimuli of the same orientation (Campbell ef al., 1970; Hirsch and Hylton, 1982). Likewise, orientation discrimination has been measured with stimuli containing similar spatial frequencies (Andrews, 1967; Westheimer et af., 1976). Also, most other spatial and temporal parameters of the stimuli to be discriminated were similar, and consequently each stimulus would have activated almost identical populations of neurones in the visual cortex. In this report we ask if this is a necessary condition to achieve the finest discriminations, or whether comparable performance can be achieved when the two stimuli to be discriminated activate neurones. separate populations of cortical Specifically, is spatial frequency discrimination between orthogonal stimuli equal in accuracy to discrimination between parallel gratings? And, conversely, is orientation discrimination between stimuli that differ in spatial frequency as accurate as discrimination where the stimuli are of equal frequencies?
Our data show that orientation and spatial frequency discrimination thresholds are essentially unaffected by large differences in spatial frequency and orientation, respectively. While preparing this manuscript we learned of another investigation (Burbeck and Regan, 1983) that, using different methods, obtained similar results. METHODS
Apparatus
A microprocessor controlled grating generator (Milkman et al., 1978) was used to display sinusoidal luminance gratings (mean luminance 50 cd/m*) on an oscilloscope (Tektronix 606). The display was masked down to an 8 cm (4 deg) diameter circular field and was viewed binocularly from 114 cm. Stimuli were presented in pairs with each presentation lasting 500 msec. The presentations were separated by 500 msec during which the screen luminance was uniform (luminance equal to the space average of the grating). The onset of each stimulus was signalled by a tone. Rotation of the grating through 90deg, required to perform spatial frequency discrimination between orthogonal stimuli, was achieved by passing the X and Y signals through a coordinate rotator consisting of analog multipliers (Milkman et al., 1978). Spatial frequencies of horizontal and vertical gratings were calibrated to within 0.5% of each other. Fine control of grating orientation, needed to assess orientation discrimination thresholds, was achieved by adding to the X axis half a cycle of a triangular wave form synchronized to the Y axis sweep. Experimental rationale At first these experiments
orientation
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discrimination
seem straightforward: simply requires a com-
IS90
ARTHURBRADLEY and BERNTC. Scorns
parison of stimulus pairs of the same or different spatial frequencies. Likewise, spatial frequency discrimination requires a comparison of stimulus pairs containing either parallel or orthogonal orientations. However, with the 2 AFC method several problems arise when one tries to ensure that the only cues to correct identification are differences along the dimension of interest and not along the secondary dimension. To prevent the secondary dimension from being used as a cue, the reference or test stimulus must be randomly associated with the secondary variable. For example, in spatial frequency discrimination, while keeping the stimuli within each pair orthogonal, one would randomly make the reference stimulus vertical in 50% of the presentations and horizontal in the other 50%. With such a procedure it might appear at first that, (I) the only cue to discrimination is the difference along the dimension of interest and, (2) that discriminations will be made between stimuli that differ substantially along some secondary dimension. However, the randomization necessary to fulfill the first goal may compromise the second. Because the stimuli are presented sequentially, it would be possible, for example, in the case of spatial frequency discrimination, that the horizontal test stimulus in one pair was not compared to a vertical grating within the same pair but rather to a horizontal stimulus in some previous stimulus pair. Hence, identical discrimination thresholds for pairs of parallel and orthogonal stimuli may simply reflect an ability to compare stimuli over time. This problem is not easily avoided with a 2 AFC method, but can be circumvented with a method of adjustment procedure that requires the subject to match a variable test stimulus to a predefined reference. The reference and test stimuli can be uniquely related to a given secondary variable. For example, one can have the subject match the orientation of a 8 c/deg test stimulus to a I c/deg reference. Accuracy of the matches (SD of the settings) provides a measure of discrimination. This method has a limitation: in order for an observer to match stimuli he must apply a subjective criterion of equality. Consequently, an increase in SD for stimuli that are dissimiiar along a secondary dimension may reflect an inability to transfer the criterion. The problems discussed above apply equally to both orientation and spatial frequency discrimination experiments. In addition to these problems there is one complication associated only with spatial frequency discrimination between orthogonal gratings. It has been shown that vertical and horizontal gratings of equal objective spatial frequency appear different: horizontal gratings are perceived to have lower frequencies (Georgeson, 1980). This raises the problem of how to determine the just noticable difference (j.n.d.) for spatial frequency when zero physical difference may be perfectly discriminable. We have solved this problem by measuring the range of spatial frequencies for both orthogonal and paral-
lel stimuli that cannot be discriminated from a given reference. Although this range may not be centered on an objective match. its extent provides a measure of the j.n.d. not confounded by perceptual shifts. Because of the necessity to assign the reference and test frequency randomly to vertical and horizontal orientations (see above), a second problem arises. The spatial frequency range of horizontal stimuli that cannot be discriminated from that of a vertical reference frequency will be shifted to higher frequencies. The corresponding range of frequencies of a vertica1 test stimulus will be centered below the objective frequency of a horizontal reference. Therefore, if one performed the 2 AFC experiment with reference and test stimuli randomly assigned to vertical and horizontal orientations, these two ranges would merge into a single expanded range. Consequently, a false appearance that spatial frequency discrimination is poorer for orthogonal than for parallel stimuli would ensue. To avoid this problem we measured separately the ranges for each of the four combinations of reference/test pairs: V/V, H/H, V/H and H/V. Stimulus pairs from these four combinations were randomly interleaved and presented within the same series. Also, the order of test and reference stimuli was randomized within each pair. To prevent bar position from being a useful cue, grating phase was randomized between all presentations. Also, in the spatial frequency discrimination experiment, grating contrast of each presentation was randomly assigned within a + 2 dB range around a SO”%mean. In the orientation discrimination experiments, grating contrast was maintained at 50%. Procedure ~rje~~~fj~n d~~crj~~~ur~~~.(If Orientation discrimination thresholds were determined with a temporal 2 AFC staircase procedure (three correct step down. one error step up; step size was 2dB) that asymptotes at the 79% correct level (Levitt, 1971). For each stimulus pair, the subject was required to identify, by pressing one of two buttons, which presentation contained the grating tilted most clockwise. The means of the last five out of seven reversals of each staircase were used as threshold estimates. Thresholds were determined for all ten combinations of 1, 2, 4 and 8 c/deg gratings and all ten staircases were randomly interleaved during the experiment. This entire series was repeated four times for observers AB and BCS and twice for TO. The reference orientation (vertical or oblique) was kept constant during a series. (2) Method of adjustment orientation matches were made for all possible combinations of the four spatial frequencies but they were not interleaved: ten matches were made for one combination, followed by ten matches for a second combination, etc. The reference stimulus was presented for l/2 sec. This was followed by a 1/2sec interval in which the screen was uniformly illuminated after which the
Spatial discrimination variable grating was presented for i/2 sec. The variable stimulus was followed by a I see period during which its orientation could be adjusted clockwise or countercIockwise by pressing the right or left button. This sequence was repeated until an acceptable match was reached which the observer signalled by pressing both buttons. In both experiments care was taken to shield any extraneous straight contours from view. Spatial ~eq~ency d~~ri~i~ati~n. (If Thresholds were determined with a 2 AFC method of fixed stimuli. A series of (10-14) test stimuli spanning the range from 3.4 to 4.6 c/deg in equal logarithmic steps were paired with a 4c/deg reference stimulus. The task of the subject was to indicate, by pressing one of two buttons, which stimulus was higher in frequency. Each of the four psychometric functions (VV, HH, VH and HV) spanned the range from where the test stimulus was always identified as having higher frequency (100%) to where it was almost never (0%) identified as such. For each of the four stimulus combinations we determined the range of spatial frequencies that were identified to have a higher frequency than the 4 c/deg reference on less than 15% but more than 25% of the trials. (2) Method of adjustment matches were also obtained for the four combinations or orientations, but as in the orientation matching experiment each condition was run sequentially and the standard deviations of the matches were used to estimate discrimination performance. Unlike the orientation matching experiment, subjects adjusted the frequency by manipulating a ten-turn potentiometer.
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To evaluate quantitatively the effect of spatial frequency differences we compared the orientation di~~mination thresholds obtained with grating pairs containing either equal or different frequencies. We calculated the ratio between the threshold for each different frequency pair (e.g. 1 & 2 cideg) with the mean threshold for the two associated samefrequency pairs (e.g. 1 & 1, and 2 & 2 cideg). A ratio of one indicates that the thresholds obtained with dissimilar frequencies are equal to the average threshold of the component frequencies. We have averaged the ratios across subjects and frequencies. For one.
RESULTS Orientation discrimination
Our goal was to evaluate the effect of spatial frequency d,&rences on orientation discrimination. We first examined the effect of spatial frequency per se, i.e. with grating pairs of I & 1, 2 & 2, 4 & 4 and 8 & 8 cycles per degree. The results, shown in Fig. 1 (filled symbols), indicate that, for vertical reference stimuli, orientation discrimination thresholds do not change substantially with spatial frequency. For the purpose of comparison these data are repeated in each of the four panels for each observer (AB, BCS and TO). Orientation discrimination thresholds for stimulus pairs containing gratings of different frequencies are plotted as open symbols. Each panel contains data obtained with stimulus pairs that have one frequency in common. This frequency is indicated by the vertical bars (5 1 SD). Data points are plotted along the abscissae according to the frequency of the second stimulus in each pair, For example, all orientation discrimination results involving the 1cfdeg grating, i.e. 1 & 2, 1 & 4 and 1 & 8 are plotted in the top left panels at 2,4 and 8 c/deg, respectively. All three subjects show similar thresholds for same- and different-frequency pairs. V.R.z+,‘--L
OLLL_-L-t
1.5
1.0 Z\”
0--+--.-e
1
2
05 ; 01 4
8
Fig. I. Orientation discrimination thresholds (deg) obtained with vertical reference stimuli are plotted against spatial frequency (c/deg) for three observers (AB, BCS and TO). Data for each observer are given in four panels. Filled symbols show orientation di~~mination between grating pairs containing the same spatial frequencies (1 & I, 2 & 2, 4 &t 4 and 8 & 8 c/deg). Open symbols show data obtained with pairs containing different spatial frequencies (e.g. 1 & 2, 1 & 4, 1 & 8, etc). Plotted in each of the four panels are data obtained with stimulus pairs containing one common frequency (identified by the vertical bars; &I SD of the staircase reversal values). For example, the upper left hand panels contain data for the frequency pairs t & 2, 1& 4 and 1 & 8 c/deg, and the upper right hand panels show data obtained with 2 & I, 2 & 4 and 2 & 8 c/deg. etc.
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ARIHLIR
BRADLEY
and BERST
two and three octaves difference, these ratios were 1.054. 1.014 and 0.990, respectively. If spatial frequency differences had impaired orientation discrimination, we would have expected the ratios to be greater than t.0, and to increase with spatial frequency difference. Neither of these trends are evident. Interpretation of these data is not altogether straightforward. Literature on the “oblique effect” suggests that observers are able to utilize an internal, vertical reference (Bouma and Andriessen, 1968) in visual tasks involving vertical stimuii. Since the subjects were required to detect a titt from vertical, it could be argued that the observer compares the tilt of the stimulus to such an internal reference. If so, the vertical reference stimulus, its spatial frequency, and consequently the frequency difference might have been irrelevant. This may account for the results. In an attempt to circumvent this problem we repeated the same experiment with oblique reference gratings tilted 45 deg clockwise from vertical. Orientation discrimination data with the oblique reference are plotted in Fig. 2 for three observers. AB 4
0
I
/o
.-.
3L-
2 .-0
C. SKOTTC’N
Results obtained with pairs of equal frequencies (filled symbols) reflect elevated orientation discrimination thresholds for oblique gratings (Caelli el al., 1983). Also. thresholds increase with spatial frequency confirming Caelli er al. (1983). Increased va~ability is aiso apparent. However, there are no large additional increases in orientation discrimination thresholds for stimulus pairs containing different frequencies. Again. we calculated ratios of the thresholds for different frequencies versus the average of the thresholds for the component frequencies. Averaged across three observers. these ratios were I. 116, 1.033 and 1.027 for differences of one, two and three octaves, respectively. As outlined in the experimental rationale, a failure to find any effect of frequency differences with the 2 AFC method may be attributable to an artifact of interleaving the stimuli, i.e. of the subject utilizing information other than that contained within each stimulus pair. To control for this possibility we performed a method of adjustment matching experiment using the same four spatial frequencies. In this experiment the subject was asked to adjust the orientation of a test stimulus until it matched that of a fixed vertical reference. The results for two observers (AB and BCS) are presented in Fig. 3. Standard
1i
AB 0
lOI t
o .-•-•-. 0
05 0’ i
Spotiol
?
24
B
Spotiol
frequency
(c/degJ
Fig. 2. Orientation discrimination thresholds for oblique stimuli are plotted against spatial frequency. Axes, symbols and graph format are the same as in Fig. I.
frequency
(C/&g
1
Fig. 3. Standard deviations (in deg) of orientation matches are plotted against spatial frequency (cjdeg) for two observers (AB and KS). Data obtained with stimuli of similar and dissimilar frequencies are given with filled and open symbols, respectively. Each of the four panels shows results for one reference frequency (indicated by an arrow). Abscissae and graph format are the same as in Figs I and 2.
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Spatial discrimination
/& .*
25 I-
c
Spatial
frequency
(c/deg 1
Fig. 4. Percentage of presentations in which the variable spatial frequency was identified as higher than the reference is plotted as a function of the spatial frequency of the variable grating. The figure gives the results for observer AB. Each panel shows results obtained with one combination of grating orientations (indicated by the insets). R and Vdenote reference and variable (= test) stimulus, respectively. Solid curves represent least-squares fits to the data (see text).
deviations of the matches are plotted against spatial frequency. Filled and open symbols represent data obtained with equal and different frequencies, respectively. Each panel shows data obtained with a given reference frequency (cf. Figs 1 and 2) indicated by an arrow. Although AB generally showed larger variability than did BCS, there are no large increases in standard deviations when reference and test stimuli had different spatial frequencies. However, quantitative comparisons between sameand different-frequency pairs do show slightly larger standard deviations when frequency differences of two
and three octaves were present. Ratios of the standard deviations for stimuli of unequal frequencies to the mean standard deviations for the component frequencies were 0.936, 1.192 and 1.362 for one, two and three octaves difference, respectively. we found that introducing To summarize, differences in spatial frequency had no effect on orientation discrimination when the test was performed with a 2 AFC method. However, when using a matching paradigm we found a slight decrease in the accuracy of the matches when the gratings differed in frequency.
,I, 3.4
4.0
4.4
Spatial
4.8
4.0
34
frequency
(c/deg)
Fig. 5. Same as Fig. 4 but for observer BCS.
4.4
4.8
~~~THUR BRADLEY and BERNTC. SKOIXX
I s9.4
40
44 Spot101
48
34
frequency
discrimination
Using a 2 AFC method of constant stimuli we determined the per cent of trials on which the test stimulus was identified as higher in frequency than a 4 c/deg reference stimulus. As the actual frequency of the test dropped from 4.6 to 3.4 c/deg the percentage of trials in which it was identified as higher dropped from 100% to almost 0%. This can be seen for each of the three observers in Figs 4, 5 and 6. Each figure consists of four panels, one for each combination of orientations (shown by the insets). Each data set has been fit by least squares to the function: exp( - (~1.4)~) (Quick, 1974; Tolhurst et al., y=l-1983). Two features of these data are of interest. First, the ranges of test frequencies that were identified to be higher in spatial frequency than the reference on more than 25% or less than 75% of the trials provide a measure of discrimination. These ranges are given in Table I for all three observers and all four conditions. Although there are substantial differences between subjects (e.g. BCS exhibits frequency ranges nearly double those of AB and TO), all three subjects
,
,
40
44
48
(c/degi
Fig. 6. Same as Fig. 4 but for observer
Spatial frequency
,
TO.
exhibit very similar ranges for parallel vertical, parallel horizontal and orthogonal gratings. Frequency ranges averaged across all three observers for parallel and orthogonal stimuli are essentially identical: 0.1172 and 0.1170 octaves, respectively. Since these values correspond to the range between the 25 to 75% points on the psychometric function, the discrimination threshold for a 75% correct criterion would correspond to half this range. The average discrimination thresholds are 0.0586 and 0.0585 octaves, for parallel and orthogonal stimuli, respectively, which are comparable to thresholds previously obtained with parallel gratings (Campbell ef al., 1970; Hirsch and Hylton, 1982; Burbeck and Regan, 1983). These data also reflect the “vertical-horizontal illusion” (see experimental rationale). If there were no shifts in perceived spatial frequency with orientation, the psychometric functions should cross the 50% level (i.e. chance performance) at the frequency of the reference stimulus (i.e. 4c/deg). This position
Table 2. Spatial frequency matching data for four subjects (AB. BCS, TO, AR) are shown for all four combinations of reference and test (=variable) stimulus orientations (VV, HH, VH. HV) Orientation combinations
Table 1. The range of spatial frequencies, in octaves, identified as higher than a 4cideg reference on not less than 2S or more than 75:: of the presentations
AB BCS TO
vv
HH
HV
0.0924 0.1870 0.08 11
0.0777 0. I684 0.0957
0.0935 0. I838 0.0788
AB BCS
Orientation combinations Subjects
Subjects
VH
_.-__T 0.0976 _ 0.1584 ‘I 0.0900
Ranges are given for all three observers and ail four combinations of orientations. H = horizontal and V = vertical. The first and second character in each pair denote the orientation of the reference and variable gratings, respectively.
TO AR
w
S.Oll io.12 3.95: iO.17 4.011 10.08 4.021 /0.19
HH
3.991 io.09 4.Ol/ IO.13 4.031 /0.08 4.10/ 10.35
HV
3.991 ;o.i4 3.82' IO.19 4.01,' ;0.10 3.90 ,025
VH
--
4.071 10.19 4.03: IO.17 4.14: /0.13 4.17/ IO.23
For each combination both the mean tabove) and the standard deviations (below) of the matches are given in c’deg. Datafrom AB and KS are the result of 20 matches and data from TO and AR the values are the result of ten matches.
Spatial discrimination has been indicated by a cross in each panel. Spatial frequency discrimination functions for parallel orientations cross the SOT/, level close to this position. However, for AB and TO there are horizontal displacements of the functions to higher and lower frequencies for the vertical reference/horizontal test and horizontal reference/vertical test pairs, respectively. Although slightly displaced, a similar trend can be seen for BCS. These shifts corroborate the results from Georgeson’s (1980) method of adjustment experiment which showed that horizontal sinusoidal gratings appear lower in frequency than vertical gratings of the same physical frequency. The magnitude of this perceptual shift can be estimated by comparing the frequencies corresponding to the 50% crossings for the functions obtained with a vertical reference and horizontal test on the one hand and a horizontal reference and vertical test stimulus on the other. The shift in perceived frequency corresponds to half the difference between these points. For observers AB, BCS and TO these shifts were 0.038 ( = 2.7%) 0.032 (= 2.2%) and 0.05 1 (= 3.7%) octaves, respectively. We performed a method of adjustment frequency matching experiment similar to that described for orientation. Results from this experiment are given in Table 2 for four observers. For each observer four sets of data are given: the mean and standard deviations for the four combinations of stimulus orientations. As with the 2 AFC method the data show evidence of a perceived frequency difference between horizontal and vertical gratings. For the four reference/test pairs, the average of the matches are 3.93,4.03,4.00 and 4.1 I for H/V, H/H, V/V and V/H, respectively. On average, matches performed between orthogonal stimuli are slightly less accurate. Standard deviations, averaged for four observers were 0.175 c/deg for orthogonal stimuli and 0. I5 I c/deg for parallel gratings, a difference of 16%. In summary, differences in orientation have little or no effect on spatial frequency discrimination when tested with either a two AFC or method of adjustment technique. DISCUSSlON
Our data show that, around vertical, the detection of small orientation differences between two stimuli is largely unaffected by spatial frequency over a three octave range (l-8 c/deg). This is not the case at obliques, where orientation discrimination thresholds show a consistent increase with spatial frequency. In neither case are thresholds elevated when the spatial frequency content of the two stimuli differ. Likewise, spatial frequency discrimination thresholds are essentially identical for horizontal and vertical gratings, and are not different for orthogonal or parallel stimuli. Our results are in good agreement withThose of Burbeck and Regan (1983). who, using a somewhat different forced choice procedure, also find that spatial frequency differences do not affect orientation
1895
discrimination about a vertical reference. Also, they show that 90 deg orientation differences do not affect spatial frequency discrimination when vertical and horizontal gratings were used. Burbeck and Regan concluded from their data that orientation discrimination is independent of spatial frequency, and spatial frequency discrimination is independent of orientation. Our data support this conclusion but only for vertical and horizontal stimuli. Although we find no effect of spatial frequency differences on orientation discrimination at an oblique orientation, our data, and those of Caelli et al. (1983) show that orientation discrimination is clearly affected by spatial frequency at oblique orientations. Also, recent data by Hirsch and Hylton (1984) suggest that spatial frequency discrimination is not independent of orientation. Therefore, although orientation and spatial frequency may not be completely independent of each other, we confirm Burbeck and Regan’s observation that differences along one of these dimensions do not affect discrimination along the other. The slightly elevated thresholds observed with the method of adjustment matching procedure may reflect a genuine resolution difference, which we fail to detect in the discrimination (2 AFC) experiment because the subject utilizes information from previous stimuli (see Experimental rationale). Alternatively, a failure to transfer the subjective criterion between different stimuli may be the cause. Our experiments cannot distinguish between these two possibilities (see Experimental rationale), but, irrespective of the cause, the effects are small (0. I3 and 0.06 log units for orientation and spatial frequency discrimination, respectively). Although our experiments were psychophysical, one of our primary motivations arose from neurophysiological considerations. We chose the complementary variables of orientation and spatial frequency because primary cortical neurones respond to select ranges along both of these dimensions (Hubel and Wiesel, 1962, 1968; Campbell et al., 1969; Schiller ef al., 1976). Consequently large differences along either dimension will activate largely nonoverlapping sets of neurones in the primary visual cortex. Therefore, in our experiments, we were able to test the hypothesis that fine behavioural discrimination relies on the comparison of neural responses in the same population of primary cortical neurones. Our data do not support this hypothesis. Drawing this conclusion assumes that there are no cortical neurones that are finely tuned along one of these dimensions but broadly tuned along the other. In area 17 of primates there are some neurones that are non-selective for orientation (Hubel and Wiesel, 1968). However, it has been shown that neurones broadly tuned for orientation also tend to be broadly tuned for spatial frequency (DeValois er al., 1982). Such neurones would be less suited to transmit subtle differences in stimulus orientation or spatial frequency (Skottun et al., 1983).
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ARTHUR BRADLEY and BERNT C. S~omx
.-lcX-no~~ledgemenr-This work was supported by the Norwegian Research Council for Science and Humanities (NXVF). REFERENCES Andrews D. P. (1967) Perception of contour orientation in the central fovea. Part I: Short lines. Vision Res. 7, 975-997. Bouma H. and Andriessen J. J. (1968) Perceived orientation of isolated line segments. Vision Res. 8, 493-507. Burbeck C. A. and Regan D. (1983) Independence of orientation and size in spatial discriminations. J. opr. Sot. Am. 73, 1691-1694. Campbell F. W.. Cooper G. F. and Enroth-Cugell C. (1969) The spatial selectivity of the visual cells of the cat. J. Ph.vsiol. 203, 223-235. Campbell F. W., Nachmias J. and Jukes J. (1970) Spatialfrequency discrimination in human vision. J. opt. Sot. Am. 60, 555-559. Caelli T., Brettel H., Rentschler I. and Hilz R. (1983) Discrimination thresholds in the two-dimensional spatial frequency domain. Vision Res. 23, 129-133. DeValois R. L., Albrecht D. G. and Thorell L. G. (1982) Spatial frequency selectivity of cells in macaque visual cortex. Vision Res. 22, 545-559. Georgeson M. A. (1980) Spatial frequency analysis in early visual processing. Phil. Trans. R. $0~. Lbnd. 8290, I l-22. Hirsch J. and Hylton R. (1982) Limits of spatial-frequency discrimination as evidence of neural interpolation. J. opt. Sot. Am. 72, 1367-1374. Hirsch J. and Hylton R. (1984) Orientation dependence of visual hyperacuity contains a component with hexagonal symmetry. J. opr. Sot. Am. A 1, 30&308.
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