0042-4989/91 $3.00 + 0.00 Copyright 6 1991 Pergamon Press plc
Vision Res. Vol. 31, No. 9, pp. 16274631, 1991 Printed in Great Britain. Ail rights mewed
SPATIAL LOCALIZATION FRANK
L. KooI,‘*
ACROSS CHANNELS
RUSELL L. DE VALOIS’and EUGENE SWITKFZ?
‘Physiological Optics Group and Department of Psychology, University of California, Berkeley, CA 94720 and 2Departments of Psychobiology and Chemistry, University of California, Santa Crux, CA 95064, U.S.A. (Received 14 August 1990; in revised form I8 December 1990) Abstract-We have studied vernier acuity for patterns in which the stimuli to be aligned either are similar in their spatial and color characteristics or differ in these properties. The question which we address is whether spatial localization is independent of the channels being stimulated by the patterns to be aligned. We found that the precision of vernier alignment of Gabor patches was very similar irrespective of whether the patches were the same or different in spatial frequency, orientation, or color. it appears that the visual system extracts very precise location information independent of the similarity or dissimilarity of the spatiochromatic selectivity of the channels carrying that information. Spatial vision
Color vision
Localization
Vernier acuity
YNTRODUCI’ION
There is now very extensive psychophysical and physiological evidence for the presence of multiple two-dimensional spatial frequency channels in the early processing of visual information (see De Valois & De Valois, 1988; for summary and discussion). Although bandwidths vary widely across cells in the striate cortex (Vl), the vast majority of units are sufficiently narrowly tuned in o~entation and spatial frequency that they would not respond significantly to both of two gratings separated by 90 deg in orientation or by 2 octaves in spatial frequency (De Valois, Albrecht 8c Thorell, 1982). The evidence at the striate level is not as clear as to the extent of the separation into different channels of information along different axes in three dimensional (3D) color space (Lennie, Krauskopf & Sclar, 1990), but it is certainly clear that relatively few cells respond both to luminance variations and to all color variations. . In addition to their 2D spatial frequency and their color tuning, striate units convey information about spatial location, since they have spatially-localized receptive fields, and the retinotopic mapping onto the striate cortex is quite precise (Tootell, Silverman, Switkes & De Valois, 1982). Within any given small region of striate cortex, then, are a group
*Presentaddress: TN0 Institute for Perception, Kampweg 5, 3769 DE Soesterberg,The Netherlands.
Feature channels
of cells each tuned to a different 2D spatial frequency region, but all with their receptive fields centered on the same location in visual space. The question we are raising, and attempting to answer in this experiment, is the extent to which the visual system can extract, and compare across regions, locution information quite independent of the spatial frequency or the color channel carrying that info~ation. Specifically, we examine the extent to which one can precisely judge the vertical alignment of two patterns in a vernier acuity task when the two patterns activate Vl cells of different channel types in the two regions. It has been previously shown by Westheimer and McKee (1977) that observers do very well with the vernier alignment of two or more patterns which are very different from each other, such as chevrons and lines. However, the patterns they used all had quite broad spatial frequency spectra and each would thus activate virtually all striate cells in a region, although of course in different proportions. In this experiment we examine this question using patterns chosen to activate largely nonoverlapping populations of Vl cell types in the two regions being compared. A preliminary account of this research was reported earlier (Kooi, De Valois & Switkes, 1987). Aspects of this problem have also been addressed by Burbeck (1987, 1988), Toet and Koenderink (1988), and Hess and Holliday (1990).
1627
1628
FRANKL. KOOIet al. METHODS
Stimuli were generated on Tektronix color monitors controlled by a Lexidata graphics unit and a NOVA 4 x computer (see Switkes, Bradley & De Vaiois, I988 for a more complete description). The stimuli were two circular Gabar patches placed one above the other with the patterns inside the patches (gratings or “blobs”) specific to the various experiments. On each triai the upper patch was presented slightly to the left or right of the lower one and the observer pressed one of two buttons to indicate their judgment of the offset of the upper patch. The displays were viewed through a mask around which a square was drawn. This square, as well as the vex&al and horizontal orientations of the gratings, helped the observers establish a vertical reference. Pairs having various relative displacements were precomputed and stored in graphics memory. This allowed for pre~nta~on of sub-pixel relative displacement of the two patches. Details af stimulus configuration and methodology differed for the various experiments.
In this experiment we employed a Tektronix 650 monitor viewed at a distance of 330 cm through a rectangular mask of 3.9 x 2.8 deg. The Gabor patches consisted of 6 c/deg cosine or sine wave gratings with Gaussian envelopes of standard deviation of 0.0833 deg (one-half of a period) in both the x and y directions. The centers of the two patches were separated vertically by 25 min arc. The position of the pair within the viewing aperture was randomized from trial to trial. The presentations were preceded by a warning buzzer and two stimulus duration conditions were used: 1OOmsec or continuous presentation until the observer responded” The primary purpose of this experiment was to compare vernier acuity for displa~ment of stimuli with similar o~entations to that for stimuii differing in orientation. Hence three conditions were employed where the orientations of the gratings were either both vertical, both horizontal, or vertical (upper) and horizontal flower). High contrasts (90%) were used and the chromatic&y of these luminance varying gratings was set to be the white defined by CIE coordinates (0,310, 0.316) of illuminant C, The method af constant stimuli employing four horizontal displacements of various sizes to either side of vertical and the aligned pattern
were used in a given run. Each pair was presented 10 times in a randomized order giving 90 presentations per run. For each observer and pattern combination, the sizes of the displacements were chosen to span the range from 100% correct performance to chance. Thresholds were calculated using probit analysis (Finney, 197 1) as in the accompanying paper (De Valois & De Valois, 1991). One of the authors (FIX) and a naive subject served as observers. Experiment
2. Spatial frequency
In this experiment the observers viewed a Tektronix 690 monitor at a distance of 172cm through a circular mask of 5.1 deg. The two Gabor patches were vertically separated by 75 min arc. In order to compare vernier acuity for targets with similar or differing spatial frequencies, test patches of 6 and 2.1 cfdeg were used, Again the Gaussian envelopes were set to have one-half period standard devia~ons (0.0833 and 0.238 deg) yielding a corresponding number of cycles, but differing extent, for the Gabor patches at the two frequencies. In the three conditions pairs of Gabor patches with both high, both low, or low (upper patch) and high (lower patch) spatial frequency were presented. All gratings were horizontally oriented, cosine phase, and luminance modulated with 90% contrast at the chromaticity of illuminant C. In this experiment the stimuli were presented using a 2AFC staircase technique [Essock, Williams, Enoch & Raphael, 1984). Eleven relative displacements, varying in 4 sac arc steps, were available. Two consecutive correct responses resulted in presentation of a smaller offset pair while one incorrect response increased the offset by one level. Threshold was calculated as the mean of 6 reversals. Each data point is based on a minimum of 12 trials. Experiment
3. Color us color
Viewing conditions and data analysis were simiiar to those in expt 2. Gabor patches contained 2.1 c/deg horizontal gratings. The gratings were isoluminant and varied in color along one of two chromatic axes: an LM-axis (constant-S) where the grating’s color modulation yielded modulation of L- and M-cone activity (but not S-cone) or an S-axis (tritan) where the grating modulated S-cone (but not L- or M-cone) activity (Krauskopf, Williams & Heeley, 1982). Far each of the two types of gratings the means chromaticity was that of illuminant C. The relative chromatic contrast
1629
Spatial localization across channels
for gratings along each of these axis was adjusted to yield similar vernier acuities for the cases when both Gabor patches were gratings along the LM- or along the Saxis. Isoluminance was determined by flicker photometry.
The viewing conditions and analysis procedures were similar to those of expt 2. In expt 4 the test patches were Gaussian modulations of the mean luminance or mean chromaticity with standard deviation 0.238 deg (i.e. Gabor patterns in the zero spatial frequency limit or “blobs”). The luminance patches were decrements from the mean luminance and the color patches correspond to an isoluminant chromaticity variation from illuminant C towards a red along the LMaxis (increasing L-cone decreasing M-cone, and constant S-cone activity). Three conditions were tested: both patches luminance, both patches color, and upper patch color lower patch luminance. The relative amplitudes of the luminance and chromaticity variations were chosen to yield equal offset acuity in the luminance vs luminance and color vs color conditions.
-..-...-
__-__-I--
~ ,5(I
-25
0
25
Offset (set arc} Fig. I. Psychometricfunctionsfor the judgmentof position
of upper Gabor patch relative to lower patch. Data for unlimitedviewing time and the four combinations of grating orientation and phase used in expt 1 are shown. Negative offsets indicate upper Gabor patch was physically to the left of the lower. vit 3IB-K
~
I-
401
A TH 100 msec
0 SL unlimited
0 FK 100 msec
0 FK unlimited
0,
J
Her/ Hor
Z?/
3
Orientation
Her/ sine Hor ( phase>
Combinations
I
Fig, 2. Dispiacement thresholds for Gabor patches of 6 c/deg, 0.5 see sinusoidal gratin@ in the four orientation and phase combinations.
RESULTS
Experiment 1. Orientation Data and results from the experiments testing the effects of relative o~en~tion are presented in Figs 1 and 2. Figure 1 shows typical psychometric functions for four stimulus conditions employed for runs where the observers had unlimited viewing time before they made a response. Displacement thresholds obtained by probit analysis (one-half the difference between offsets required for 75% correct judgments of leftward and rightward displa~ments) are plotted in Fig. 2. From these plots several points are ciear. The l&l2 set arc thresholds (lower curves, Fig. 2) illustrate that, given sufficient viewing time and stimulus contrast, observers can localize the relative position of the envelopes of Gabor patches with an accuracy similar to that of other hyperacuity tasks (Williams, Enoch & Essock, 1984). The similarity of the psychometric functions (Fig. 1) and the displacement thresholds (Fig. 2) for the four stimulus configurations indicates that: (i) thresholds are the same or only slightly higher for Gabor gratings oriented along the direction of displacement (horizontal vs horizontal) compared to those perpendicular (vertical vs vertical) to it; (ii) thresholds are independent of the placement of the grating within the Guassian envelope (cosine vs sine phase), and most si~ifi~ntly
;
(iii) the ability of the visual system to extract information about relative position is not diminished when comparing stimuli which activate m~hanisms selective for differing
1630
FRANKL. Kocn et al.
” :
60-
z u c, 5 ?-
50
+ Spatial
Frequency
Combinations
(c/deg)
relative to the comparison uli having similar o~entations.
of stim-
Experiment 2. Spatialfrequency Figure 3 indicates displa~ment threshold for the three spatial frequency conditions used in this experiment. As observed by Toet and K~nderink (1988) utilizing an alig~ent paradigm, the threshold does not depend on the spatial frequency of the Gabor patch. In a somewhat different task, Burbeck (1987) also showed that large-scale localization was independent of the spatial frequencies of the two targets. In expt 2 absolute vernier thresholds are somewhat greater than in our orientation studies while significantly lower than those measured by Toet and Koenderink (1988). The former arises from the greater inter-Gabor separation employed in expt 2, while the latter is a consequence of the much greater grating contrast in our experiments (90°/ contrast) relative
0
,
I
LM-axis/ LM-axis.
S-axis/ S-axis.
Color
30:
Color/Color
Color/Lum
Fig. 5. Displacement thresholds for color (isoluminant) and luminance decrement Gabor ‘*blobs”. The color variation was along an I&f-axis, from white at the edge of the patch towards red at the center. Data for the three conditions of expt 4 are shown.
to that used by Toet and Koenderink {near threshold contrast). The finding most relevant to our study is that offset thresholds for the case in which the Gabor patches would activate mechanisms tuned to distinct spatial frequencies (2.1 vs 6 c/deg) are no worse than those where the localization task involves mechanisms of the same spatial frequency (2.1 vs 2.1 or 6 vs 6 c/deg). A similar obse~~tion regarding an observer’s ability to detect differences in separation between targets differing in spatial frequency content has been reported by Burbeck (1988). Experiment 3. Color Figure 4 compares displacement detection performance for 2.1 c/deg Gabor patches of various colors. The contrasts of the gratings along the LX and S axes were chosen to give nearly the same offset thresholds (-82 set arc) for the LM vs LM and S vs S cases. However with this contrast specification, the observers’ ability to detect an offset in the LM- vs S-axis case was no worse than in the other two cases even though the two targets were detected by distinct cone mechanisms. Experiment 4. Color OSluminance
TH
@ FK
t-mJ
!
40
Combinations
Fig. 3. Displacement thresholds for Gabor patches of horizontal gratings in the three spatial frequency conditions of expt 2. orientations
+-----.
J t#daxis/ S-axis
Combinations
Fig. 4. Disp~~ment thresholds for Gabor patches of 2.1 c/dcg isoiuminant gratings along color axes corresponding to modulation of only long and middle waveiength sensitive cones (L&f-axis) and to m~ulation of only short wavelength sensitive cones (S-axis). Data for the three color ~mbinations of expt 3 are shown.
In Fig+ 5 results for localization of Gaussian “blobs” are shown. As in the previous experiment, the contrasts of the chromatic and luminance-d~rement blobs was chosen so that the offset thresholds for the color vs color and luminance vs luminance conditions were similar (-48 set arc). Under these conditions the observer was able to detect offsets between a color and a luminance pattern with the same accuracy that was found for the other two conditions.
1631
Spatial localization across channels DISCUSSION
The main conclusion of this study is that vernier alignment is virtually as good when the same types of striate cortex cells are involved in detecting the two patterns to be compared as when different cell types are involved in the two areas. This is not what one would expect if the predominant comparisons in a localization task were between cells tuned to the same orientation and spatial frequency, or among those of the same color type. While there are a few striate cells that are so broadly tuned in orientation or spatial frequency that they will respond to both of the components used in our various “crossed” conditions (i.e. horizontal and vertical gratings or gratings differing threefold in spatial frequency), these are a small minority compared to those which would be activated by gratings of the same orientation or spatial frequency. Correspondingly, some striate cells might respond both to chromatic gratings modulated along the LM-axis and those on the S-axis, but they again constitute a small subset of the population. One might also argue that vernier judgments tapped information at the geniculate rather than striate level. In that case, while one might expect no orientational effects, the crossed-color effects should be strong since parvocellular geniculate neurons are strongly segregated into red-green and blue-yellow classes (De Valois, Abramov & Jacobs, 1966; Derrington, Krauskopf & Lennie, 1984). Toet (1987) reported a somewhat similar finding, namely that vernier acuity is very similar with Gaussian blobs when both blobs are increments (or decrements) as when one is an increment and the other a decrement. Such incremental and decremental patterns would be expected to activate different cell types in the geniculostriate projection. However, most if not all complex (as opposed to simple) cortical cells in Vl respond equally well to increments and decrements in the same location. Thus this experiment would not, as ours was intended to do, activate entirely different types of cells in the two regions being compared. It is also of interest that our ability to localize a patch is largely independent of the particular stimulus parameters used, at least in the case of those we studied. One can localize two patches of low spatial frequency about as well as two high-frequency patches (as also reported by Toet & Koenderink, 1988), and two patches with horizontal gratings almost as readily as vertical ones. It thus appears that the visual
system extracts location information from a given region regardless of cell type, and compares that with the location information from the other area, again regardless of its source, to determine the relative location of the two patches. REFERENCES Burbeck, C. A. (1987). Position and spatial frequency in large-scale localization judgments. Vision Research, 27, 417427. Burbeck, C. A. (1988). Large-scale relative localization across spatial frequency channels. Vision Research, 28, 857-859. Derrington, A. M., Krauskopf, J. & Lennie, P. (1984). Chromatic mechanisms in lateral geniculate nucleus of macaque. Journal of Physiology, London, 357, 241-265. De Valois, R. L. & De Valois, K. K. (1988). Spatial vision. New York: Oxford University Press. De Valois, R. L. and De Valois K. K. (1991) Vernier acuity with stationary moving Gabors. Vision Research, 31, 1627-1631.
De Valois, R. L., Abramov, I. & Jacobs, G. H. (1966). Analysis of response patterns of LGN cells. Journal of the Optical Society of America, 56, 966-977.
De Valois, R. L., Albrecht, D. G. & Thorell, L. G. (1982). Spatial frequency selectivity of cells in the monkey visual system. Vision Research, 22. 545-559. Essock, E. A., Williams, R. A., Enoch, J. M. & Raphael, S. (1984). The effects of image degradation by cataract on vernier acuity. Investigative Ophthalmology and Visual Science, 25, 1043-1050. Finney, D. J. (1971). Probit analysis. Cambridge: Cambridge University Press. Hess, R. F. & Holliday, I. E. (1990). Spatial localization of Gabor patches; the effect of contrast, spatial frequency, and size. Investigative Ophthalmology and Visual Science, 31, 326.
Kooi, F. L., De Valois, R. L. & Switkes, E. (1987). Vernier acuity with Gabor patches. Investigative Ophthalmology and Visual Science, 28, 360.
Krauskopf, J., Williams D. R. & Heeley, D. W. (1982). Cardinal directions of color space. Vision Research, 22, 1123-1131.
Lennie, P., Krauskopf, J. ik Sclar, G. (1990). Chromatic mechanisms in striate cortex of macaque. Journal of Neuroscience,
10, 649669.
Switkes, E., Bradley, A. &De Valois, K. K. (1980). Contrast dependence and mechanisms of masking interactions among chromatic and luminance gratings. Journal of the Optical Society of America, AS, 1149-l 162. Toet, A. (1987). Visual perception of spatial order. Doctoral dissertation, University of Utrecht. Toet, A. & Koenderink, J. J. (1988). Differential spatial displacement discrimination thresholds for gabor patches, Vision Research, 28, 133-143. Tootell, R. B. H., Silverman, M. S., Switkes, E. &De Valois, R. L. (1982). Deoxyglucose analysis of retinotopic organization in primate striate cortex. Science, 218, 902-904. Westheimer, G. & McKee, S. P. (1977). Spatial contigurations for visual hyperacuity. Vision Research, 17.941-947. Williams, R. A., Enoch, J. M. & Essock, E. A. (1984). The resistance of selected hyperacuity configurations to retinal image degradation. Inuesfigoriue Ophrhafmoiogy and Visual Science, 25, 389-399.
Vision Res. Vol. 31, No. 9, pp. 16274631, 1991 Printed in Great Britain. Ail rights mewed
SPATIAL LOCALIZATION FRANK
L. KooI,‘*
ACROSS CHANNELS
RUSELL L. DE VALOIS’and EUGENE SWITKFZ?
‘Physiological Optics Group and Department of Psychology, University of California, Berkeley, CA 94720 and 2Departments of Psychobiology and Chemistry, University of California, Santa Crux, CA 95064, U.S.A. (Received 14 August 1990; in revised form I8 December 1990) Abstract-We have studied vernier acuity for patterns in which the stimuli to be aligned either are similar in their spatial and color characteristics or differ in these properties. The question which we address is whether spatial localization is independent of the channels being stimulated by the patterns to be aligned. We found that the precision of vernier alignment of Gabor patches was very similar irrespective of whether the patches were the same or different in spatial frequency, orientation, or color. it appears that the visual system extracts very precise location information independent of the similarity or dissimilarity of the spatiochromatic selectivity of the channels carrying that information. Spatial vision
Color vision
Localization
Vernier acuity
YNTRODUCI’ION
There is now very extensive psychophysical and physiological evidence for the presence of multiple two-dimensional spatial frequency channels in the early processing of visual information (see De Valois & De Valois, 1988; for summary and discussion). Although bandwidths vary widely across cells in the striate cortex (Vl), the vast majority of units are sufficiently narrowly tuned in o~entation and spatial frequency that they would not respond significantly to both of two gratings separated by 90 deg in orientation or by 2 octaves in spatial frequency (De Valois, Albrecht 8c Thorell, 1982). The evidence at the striate level is not as clear as to the extent of the separation into different channels of information along different axes in three dimensional (3D) color space (Lennie, Krauskopf & Sclar, 1990), but it is certainly clear that relatively few cells respond both to luminance variations and to all color variations. . In addition to their 2D spatial frequency and their color tuning, striate units convey information about spatial location, since they have spatially-localized receptive fields, and the retinotopic mapping onto the striate cortex is quite precise (Tootell, Silverman, Switkes & De Valois, 1982). Within any given small region of striate cortex, then, are a group
*Presentaddress: TN0 Institute for Perception, Kampweg 5, 3769 DE Soesterberg,The Netherlands.
Feature channels
of cells each tuned to a different 2D spatial frequency region, but all with their receptive fields centered on the same location in visual space. The question we are raising, and attempting to answer in this experiment, is the extent to which the visual system can extract, and compare across regions, locution information quite independent of the spatial frequency or the color channel carrying that info~ation. Specifically, we examine the extent to which one can precisely judge the vertical alignment of two patterns in a vernier acuity task when the two patterns activate Vl cells of different channel types in the two regions. It has been previously shown by Westheimer and McKee (1977) that observers do very well with the vernier alignment of two or more patterns which are very different from each other, such as chevrons and lines. However, the patterns they used all had quite broad spatial frequency spectra and each would thus activate virtually all striate cells in a region, although of course in different proportions. In this experiment we examine this question using patterns chosen to activate largely nonoverlapping populations of Vl cell types in the two regions being compared. A preliminary account of this research was reported earlier (Kooi, De Valois & Switkes, 1987). Aspects of this problem have also been addressed by Burbeck (1987, 1988), Toet and Koenderink (1988), and Hess and Holliday (1990).
1627
1628
FRANKL. KOOIet al. METHODS
Stimuli were generated on Tektronix color monitors controlled by a Lexidata graphics unit and a NOVA 4 x computer (see Switkes, Bradley & De Vaiois, I988 for a more complete description). The stimuli were two circular Gabar patches placed one above the other with the patterns inside the patches (gratings or “blobs”) specific to the various experiments. On each triai the upper patch was presented slightly to the left or right of the lower one and the observer pressed one of two buttons to indicate their judgment of the offset of the upper patch. The displays were viewed through a mask around which a square was drawn. This square, as well as the vex&al and horizontal orientations of the gratings, helped the observers establish a vertical reference. Pairs having various relative displacements were precomputed and stored in graphics memory. This allowed for pre~nta~on of sub-pixel relative displacement of the two patches. Details af stimulus configuration and methodology differed for the various experiments.
In this experiment we employed a Tektronix 650 monitor viewed at a distance of 330 cm through a rectangular mask of 3.9 x 2.8 deg. The Gabor patches consisted of 6 c/deg cosine or sine wave gratings with Gaussian envelopes of standard deviation of 0.0833 deg (one-half of a period) in both the x and y directions. The centers of the two patches were separated vertically by 25 min arc. The position of the pair within the viewing aperture was randomized from trial to trial. The presentations were preceded by a warning buzzer and two stimulus duration conditions were used: 1OOmsec or continuous presentation until the observer responded” The primary purpose of this experiment was to compare vernier acuity for displa~ment of stimuli with similar o~entations to that for stimuii differing in orientation. Hence three conditions were employed where the orientations of the gratings were either both vertical, both horizontal, or vertical (upper) and horizontal flower). High contrasts (90%) were used and the chromatic&y of these luminance varying gratings was set to be the white defined by CIE coordinates (0,310, 0.316) of illuminant C, The method af constant stimuli employing four horizontal displacements of various sizes to either side of vertical and the aligned pattern
were used in a given run. Each pair was presented 10 times in a randomized order giving 90 presentations per run. For each observer and pattern combination, the sizes of the displacements were chosen to span the range from 100% correct performance to chance. Thresholds were calculated using probit analysis (Finney, 197 1) as in the accompanying paper (De Valois & De Valois, 1991). One of the authors (FIX) and a naive subject served as observers. Experiment
2. Spatial frequency
In this experiment the observers viewed a Tektronix 690 monitor at a distance of 172cm through a circular mask of 5.1 deg. The two Gabor patches were vertically separated by 75 min arc. In order to compare vernier acuity for targets with similar or differing spatial frequencies, test patches of 6 and 2.1 cfdeg were used, Again the Gaussian envelopes were set to have one-half period standard devia~ons (0.0833 and 0.238 deg) yielding a corresponding number of cycles, but differing extent, for the Gabor patches at the two frequencies. In the three conditions pairs of Gabor patches with both high, both low, or low (upper patch) and high (lower patch) spatial frequency were presented. All gratings were horizontally oriented, cosine phase, and luminance modulated with 90% contrast at the chromaticity of illuminant C. In this experiment the stimuli were presented using a 2AFC staircase technique [Essock, Williams, Enoch & Raphael, 1984). Eleven relative displacements, varying in 4 sac arc steps, were available. Two consecutive correct responses resulted in presentation of a smaller offset pair while one incorrect response increased the offset by one level. Threshold was calculated as the mean of 6 reversals. Each data point is based on a minimum of 12 trials. Experiment
3. Color us color
Viewing conditions and data analysis were simiiar to those in expt 2. Gabor patches contained 2.1 c/deg horizontal gratings. The gratings were isoluminant and varied in color along one of two chromatic axes: an LM-axis (constant-S) where the grating’s color modulation yielded modulation of L- and M-cone activity (but not S-cone) or an S-axis (tritan) where the grating modulated S-cone (but not L- or M-cone) activity (Krauskopf, Williams & Heeley, 1982). Far each of the two types of gratings the means chromaticity was that of illuminant C. The relative chromatic contrast
1629
Spatial localization across channels
for gratings along each of these axis was adjusted to yield similar vernier acuities for the cases when both Gabor patches were gratings along the LM- or along the Saxis. Isoluminance was determined by flicker photometry.
The viewing conditions and analysis procedures were similar to those of expt 2. In expt 4 the test patches were Gaussian modulations of the mean luminance or mean chromaticity with standard deviation 0.238 deg (i.e. Gabor patterns in the zero spatial frequency limit or “blobs”). The luminance patches were decrements from the mean luminance and the color patches correspond to an isoluminant chromaticity variation from illuminant C towards a red along the LMaxis (increasing L-cone decreasing M-cone, and constant S-cone activity). Three conditions were tested: both patches luminance, both patches color, and upper patch color lower patch luminance. The relative amplitudes of the luminance and chromaticity variations were chosen to yield equal offset acuity in the luminance vs luminance and color vs color conditions.
-..-...-
__-__-I--
~ ,5(I
-25
0
25
Offset (set arc} Fig. I. Psychometricfunctionsfor the judgmentof position
of upper Gabor patch relative to lower patch. Data for unlimitedviewing time and the four combinations of grating orientation and phase used in expt 1 are shown. Negative offsets indicate upper Gabor patch was physically to the left of the lower. vit 3IB-K
~
I-
401
A TH 100 msec
0 SL unlimited
0 FK 100 msec
0 FK unlimited
0,
J
Her/ Hor
Z?/
3
Orientation
Her/ sine Hor ( phase>
Combinations
I
Fig, 2. Dispiacement thresholds for Gabor patches of 6 c/deg, 0.5 see sinusoidal gratin@ in the four orientation and phase combinations.
RESULTS
Experiment 1. Orientation Data and results from the experiments testing the effects of relative o~en~tion are presented in Figs 1 and 2. Figure 1 shows typical psychometric functions for four stimulus conditions employed for runs where the observers had unlimited viewing time before they made a response. Displacement thresholds obtained by probit analysis (one-half the difference between offsets required for 75% correct judgments of leftward and rightward displa~ments) are plotted in Fig. 2. From these plots several points are ciear. The l&l2 set arc thresholds (lower curves, Fig. 2) illustrate that, given sufficient viewing time and stimulus contrast, observers can localize the relative position of the envelopes of Gabor patches with an accuracy similar to that of other hyperacuity tasks (Williams, Enoch & Essock, 1984). The similarity of the psychometric functions (Fig. 1) and the displacement thresholds (Fig. 2) for the four stimulus configurations indicates that: (i) thresholds are the same or only slightly higher for Gabor gratings oriented along the direction of displacement (horizontal vs horizontal) compared to those perpendicular (vertical vs vertical) to it; (ii) thresholds are independent of the placement of the grating within the Guassian envelope (cosine vs sine phase), and most si~ifi~ntly
;
(iii) the ability of the visual system to extract information about relative position is not diminished when comparing stimuli which activate m~hanisms selective for differing
1630
FRANKL. Kocn et al.
” :
60-
z u c, 5 ?-
50
+ Spatial
Frequency
Combinations
(c/deg)
relative to the comparison uli having similar o~entations.
of stim-
Experiment 2. Spatialfrequency Figure 3 indicates displa~ment threshold for the three spatial frequency conditions used in this experiment. As observed by Toet and K~nderink (1988) utilizing an alig~ent paradigm, the threshold does not depend on the spatial frequency of the Gabor patch. In a somewhat different task, Burbeck (1987) also showed that large-scale localization was independent of the spatial frequencies of the two targets. In expt 2 absolute vernier thresholds are somewhat greater than in our orientation studies while significantly lower than those measured by Toet and Koenderink (1988). The former arises from the greater inter-Gabor separation employed in expt 2, while the latter is a consequence of the much greater grating contrast in our experiments (90°/ contrast) relative
0
,
I
LM-axis/ LM-axis.
S-axis/ S-axis.
Color
30:
Color/Color
Color/Lum
Fig. 5. Displacement thresholds for color (isoluminant) and luminance decrement Gabor ‘*blobs”. The color variation was along an I&f-axis, from white at the edge of the patch towards red at the center. Data for the three conditions of expt 4 are shown.
to that used by Toet and Koenderink {near threshold contrast). The finding most relevant to our study is that offset thresholds for the case in which the Gabor patches would activate mechanisms tuned to distinct spatial frequencies (2.1 vs 6 c/deg) are no worse than those where the localization task involves mechanisms of the same spatial frequency (2.1 vs 2.1 or 6 vs 6 c/deg). A similar obse~~tion regarding an observer’s ability to detect differences in separation between targets differing in spatial frequency content has been reported by Burbeck (1988). Experiment 3. Color Figure 4 compares displacement detection performance for 2.1 c/deg Gabor patches of various colors. The contrasts of the gratings along the LX and S axes were chosen to give nearly the same offset thresholds (-82 set arc) for the LM vs LM and S vs S cases. However with this contrast specification, the observers’ ability to detect an offset in the LM- vs S-axis case was no worse than in the other two cases even though the two targets were detected by distinct cone mechanisms. Experiment 4. Color OSluminance
TH
@ FK
t-mJ
!
40
Combinations
Fig. 3. Displacement thresholds for Gabor patches of horizontal gratings in the three spatial frequency conditions of expt 2. orientations
+-----.
J t#daxis/ S-axis
Combinations
Fig. 4. Disp~~ment thresholds for Gabor patches of 2.1 c/dcg isoiuminant gratings along color axes corresponding to modulation of only long and middle waveiength sensitive cones (L&f-axis) and to m~ulation of only short wavelength sensitive cones (S-axis). Data for the three color ~mbinations of expt 3 are shown.
In Fig+ 5 results for localization of Gaussian “blobs” are shown. As in the previous experiment, the contrasts of the chromatic and luminance-d~rement blobs was chosen so that the offset thresholds for the color vs color and luminance vs luminance conditions were similar (-48 set arc). Under these conditions the observer was able to detect offsets between a color and a luminance pattern with the same accuracy that was found for the other two conditions.
1631
Spatial localization across channels DISCUSSION
The main conclusion of this study is that vernier alignment is virtually as good when the same types of striate cortex cells are involved in detecting the two patterns to be compared as when different cell types are involved in the two areas. This is not what one would expect if the predominant comparisons in a localization task were between cells tuned to the same orientation and spatial frequency, or among those of the same color type. While there are a few striate cells that are so broadly tuned in orientation or spatial frequency that they will respond to both of the components used in our various “crossed” conditions (i.e. horizontal and vertical gratings or gratings differing threefold in spatial frequency), these are a small minority compared to those which would be activated by gratings of the same orientation or spatial frequency. Correspondingly, some striate cells might respond both to chromatic gratings modulated along the LM-axis and those on the S-axis, but they again constitute a small subset of the population. One might also argue that vernier judgments tapped information at the geniculate rather than striate level. In that case, while one might expect no orientational effects, the crossed-color effects should be strong since parvocellular geniculate neurons are strongly segregated into red-green and blue-yellow classes (De Valois, Abramov & Jacobs, 1966; Derrington, Krauskopf & Lennie, 1984). Toet (1987) reported a somewhat similar finding, namely that vernier acuity is very similar with Gaussian blobs when both blobs are increments (or decrements) as when one is an increment and the other a decrement. Such incremental and decremental patterns would be expected to activate different cell types in the geniculostriate projection. However, most if not all complex (as opposed to simple) cortical cells in Vl respond equally well to increments and decrements in the same location. Thus this experiment would not, as ours was intended to do, activate entirely different types of cells in the two regions being compared. It is also of interest that our ability to localize a patch is largely independent of the particular stimulus parameters used, at least in the case of those we studied. One can localize two patches of low spatial frequency about as well as two high-frequency patches (as also reported by Toet & Koenderink, 1988), and two patches with horizontal gratings almost as readily as vertical ones. It thus appears that the visual
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