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Spatial frequency tuning of transient non-oriented units
Viiion Res Vol.25.No. I.pp 67-72.1985 Printed in Great Britain. All rights reserved
SPATIAL
Copyright
01343-6989.85 53.00 + 0 00 r‘ 1985 Pergamon Press Ltd
FREQUENCY TUNING OF TRANSIENT NON-ORIENTED UNITS
VINCENT P. FERRERA and HUGH R. WILSON Committee on Neurobiology and Department of Pharmacological and Physiological Sciences, University of Chicago, 920 East 58th Street, Chicago, IL 60637, U.S.A. (Received 26 April 1984; in revised form 14 August 1984)
Abstract-Thresholds for a vertical test stimulus with a 1.0 octave bandwidth were measured as a function of the spatial frequency of a horizontal flickering cosine mask. Both test and mask were temporally modulated at 8.0Hz. as low temporal frequencies were found to produce very little masking. Separate experiments were run at each of 10 test frequencies from 0.25 to 8.0 cycles per degree (c/deg) at 0.5 octave intervals. Masking curves thus obtained for each of three subjects were used to compute the spatial frequency sensitivities of three non-oriented mechanisms. Compared to previous masking studies of orientation selective units, non-oriented units have somewhat broader spatial frequency sensitivity curves, in agreement with primate neurophysiology.
INTRODUCTION
Circularly symmetric receptive fields are characteristic of cells in the retina, lateral geniculate nucleus and layer IV of the cortex of both cats and primates (Hubel and Wiesel, 1962, 1968). However, little work
has been done using human visual psychophysics to distinguish the spatial frequency response of such units from that of orientation selective units. Wilson et al. (1983) and Phillips and Wilson (1984) have used oblique cosine gratings to mask localized patterns in order to estimate the spatial frequency tuning of orientation selective units. Their results show that the masking threshold elevation under sustained temporal conditions decreases as the angle between test and mask increases so that with a relative orientation of 45.0 deg or more there is virtually no masking. If one wishes to measure the spatial frequency tuning of circularly symmetric units, it would be natural to employ masks orthogonal (i.e. at right angles) to the test pattern. Burbeck and Kelly (1981) have used orthogonal masking to demonstrate significant threshold elevations under transient conditions. However, they only made a few measurements of threshold elevation as a function of mask, spatial frequency. In the present study, we used threshold elevation due to an orthogonal mask to estimate the spatial frequency tuning of low spatial frequency mechanisms under transient conditions. Comparison of these results with those of Wilson et al. (1983) shows that the tuning of transient non-oriented units is broader than that of orientation selective units. METHODS
dimensional and was defined by a list of 512 luminance values. The display, which had a mean luminance of 17.5cd/m?, was viewed through a circular aperture in a cardboard mask that was illuminated at the same mean level and approximate hue as the monitor. All masks used were cosine gratings, which were fixed at 40% contrast for most measurements. Additional measurements of masking as a function of mask contrast were also made. The test stimuli had a luminance profile defined by the sixth spatial derivative of a Gaussian (D6): D6(x,a)
= - J.& (e - r*/a’)
where CTis the space constant in degrees of visual angle. A plot of this function can be seen in Wilson et al. (1983). The Fourier transform, with respect to X, of a D6 pattern has a peak spatial frequency, W,,,, related to Q by the following expression: W,,,=(Ul)‘JJ
(2)
D6 patterns were chosen becuase they are spatially localized and thus minimize effects due to the spatial inhomogeneity of the visual system, and because they have a relatively narrow frequency bandwidth of 1.0 octave. For further discussion of the mathematical properties of these patterns see Swanson, Wilson and Giese (1984). At 0.25 and 0.35 c/deg, a D6 was too broad to fit on the monitor and, therefore, a difference of Gaussians (DOG) was used for the test. The luminance profile of a DOG can be described by the following equation: DOG (X, a) = 3e-~*/*z_ 2e-.r?(l L+
Patterns were generated by a Digital Equipment Corporation PDP/8 computer, passed through a D/A converter, and displayed on a Tektronix 608 Monitor with a P3l phosphor screen. Each pattern was one-
(1)
(3)
Wilson et al. have shown that results using DOGS do not differ significantly from those using D6s at low spatial frequencies. 67
The presentanon of the mask at an angle orthogonal to the test was accomphshed wth an electronx raster rotator The computer read out frames of the Lertlcal test and horizontal mask at 120 Hz so that
the two appeared to be physically superimposed with no perceptible flicker. The masking gratmgs were temporally modulated by 1 0 set of an 8.0 Hz sins wave and were ramped on and off by using a trapezoidal envelope with on- and off-ramps of 0.25 set duration. These ramps have been shown by Bergen (198 I) to minimize the effects of transients at stimulus onset and offset. Each trial was of 1.0 set duration, during which the test was modulated by one cycle of an 8.0 hz square wave in sine phase (i.e. positive for l/16 sec. and then negative for l/16 set). The onset of the test pattern was timed so that there was a phase shift of 90deg between the temporal modulations of the test and mask. However, the relative temporal phase is not critical. as Burbeck and Kelly ( I98 1) have found that a 90 deg temporal phase shift between test and mask produced the same threshold elevations as the in-phase condition. Subjects sat facing the display with their heads comfortably positioned in a chin rest. Viewing was monocular, and the other eye was covered with a translucent occluder. Subjects were instructed to fixate the center of the circular field, which was 4.0 deg in diameter for test frequencies of I.0 and above. and 8.0 deg in diameter for lower frequencies. Field sizes were chosen to be exactly the same as those used in the Lehky and Wilson (1984) study so as to facilitate comparison of results. NO fixation mark was used. The subject initiated each trial by pressing a button which triggered a I set stimulus presentation. after which the subject pressed the appropriate button to indicate whether or not they had seen the test. Based on this response. the computer either increased or decreased the test contrast for the next presentation using a modified version of the randomized double staircase technique described by Cornsweet (1962). Details of this technique may be found elsewhere (Wilson, 1979). In a single experiment. thresholds were measured for a single test pattern of fixed spatial frequency, which was either superimposed on a uniform background (unmasked condition) or else on one of seven different masks. Several experiments were done at each test frequency in order to encompass a range of masks from 0.25 to 8.0 c/deg. In each experiment, the seven masks plus unmasked condition were presented in random order. In order to estimate the spatial frequency tuning of human visual mechanisms, threshold elevations for othogonal masking were measured as a function of mask soatial freauencv and contrast. The data were then analyzed using the model of Wilson et al. (1983), which is very similar to those used in previous masking and increment threshold studies (Carlson. 1978: Legge and Foley, 1980; Wilson, 1980). In this model, it is assumed that the stimulus is first pro-
ccssed in parallel b) .I number of IInc’ar JP,LLIA! frequent) lilters. The output of each filter I\ then passed through a non-Imeant>. u hxh ml\ be
different for each filter. Uncorrelated noise I< added to each response. and the resultant signals then provide the Input to J signal detector which determines whether the response to the combination of test and mask is significantly different from the response to the mask alone The data analysis routine esttmates the spatial frequency tumng of the filters by compensating for the presence of the non-linearity. Details may be found in Wilson ct 111.(1983). RESULTS
Complete data sets were gathered on three subjects, one of whom was a naive observer, On each subject separate experiments were run to obtain threshold elevation curves for all test frequencies from 0.25 to 2.8 or 4.0 c/deg in 0.5 octave steps. Thus, data analysis was based on 8 to 9 masking curves for each subject. Data for two subjects (V.P.F. and S.K.B.) at selected test frequencies are shown in Figs I and 2. These masking curves are characteristically broad, having poorly defined peaks and little decrease in masking at low mask frequencies. There is a general trend for masking to decrease as the spatial frequency of the test pattern increases, in keeping with the results of Burbeck and Kelly (1981) and Wilson e; al. (1983). Furthermore, as is evident in the top panels of Figs I and 2, test frequencies up to 1.O octave apart often tend to produce curves which are nearly identical in shape, which suggests that they are detected by the same underlying spatial mechanisms. Thus, our
s2-
‘,‘-.-. o_g-o’o-, \
o
. 0 35 c/de* 0 0 71 c/a*g “PF . .
Fig. I. Threshold elevation as a function of mask spatial frequency for selected test frequencies (subject V.P.F.). In each experiment test spatial frequency was heid constant while mask frequency varied. Curves from neighboring test frequencies are often similar in shape suggesting a common underlying spatial filter
Spatial frequency tuning of transient non-oriented units
69
in the Discussion.
Mask
SPQIIOI frequency
ic/deql
Fig. 2. iMasking data at selected test frequencies for a second subject (S.K.B.). Solid and dashed curves represent theoretical predictions. The rest of the description is the same as for Fig. I.
experiments seem to be measuring the sensitivities of a small number of broadly tuned mechanisms. Based on the criterion that each mechanism be more sensitive than any of the others to at least one test frequency, it was possible to compute distinct mechanisms from three different masking curves for each subject. These masking curves had to be chosen with peaks far enough apart so that no single mechanism could provide an adequate fit to more than one of them. In order to compute the spatial frequency sensitivities of these mechanisms, it was first necessary to measure the characteristics of the nonlinear stage. This was accomplished in a separate set of experiments in which threshold elevation was measured as a function of mask contrast in cases where the spatial frequencies of the mask and test were identical. These results, when plotted on a log-log scale, can be accurately fit with a straight line (see Fig. 3). This indicates a power law relationship between threshold elevation and mask contrast whose exponent is given by the slope of the straight line. Within experimental error, these exponents turned out to be the same for all subjects: 0.46 for the lowest three test frequencies and 0.26 for a test of 2.0 c/deg. The former exponent is comparable to the value of 0.55 found for oblique masking at low and intermediate spatial frequencies under sustained temporal conditions (Wilson et al., l983), but it is much lower than the average value of 0.80 obtained under transient conditions by Lehky and Wilson (1984). Similarly, the exponent of 0.26 at 2.0 c/deg is significantly lower than the value of about 0.55 found for oblique masking under either sustained or transient conditions. A possible explanation for the existence of smaller power law exponents derived from orthogonal as opposed to oblique masking will be presented
Fits to the data obtained from these three mechanisms and including these nonlinearities are shown for two subjects at selected test frequencies as the continuous curves in Figs I and 2. The fits accounted for 88.0 and 93.07,, of the variance for these subjects. Fits for a third subject showed a similarly high correlation with the data. The data analysis and prediction procedure is identical to that described by Wilson et al. (1983). For all three subjects, the three mechanisms had quite similar tuning and, therefore, the averages have been plotted in Fig. 4 a-c. The largest of these mechanisms is lowpass while the other two are broadly tuned but have a noticeable drop in response at low frequencies. It should be stressed that our technique only provides reliable masking data at low spatial frequencies and under transient conditions. Although we cannot estimate their characteristics, it is clear that the visual system must contain one or more sustained mechanisms sensitive to higher spatial frequencies in addition to the transient mechanisms in Fig. 4. However, our orthogonal masking paradigm did not produce significant threshold elevations at higher spatial frequencies or under sustained conditions, thus preventing us from studying them. This is in accord with the results of Burbeck and Kelly (198 I), who found little threshold elevation at higher spatial frequencies, except when very high mask contrasts were used. DISCUSSION
Under the constraints of the model employed here, we have found that accurate predictions require three mechanisms with distinct spatial frequency tuning. Thus, the data we have gathered are not consistent
. 4 -
025c/dq
Slo,x . Q46 0
05c/daq
Fig. 3. Threshold elevation as a function of mask contrast. For each experiment, test and mask spatial frequency were identical. The linear fit on log-log scale implies a power law relationship between threshold elevation and mask contrast.
70
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VINCWT
FERRERA
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,
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050
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and
HUGH R
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The fact that slgntticant threshold ele\,,1i!<>q>\lerc 01114obtamable with transxnt temporal presentJrlt>n, and at low spatlal frequenws sugg.cs~s th3: \‘)::I results reflect the underlqlng propertles ot’ transient umts. This agrees with the results of Cleland er Al{ (1979). which shou that rranslentl! responding <‘II retinal ganglion cells hate larger receptive fields thnn their sustained counterparts In addition. several models of human spatiotemporal VISIONunder transient condit!ons at low spatial frequencies hake tneluded a non-lmear stage (Kelly, 1981; Kelly and Savoie. 1978: Bergen and Wilson. 1985). This strengthens the similarity between human transient units with circular symmetry and the non-linear Y-cells in the cat retina (,Enroth-Cugell and Robson. 1966; Hochstein and Shapley, 1976). Our study also indicates that sustained units with circular symmetq cannot be masked very effectively, as was also observed by Burbeck and Kelly (1981). This suggests that these units may have an almost linear response to image contrast as is the case with X-cells in the cat retina (Enroth-Cugell and Robson, 1966). Based on our experiments alone, it should be noted that the circular symmetry of the umts in question cannot be unequivocally asserted: as measurements were made at only one relative orientation between test and mask (i.e. 90degf. However, our data do suffice to exclude two cases of interest. First, Daugman (1980) has pointed out certain properties of a parttcular model of elongated receptive fields RF(x,_v), which may be described by the equation: RF (x,y) = A exp [ - (x’isf i y’;si)]
010
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80
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Fig. 4. (a-c). Tuning curves for three non-oriented mechanisms compared with those for orientation selective mechanisms. Aithough the former are somewhat more broadly tuned, similarities in the shapes of these tuning curves suggest that non-oriented units may provide the main input to orientation selective units.
with a single transient, non-oriented mechanism. This conciusion is at variance with the threshold model of Burbeck and Kelly (Burbcck and Kelly, 1980; Kelly, 1983). Their model assumes that a single size of receptive fteId with an excitatory center and inhibitory surround having different spatial and tempo ral filtering characteristics accounts for all visual thresholds.
So long as S, = ksz and S, = ks,, k * I .O; this receptive field will have an ellipsoidal shape. This receptive field model will have bandpass spatial frequency tuning at the orthogonal .\: and y orientations, but the sensitivity curve at one orientation will be shifted to a lower spatial frequency range due to the larger space constants. The sensitivity curves in Fig. 4 are incompatible with this model, as there is no significant spatial frequency shift to lower spatial frequencies for the orthogonal as opposed to oblique masking results. Second, our data contradict the notion that orthogonal masking results from a slight residual sensitivity of orientation selective units to masks perpendicular to the optimal orientation. Daugrnan (1982) and Phillips and Wilson (1984) have shown that orientation selective units may be described by a product of orthogonal functions in Cartesian but not polar coordinates. This is a special case of the equation above where s, = sj. In this case, it is possible for the filter to retain sensitivity to patterns at an orientation orthogonal to the preferred orientation. However, the spatial frequency response will be bandpass at the preferred orientation and lowpass at the orthogonal orientation, and therefore the oblique and orthogonal masking results in Fig. 4b
Spatial frequency tunmg of transient non-oriented unrts and 4c refute this inte~retation of orthogonal masking. Only mechanisms with roughly circular symmetry remain as a likely explanation for our data. it was noted previously that the compressive power law non-linearity evident in Fig. 3 has si~i~cantly smaller exponents for orthogonal than for oblique masking. First, note that smaller exponents for functions relating test threshold to mask contraxt are ~ndicatii~eof a more near@ linear s_vsrern.This is easily
grasped from the observation that thresholds in a linear system with contrast independent noise would be unaffected by mask contrast (i.e. would show a slope of zero in Fig 3). Given this, a plausible interpretation may be offered for the low exponents in Fig. 3. If orthogonal masking taps properties at a circularly symmetric stage of the visual system that subsequently provides input to the orientation selective units revealed by oblique masking, and if each of these two stages involves a compressive non-linearity; then increment threshold measurements at the later stage should show a larger exponent than at the earher. This results from the cascading of successive compressive non-linearities, which produce a more pronounced non-linearity. Otherwise stated, shallower slopes for threshold elevation as a function of mask contrast in circularly symmetric units (orthogonal masking) as opposed to orientation selective units (oblique masking) are to be expected if the former provide input for the latter. Finally, it is of interest to compare the spatial frequency tuning of non-oriented units with that of orientation selective units under transient conditions. The results for orientation selective units were obtained under the same temporal conditions described above, but the mask was oriented at 14.5 deg relative to the vertical test (Lehky and Wilson, 1984). Phillips and Wilson (1984) have shown this angle to be well within the bandwidth of orientation selective units. As shown in Fig. 4, orientation selective units tend to be somewhat more narrowly tuned, especially in the tails of their sensitivity curves. This agrees with physiological evidence which shows there to be a progressive narrowing of spatial frequency bandwidths from retina to visual cortex in both cats (Maffei and Fiorentini, 1972) and monkeys (DeValois et af., 1983). However, the general similarity between the oriented and non-oriented tuning curves in Fig. 4 suggests that a significant portion of the spatial
frequency tuning of orientation selective transient units is already present in the circularly symmetric units which presumably provide their input. Acknorc,lerlgemenl-This research was supported in part by NIH grant No. PHS 501 EY 02158 to H.R.W. REFERENCES
Bergen J. R. (1981) A quantitative model of human spatiotemporal vision at threshold. Unpublished dissertation, University of Chicago, March. 1981. Bergen J. R: and Wilson H. R. (1985) Prediction of flicker sensitivities from temporal pulse data. Vision Res. In press.
71
Burbeck C. R. and Kelly D. H. (1980) Spatiotem~ml characteristics excitatoryof visual mechanisms: inhibitory model. J. opr. Sot. Am. 70, 1121-I 126. Burbeck C. A. and Kelly D. H. (1981) Contrast gain measurements and the transient;sustained dtchotomy. J. opr. Sot. Am. 71, 1335-1342. Carlson C. R. (1978) Thresholds for perceived image sharpness. Photograph. Sci. Engng 22, 69-71. Carlson C. R. and Cohen R. W. (1980) A simple psychophysical model for predicting the visibility of displayed info~ation. froc. SID 21, 2PP-346. Cleland B. G.. Harding T. H. and Tulanay-Keesey U. (1979) Visual resolution and receptive field size: examination of two kinds of cat retinal ganglion cell. Science 205, 1015-1017. Cleland B. G. and Levick W. R. (1974) Properties of rarely encountered types of ganglion cells in the cat’s retina and an overall classification. J. Phvsiol. 240, 457392. Cornsweet T. N. (1962) The staircase method in .osvcho. physics. Ant. J. Psychol. 75, 485-491. Dauaman J. G. i 1980) Two-dimensional saectral analysis of coytical receptive fi;ld properties. Vision’Res.20,84%856. Daugman J. G. (1982) Polar spectral nonseparability of two-dimensional spatial frequency channels. Inrest. Ophthai. r&al Sci. 22, 49. DeValois R. L., Albrecht D. G. and Thorell L. G. (1992) Spatial frequency selectivity of cells in macaque visual cortex. Vision Res. 22, 545-559. Enroth-Cugell C. and Robson J. G. (1966) The contrast sensitivity of retinal ganglion cells of the cat. J. Physiol. 187, 517-552. Hochstein S. and Shapley R. M. (1976) Linear and nonlinear spatial subunits in Y cat retinal ganglion cells. J. Physiol. 262, 265-284. Hubel D. H. and Wiesel T. N. (1962) Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physiol. 160, 106-154. Hubel D. H. and Wiesel T. N. (1968) Receptive and functional architecture of monkey striate cortex. J. Physioi. 195, 215-243. Kelly D. H. (1966) Frequency in visual responses. J. opr. Sac. Am. 52, 1628-1633. Kelly D. H. (1972) Adaptation effects on spatio-temporal sine wave thresholds. Vision Res. 12, 89-101. Kelly D. H. (198 I) Nonlinear visual responses to flickering sinusoidal gratings. J. opr. Sot. Am. 71, 1051-1055. Kelly D. H. (1983) Spatiotemporai variation of chromatic and achromatic contrast thresholds. J. opf. Sot. Am. 73, 742-750. Kelly D. H. and Savoie R. E. (1978) Theory of flicker and transient responses. III. An essential nonlinea~ty. J. opt. Sac. Am. 68, 1481-1490. Kuffler S. W. (1953) Discharge patterns and functional organization of mammalian retina. J. Neurophysiol.16, 37-68. Legge G. E. and Foley J. M. (1980) Contrast masking in human vision. J. opt. Sac. Am. 70, 1458-1470. Lehky S. R. and Wilson H. R. (1984) Temporal properties of visual channels measured by masking. Submitted for publication. Malfei L. and Fiorentini A. (1972) Retinogen~culate convergence and analysis of contrast. J. Neurophysioi.35, 65-72. Maffei L. and Fiorentini A. (1973) The visual cortex as a spatial frequency analyser. Vision Res. 13, 1255-1267. Phillips G. C. and Wilson H. R. (I984) Orientation bandwidths of spatial mechanisms measured by masking. J. opt. Sot. Am. 73, 226-232. Robson J. G. (1966) Spatial and temporal contrast sensitivity of the visual system. J. opt. Sot. Am. 54, 1141-I 142. Stone J. and Fukuda Y. (1974) properties of cat retinal ganglion cells: A comparison of W-cells with X-cells and Y-cells. J. Neurophysiol.37, 722-748.
-_I
VIX.CE>T
P.
FERRER-\and HC’GH R. LVILSW
Swanson u’. H.. Wilson H. R. and Giesr S. C. (IYY?) Contrast matching data predicted from contrast increment thresholds I’isiun Res. 24. 63-75. Wilson H. R. (1975) Quantitative characterization of tno types of line-spread function near the fovea. C%ion Rrs. 18. 975-95 I.
Wilson H. R. (1979)Spatiotemporal characterization ot L transient mechanisms in the human visual s>stem. L’!,vL,J~ Rrs. 20, 443-452. Wilson H. R.. McFariane D. K. and Philhps Cr. C. i 19831 Spatial frequenck tuning of orientation selective units estimated by oblique masking. Vision Rex. 23, ,977~R82.
SPATIAL
Copyright
01343-6989.85 53.00 + 0 00 r‘ 1985 Pergamon Press Ltd
FREQUENCY TUNING OF TRANSIENT NON-ORIENTED UNITS
VINCENT P. FERRERA and HUGH R. WILSON Committee on Neurobiology and Department of Pharmacological and Physiological Sciences, University of Chicago, 920 East 58th Street, Chicago, IL 60637, U.S.A. (Received 26 April 1984; in revised form 14 August 1984)
Abstract-Thresholds for a vertical test stimulus with a 1.0 octave bandwidth were measured as a function of the spatial frequency of a horizontal flickering cosine mask. Both test and mask were temporally modulated at 8.0Hz. as low temporal frequencies were found to produce very little masking. Separate experiments were run at each of 10 test frequencies from 0.25 to 8.0 cycles per degree (c/deg) at 0.5 octave intervals. Masking curves thus obtained for each of three subjects were used to compute the spatial frequency sensitivities of three non-oriented mechanisms. Compared to previous masking studies of orientation selective units, non-oriented units have somewhat broader spatial frequency sensitivity curves, in agreement with primate neurophysiology.
INTRODUCTION
Circularly symmetric receptive fields are characteristic of cells in the retina, lateral geniculate nucleus and layer IV of the cortex of both cats and primates (Hubel and Wiesel, 1962, 1968). However, little work
has been done using human visual psychophysics to distinguish the spatial frequency response of such units from that of orientation selective units. Wilson et al. (1983) and Phillips and Wilson (1984) have used oblique cosine gratings to mask localized patterns in order to estimate the spatial frequency tuning of orientation selective units. Their results show that the masking threshold elevation under sustained temporal conditions decreases as the angle between test and mask increases so that with a relative orientation of 45.0 deg or more there is virtually no masking. If one wishes to measure the spatial frequency tuning of circularly symmetric units, it would be natural to employ masks orthogonal (i.e. at right angles) to the test pattern. Burbeck and Kelly (1981) have used orthogonal masking to demonstrate significant threshold elevations under transient conditions. However, they only made a few measurements of threshold elevation as a function of mask, spatial frequency. In the present study, we used threshold elevation due to an orthogonal mask to estimate the spatial frequency tuning of low spatial frequency mechanisms under transient conditions. Comparison of these results with those of Wilson et al. (1983) shows that the tuning of transient non-oriented units is broader than that of orientation selective units. METHODS
dimensional and was defined by a list of 512 luminance values. The display, which had a mean luminance of 17.5cd/m?, was viewed through a circular aperture in a cardboard mask that was illuminated at the same mean level and approximate hue as the monitor. All masks used were cosine gratings, which were fixed at 40% contrast for most measurements. Additional measurements of masking as a function of mask contrast were also made. The test stimuli had a luminance profile defined by the sixth spatial derivative of a Gaussian (D6): D6(x,a)
= - J.& (e - r*/a’)
where CTis the space constant in degrees of visual angle. A plot of this function can be seen in Wilson et al. (1983). The Fourier transform, with respect to X, of a D6 pattern has a peak spatial frequency, W,,,, related to Q by the following expression: W,,,=(Ul)‘JJ
(2)
D6 patterns were chosen becuase they are spatially localized and thus minimize effects due to the spatial inhomogeneity of the visual system, and because they have a relatively narrow frequency bandwidth of 1.0 octave. For further discussion of the mathematical properties of these patterns see Swanson, Wilson and Giese (1984). At 0.25 and 0.35 c/deg, a D6 was too broad to fit on the monitor and, therefore, a difference of Gaussians (DOG) was used for the test. The luminance profile of a DOG can be described by the following equation: DOG (X, a) = 3e-~*/*z_ 2e-.r?(l L+
Patterns were generated by a Digital Equipment Corporation PDP/8 computer, passed through a D/A converter, and displayed on a Tektronix 608 Monitor with a P3l phosphor screen. Each pattern was one-
(1)
(3)
Wilson et al. have shown that results using DOGS do not differ significantly from those using D6s at low spatial frequencies. 67
The presentanon of the mask at an angle orthogonal to the test was accomphshed wth an electronx raster rotator The computer read out frames of the Lertlcal test and horizontal mask at 120 Hz so that
the two appeared to be physically superimposed with no perceptible flicker. The masking gratmgs were temporally modulated by 1 0 set of an 8.0 Hz sins wave and were ramped on and off by using a trapezoidal envelope with on- and off-ramps of 0.25 set duration. These ramps have been shown by Bergen (198 I) to minimize the effects of transients at stimulus onset and offset. Each trial was of 1.0 set duration, during which the test was modulated by one cycle of an 8.0 hz square wave in sine phase (i.e. positive for l/16 sec. and then negative for l/16 set). The onset of the test pattern was timed so that there was a phase shift of 90deg between the temporal modulations of the test and mask. However, the relative temporal phase is not critical. as Burbeck and Kelly ( I98 1) have found that a 90 deg temporal phase shift between test and mask produced the same threshold elevations as the in-phase condition. Subjects sat facing the display with their heads comfortably positioned in a chin rest. Viewing was monocular, and the other eye was covered with a translucent occluder. Subjects were instructed to fixate the center of the circular field, which was 4.0 deg in diameter for test frequencies of I.0 and above. and 8.0 deg in diameter for lower frequencies. Field sizes were chosen to be exactly the same as those used in the Lehky and Wilson (1984) study so as to facilitate comparison of results. NO fixation mark was used. The subject initiated each trial by pressing a button which triggered a I set stimulus presentation. after which the subject pressed the appropriate button to indicate whether or not they had seen the test. Based on this response. the computer either increased or decreased the test contrast for the next presentation using a modified version of the randomized double staircase technique described by Cornsweet (1962). Details of this technique may be found elsewhere (Wilson, 1979). In a single experiment. thresholds were measured for a single test pattern of fixed spatial frequency, which was either superimposed on a uniform background (unmasked condition) or else on one of seven different masks. Several experiments were done at each test frequency in order to encompass a range of masks from 0.25 to 8.0 c/deg. In each experiment, the seven masks plus unmasked condition were presented in random order. In order to estimate the spatial frequency tuning of human visual mechanisms, threshold elevations for othogonal masking were measured as a function of mask soatial freauencv and contrast. The data were then analyzed using the model of Wilson et al. (1983), which is very similar to those used in previous masking and increment threshold studies (Carlson. 1978: Legge and Foley, 1980; Wilson, 1980). In this model, it is assumed that the stimulus is first pro-
ccssed in parallel b) .I number of IInc’ar JP,LLIA! frequent) lilters. The output of each filter I\ then passed through a non-Imeant>. u hxh ml\ be
different for each filter. Uncorrelated noise I< added to each response. and the resultant signals then provide the Input to J signal detector which determines whether the response to the combination of test and mask is significantly different from the response to the mask alone The data analysis routine esttmates the spatial frequency tumng of the filters by compensating for the presence of the non-linearity. Details may be found in Wilson ct 111.(1983). RESULTS
Complete data sets were gathered on three subjects, one of whom was a naive observer, On each subject separate experiments were run to obtain threshold elevation curves for all test frequencies from 0.25 to 2.8 or 4.0 c/deg in 0.5 octave steps. Thus, data analysis was based on 8 to 9 masking curves for each subject. Data for two subjects (V.P.F. and S.K.B.) at selected test frequencies are shown in Figs I and 2. These masking curves are characteristically broad, having poorly defined peaks and little decrease in masking at low mask frequencies. There is a general trend for masking to decrease as the spatial frequency of the test pattern increases, in keeping with the results of Burbeck and Kelly (1981) and Wilson e; al. (1983). Furthermore, as is evident in the top panels of Figs I and 2, test frequencies up to 1.O octave apart often tend to produce curves which are nearly identical in shape, which suggests that they are detected by the same underlying spatial mechanisms. Thus, our
s2-
‘,‘-.-. o_g-o’o-, \
o
. 0 35 c/de* 0 0 71 c/a*g “PF . .
Fig. I. Threshold elevation as a function of mask spatial frequency for selected test frequencies (subject V.P.F.). In each experiment test spatial frequency was heid constant while mask frequency varied. Curves from neighboring test frequencies are often similar in shape suggesting a common underlying spatial filter
Spatial frequency tuning of transient non-oriented units
69
in the Discussion.
Mask
SPQIIOI frequency
ic/deql
Fig. 2. iMasking data at selected test frequencies for a second subject (S.K.B.). Solid and dashed curves represent theoretical predictions. The rest of the description is the same as for Fig. I.
experiments seem to be measuring the sensitivities of a small number of broadly tuned mechanisms. Based on the criterion that each mechanism be more sensitive than any of the others to at least one test frequency, it was possible to compute distinct mechanisms from three different masking curves for each subject. These masking curves had to be chosen with peaks far enough apart so that no single mechanism could provide an adequate fit to more than one of them. In order to compute the spatial frequency sensitivities of these mechanisms, it was first necessary to measure the characteristics of the nonlinear stage. This was accomplished in a separate set of experiments in which threshold elevation was measured as a function of mask contrast in cases where the spatial frequencies of the mask and test were identical. These results, when plotted on a log-log scale, can be accurately fit with a straight line (see Fig. 3). This indicates a power law relationship between threshold elevation and mask contrast whose exponent is given by the slope of the straight line. Within experimental error, these exponents turned out to be the same for all subjects: 0.46 for the lowest three test frequencies and 0.26 for a test of 2.0 c/deg. The former exponent is comparable to the value of 0.55 found for oblique masking at low and intermediate spatial frequencies under sustained temporal conditions (Wilson et al., l983), but it is much lower than the average value of 0.80 obtained under transient conditions by Lehky and Wilson (1984). Similarly, the exponent of 0.26 at 2.0 c/deg is significantly lower than the value of about 0.55 found for oblique masking under either sustained or transient conditions. A possible explanation for the existence of smaller power law exponents derived from orthogonal as opposed to oblique masking will be presented
Fits to the data obtained from these three mechanisms and including these nonlinearities are shown for two subjects at selected test frequencies as the continuous curves in Figs I and 2. The fits accounted for 88.0 and 93.07,, of the variance for these subjects. Fits for a third subject showed a similarly high correlation with the data. The data analysis and prediction procedure is identical to that described by Wilson et al. (1983). For all three subjects, the three mechanisms had quite similar tuning and, therefore, the averages have been plotted in Fig. 4 a-c. The largest of these mechanisms is lowpass while the other two are broadly tuned but have a noticeable drop in response at low frequencies. It should be stressed that our technique only provides reliable masking data at low spatial frequencies and under transient conditions. Although we cannot estimate their characteristics, it is clear that the visual system must contain one or more sustained mechanisms sensitive to higher spatial frequencies in addition to the transient mechanisms in Fig. 4. However, our orthogonal masking paradigm did not produce significant threshold elevations at higher spatial frequencies or under sustained conditions, thus preventing us from studying them. This is in accord with the results of Burbeck and Kelly (198 I), who found little threshold elevation at higher spatial frequencies, except when very high mask contrasts were used. DISCUSSION
Under the constraints of the model employed here, we have found that accurate predictions require three mechanisms with distinct spatial frequency tuning. Thus, the data we have gathered are not consistent
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The fact that slgntticant threshold ele\,,1i!<>q>\lerc 01114obtamable with transxnt temporal presentJrlt>n, and at low spatlal frequenws sugg.cs~s th3: \‘)::I results reflect the underlqlng propertles ot’ transient umts. This agrees with the results of Cleland er Al{ (1979). which shou that rranslentl! responding <‘II retinal ganglion cells hate larger receptive fields thnn their sustained counterparts In addition. several models of human spatiotemporal VISIONunder transient condit!ons at low spatial frequencies hake tneluded a non-lmear stage (Kelly, 1981; Kelly and Savoie. 1978: Bergen and Wilson. 1985). This strengthens the similarity between human transient units with circular symmetry and the non-linear Y-cells in the cat retina (,Enroth-Cugell and Robson. 1966; Hochstein and Shapley, 1976). Our study also indicates that sustained units with circular symmetq cannot be masked very effectively, as was also observed by Burbeck and Kelly (1981). This suggests that these units may have an almost linear response to image contrast as is the case with X-cells in the cat retina (Enroth-Cugell and Robson, 1966). Based on our experiments alone, it should be noted that the circular symmetry of the umts in question cannot be unequivocally asserted: as measurements were made at only one relative orientation between test and mask (i.e. 90degf. However, our data do suffice to exclude two cases of interest. First, Daugman (1980) has pointed out certain properties of a parttcular model of elongated receptive fields RF(x,_v), which may be described by the equation: RF (x,y) = A exp [ - (x’isf i y’;si)]
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Fig. 4. (a-c). Tuning curves for three non-oriented mechanisms compared with those for orientation selective mechanisms. Aithough the former are somewhat more broadly tuned, similarities in the shapes of these tuning curves suggest that non-oriented units may provide the main input to orientation selective units.
with a single transient, non-oriented mechanism. This conciusion is at variance with the threshold model of Burbeck and Kelly (Burbcck and Kelly, 1980; Kelly, 1983). Their model assumes that a single size of receptive fteId with an excitatory center and inhibitory surround having different spatial and tempo ral filtering characteristics accounts for all visual thresholds.
So long as S, = ksz and S, = ks,, k * I .O; this receptive field will have an ellipsoidal shape. This receptive field model will have bandpass spatial frequency tuning at the orthogonal .\: and y orientations, but the sensitivity curve at one orientation will be shifted to a lower spatial frequency range due to the larger space constants. The sensitivity curves in Fig. 4 are incompatible with this model, as there is no significant spatial frequency shift to lower spatial frequencies for the orthogonal as opposed to oblique masking results. Second, our data contradict the notion that orthogonal masking results from a slight residual sensitivity of orientation selective units to masks perpendicular to the optimal orientation. Daugrnan (1982) and Phillips and Wilson (1984) have shown that orientation selective units may be described by a product of orthogonal functions in Cartesian but not polar coordinates. This is a special case of the equation above where s, = sj. In this case, it is possible for the filter to retain sensitivity to patterns at an orientation orthogonal to the preferred orientation. However, the spatial frequency response will be bandpass at the preferred orientation and lowpass at the orthogonal orientation, and therefore the oblique and orthogonal masking results in Fig. 4b
Spatial frequency tunmg of transient non-oriented unrts and 4c refute this inte~retation of orthogonal masking. Only mechanisms with roughly circular symmetry remain as a likely explanation for our data. it was noted previously that the compressive power law non-linearity evident in Fig. 3 has si~i~cantly smaller exponents for orthogonal than for oblique masking. First, note that smaller exponents for functions relating test threshold to mask contraxt are ~ndicatii~eof a more near@ linear s_vsrern.This is easily
grasped from the observation that thresholds in a linear system with contrast independent noise would be unaffected by mask contrast (i.e. would show a slope of zero in Fig 3). Given this, a plausible interpretation may be offered for the low exponents in Fig. 3. If orthogonal masking taps properties at a circularly symmetric stage of the visual system that subsequently provides input to the orientation selective units revealed by oblique masking, and if each of these two stages involves a compressive non-linearity; then increment threshold measurements at the later stage should show a larger exponent than at the earher. This results from the cascading of successive compressive non-linearities, which produce a more pronounced non-linearity. Otherwise stated, shallower slopes for threshold elevation as a function of mask contrast in circularly symmetric units (orthogonal masking) as opposed to orientation selective units (oblique masking) are to be expected if the former provide input for the latter. Finally, it is of interest to compare the spatial frequency tuning of non-oriented units with that of orientation selective units under transient conditions. The results for orientation selective units were obtained under the same temporal conditions described above, but the mask was oriented at 14.5 deg relative to the vertical test (Lehky and Wilson, 1984). Phillips and Wilson (1984) have shown this angle to be well within the bandwidth of orientation selective units. As shown in Fig. 4, orientation selective units tend to be somewhat more narrowly tuned, especially in the tails of their sensitivity curves. This agrees with physiological evidence which shows there to be a progressive narrowing of spatial frequency bandwidths from retina to visual cortex in both cats (Maffei and Fiorentini, 1972) and monkeys (DeValois et af., 1983). However, the general similarity between the oriented and non-oriented tuning curves in Fig. 4 suggests that a significant portion of the spatial
frequency tuning of orientation selective transient units is already present in the circularly symmetric units which presumably provide their input. Acknorc,lerlgemenl-This research was supported in part by NIH grant No. PHS 501 EY 02158 to H.R.W. REFERENCES
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