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Pulse and steady-pedestal contrast discrimination: effect of spatial parameters
Vision Research 41 (2001) 2079– 2088 www.elsevier.com/locate/visres
Pulse and steady-pedestal contrast discrimination: effect of spatial parameters Vivianne C. Smith *, Vincent C.W. Sun, Joel Pokorny Visual Sciences Center, The Uni6ersity of Chicago, 940 East 57th Street, Chicago, IL 60637, USA Received 25 September 2000; received in revised form 21 February 2001
Abstract The goal of this study was to establish the spatial summation properties associated with inferred PC- and MC-pathway mediated psychophysical contrast discrimination. Previous work has established two paradigms that reveal characteristic signatures of these pathways. In the pulse paradigm, a four-square array was pulsed briefly, on a constant background. In the steady-pedestal paradigm, the stimulus array was presented continuously as a steady-pedestal within a constant surround. In both paradigms, one square differed from the others, giving the observer a forced choice spatial discrimination task. Area summation functions derived for the pulse paradigm decreased with area, with a slope of − 0.25 on a log– log axis. Area summation functions derived for the steady-pedestal paradigm decreased as a power function of area, approaching an asymptote above one square degree. The latter are consistent with the classical data of threshold spatial summation. © 2001 Elsevier Science Ltd. All rights reserved. Keywords: Contrast discrimination; Magnocellular; Parvocellular; Spatial summation
1. Introduction Pokorny and Smith (1997) introduced two paradigms that were interpreted to represent contrast discrimination mediated by two different retinal pathways. The spatial display was simple, a four-square stimulus array in a larger constant luminance surround as shown in Fig. 1. One paradigm, the pulse paradigm presented a steady, spatially homogeneous background, the trial consisted of a brief presentation of the four-square array at a fixed supra-threshold contrast increment or decrement replacing the background. The four-square stimulus array appeared only during the trial period, with the test square at a higher or a lower retinal illuminance than the other three (upper row of Fig. 1). The second paradigm, the steady-pedestal condition presented the four-square stimulus array continuously as a fixed increment or decrement in the larger constant luminance surround. In this paradigm, only the retinal illuminance of the test square changed during the trial period (lower row of Fig. 1). The trial presentation was * Corresponding author. Fax: + 1-773-702442. E-mail address: [email protected] (V.C. Smith).
identical for both paradigms; all that differed was the inter-trial array and adaptation. The pulse paradigm yielded shallow V-shapes where threshold depended on the contrast between pulse and background. The steady-pedestal paradigm showed monotonic variation of threshold with pedestal luminance, independent of the fixed surround luminance (sample data shown on right of Fig. 1). Temporal summation properties differed for the two paradigms, the steady-pedestal paradigm showed summation with an asymptote above 40 ms while the pulse paradigm showed summation beyond 200 ms. Pokorny and Smith (1997) interpreted the data as indicative of multiple pathway function consistent with parvocellular (PC-) pathway mediation of contrast discrimination thresholds measured in the pulse paradigm with large contrast steps, and magnocellular (MC-) pathway mediation of contrast discrimination thresholds measured in the steady-pedestal paradigm. A third paradigm (the pedestal-D-pedestal paradigm) established a very steep V-shape for small contrast excursions from the pedestal adaptation. The slopes of the V-shapes were consistent with the contrast gain functions measured in primate retinal ganglion (Lee, Pokorny, Smith, Martin, & Valberg, 1990) and
0042-6989/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved. PII: S0042-6989(01)00085-2
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lateral geniculate nucleus (Kaplan & Shapley, 1986) cells. Contrast detection from a uniform (zero contrast) background depended on the temporal parameters; a brief square-wave pulse favored the MC-pathway while a long, slowly ramped pulse favored the PC-pathway. Other researchers have emphasized the importance of parallel pathways in vision (e.g. Ingling, 1978). Increment thresholds for mid- and long-wavelength test lights on a steady white background yield differing spectral sensitivities depending on the spatio-temporal parameters of the test (King-Smith & Carden, 1976). With large, long duration test lights, a bi-lobed function representing the spectral properties of the PC-pathway is observed. With small, brief test lights, a single peaked ‘luminosity’ function representing the non-spectral properties of MC-pathway is observed. Equiluminant chromatic stimuli have been used to access the PC-pathway by many researchers (Nissen, Pokorny, & Smith, 1979; Krauskopf, Williams, & Heeley, 1982; Smith, Bowen, & Pokorny, 1984; Zaidi, Shapiro, & Hood, 1992). The pulse and steady-pedestal paradigms allowed measurement of equiluminant chromatic contrast discrimination (Smith, Pokorny, & Sun, 2000). Chromatic contrast discrimination for both paradigms showed similar V-shaped function. The V-shape was characteristic of PC-pathway function, even with steady adaptation to the pedestal. The chromaticity of the surround determined the position of the least threshold. The data suggested that the pedestal contrast determined the pathway (ON or OFF) while the increment and decrement discrimination steps were within a path-
way, i.e. a red pedestal in a white surround would stimulate an (+ L− M) or ( − M+ L) pathway while a green pedestal on the white surround would stimulate a (+ M− L) or ( − L+ M). The slopes of the chromatic V-shapes were steeper than for achromatic stimuli while the absolute sensitivity was higher, consistent with the physiological data showing steeper contrast response functions for chromatic as compared to achromatic stimuli in the PC-pathway (Lee et al., 1990). Surround widths as small as 7% were sufficient to yield the surround chromaticity-dependent V-shape. These data were interpreted to indicate that contrast signals generated at the test-surround border by cells adapted to the surround determine chromatic contrast discrimination. These chromatic data support the interpretation that the V-shaped function obtained for achromatic contrast discrimination using the pulse paradigm is mediated by the PC-pathway. Parallel pathways have also been distinguished by their spatio-temporal properties (Ingling & Drum, 1973; Tolhurst, 1975). Spatial frequency channels measured with achromatic stimuli (Bodis-Wollner & Hendley, 1979; Wilson & Bergen, 1979; Wilson, McFarlane, & Phillips, 1983) may be differentiated by their temporal response. A systematic study of the effect of temporal duration on spatial frequency channels (Legge, 1978) found broadband transient mechanisms and multiple narrowband sustained mechanisms varying in peak spatial frequency. Today we would associate such mechanisms with influences of MC- and PC-pathway activity.
Fig. 1. Stimulus configuration and sample data for the pulse (upper row) and steady-pedestal (lower row) paradigms. The drawing at left shows the adaptation field; the drawing at center shows the stimulus presentation. The graph at right shows data from Pokorny and Smith (1997).
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Our approach is unique because we attempt to differentiate the pathways by their contrast responsivity. One previous study (Chen, Bedell, & Frishman, 1996) emphasized the contrast variable but they varied the temporal frequency of their test stimulus to distinguish the pathways. In our approach, the test stimulus was identical; only the pre- and post-adaptation displays differed. Our goal in this research was to evaluate spatial summation using the pulse and steady-pedestal paradigms. In a single linear channel, spatial summation and spatial frequency resolution should be linked. Narrowband spatial frequency channels should show minimal spatial summation. When multiple channels are present, we can expect a dissociation between spatial frequency processing and spatial summation. Chromatic discrimination is known to improve with increase in field size over the central 10° of the retina (Brown, 1952; Wyszecki & Stiles, 1982; Yebra, Garcia, & Romero, 1994). This is a much larger area than the classical area-summation function measured foveally (Graham & Bartlett, 1939; Graham, Brown, & Mote, 1939; Davila & Geisler, 1991). The classical data are consistent with summation only by physical light spread or probability summation in the central 1° of the fovea (Davila & Geisler, 1991). We investigated the effect of manipulating spatial parameters on the pulse and steady-pedestal paradigms, using stimulus arrays varying from 0.32° to 7.87°. We maintained the simple center-surround display, while investigating the spatial summation properties of the two pathways by varying the size of the test array. We used a brief 26.67 ms square pulse so that thresholds measured at the surround luminance (zero contrast) would likely to be determined by the MC-pathway (Pokorny & Smith, 1997). We found that spatial summation for the steady-pedestal paradigm (presumed MC-pathway) showed an exponential form approaching an asymptote above 1 square degree, as described in the classical spatial summation literature (reviewed in Graham (1965), Baumgardt (1972)). Spatial summation for the pulse paradigm (presumed PC-pathway) showed summation over the entire range of stimulus areas, but with a shallow slope. Additionally, in order to strengthen the association of the achromatic and chromatic pulse paradigms with PC-pathway function, we reduced the surround size to 2.21° and 2.07° using the a 2.07° square array to establish whether achromatic contrast discrimination with the pulse paradigm depended solely on the presence of contrast at the borders of the test array.
2. Methods
2.1. Equipment The stimuli were generated by a Macintosh PowerPC 9500/132 Computer with a 10-bit Radius Thunder 30/
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1600 video card and were displayed on a 17 in. Radius PressView 17SR color monitor. The display resolution was set at 832×624 and the refresh rate was 75 Hz. The spectral power distributions of the phosphors were measured with an Optronics OL754 spectroradiometer with the detector flush to the screen and illumination of the central 75% of the screen. Phosphor luminance was measured in a similar manner for 1024 levels of input integer value, and a look-up table was constructed to represent relations between voltage integer value and phosphor luminance. The luminance output of the monitor was calibrated by a Minolta LS-100 luminance meter. Screen uniformity was checked at the maximum output. Consistent with the physics of the emitters, there was a roll-off in luminance at the edges of the screen. The central 75% of the screen was used, allowing an error of less than 4%. All stimuli were metameric to the equal energy spectrum. The temporal presentation was a square pulse of 26.7 ms duration (two screen refreshes at a 75 Hz monitor refresh rate). The monitor screen was viewed binocularly at 1 m. The observer sat in a comfortable chair holding the mouse pad and mouse in his/her lap. No head stabilization was used. The screen luminance for adaptation was 12 cd/m2 (approximately 115 trolands (td)) and was constant throughout the experiment. Test stimuli were presented at a series of positive and negative contrasts between 73 and 182 td.
2.1.1. Spatial configuration The maximum display size was an 8°× 8° square, centered on the screen. In the main experiment, we used an 8° surround. The test array consisted of four smaller squares separated by gaps of 0.07°. The height and width of the four-square array was varied between 0.32° and 7.87°. In a subsidiary experiment we reduced the surround to 2.21° and to 2.07°, using the 2.07° four-square array. A central (4.36% ×4.36%) fixation dot provided a fixation target for larger test arrays. For the two smallest test arrays of 0.32° and 0.57°, four fixation dots at 1° on the vertical and horizontal axes provided a fixation target. 2.2. Procedure The pulse and steady-pedestal paradigms were investigated in separate runs. The paradigms differed only in the initial pre-adaptation; all other procedural details were identical. The observer was instructed that one square might appear brighter or darker than the other three and the task was to identify the ‘odd’ square. The observer first adapted for 2 min to a uniform 115 td display that included the fixation target. For the steadypedestal paradigm, there was a further 1 min of adaptation to the four-square array. At the start of a trial, the fixation target disappeared. Each trial presented three
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was reached. The criterion was set in pilot studies to produce an efficient staircase, requiring about 60–70 trials. Once the criterion step size was reached, the staircases continued without further change in step size using a reversal rule. Two successive incorrect identifications led to an increase in test contrast on the following trial; three correct identifications lead to a decrease in test contrast. Eight to ten reversals at the criterion step size were measured for both the increment and the decrement staircases. We calculated the equivalent percent correct on a psychometric function at 0.57 (see Acknowledgements). The average contrast at which the last six reversals occurred was taken as the estimate of the threshold contrast. A 30-min paradigm allowed measurement of increment and decrement thresholds at four or five starting pedestal retinal illuminances. Thus, two sessions were required to obtain full data for one four-square array size for either the pulse or the steadypedestal paradigm. The entire session was repeated and reported data are the average of three increment and three decrement thresholds for each array size and paradigm.
2.3. Obser6ers
Fig. 2. Contrast discrimination thresholds obtained for stimulus arrays between 0.32° and 7.87°, data of observer HK. The surround retinal illuminance was 115 td, shown by an arrow on the abscissa. (A) pulse paradigm. (B) steady-pedestal paradigm.
of the squares at a common retinal illuminance and the test square, selected randomly with equal probability, at a different retinal illuminance. At the trial conclusion, the fixation target reappeared together with a cursor. The observer used the mouse to place the cursor in the stimulus position judged different. A mouse click at this position stored the result and reset the display for the next trial. No feedback was given. Trials followed a double random-alternating staircase. The pedestal retinal illuminance was fixed for each pair of staircases. In one staircase the test square threshold was measured in an increment direction, in the other in a decrement direction. Pilot data established that there were no systematic differences between increment and decrement threshold absolute contrast. At the start of a staircase, an easily discriminable test contrast was present and on succeeding trials the step size was halved until a criterion step of 0.025 log unit
The three observers (HK, female aged 23, CS, male aged 30, and IY, female aged 24) were all normal trichromats as assessed with the Ishihara pseudoisochromatic plates and the Neitz OT anomaloscope. Farnsworth 100-hue error scores were 12 for HK, 4 for CS, and 8 for IY. CS was author Vincent C. Sun. HK and IY were paid observers, and were naive as to the purpose and design of the experiment.
3. Results
3.1. Contrast functions Figs. 2–4 show results for the three observers plotted as log (DI) versus I where DI is the contrast threshold re-expressed in trolands (IDCthr), and I is the fixed surround illuminance (115 td). The upper panel shows data for the pulse paradigm and the lower panel shows data for the steady-pedestal paradigm. The different array sizes are shown by different symbols. The solid symbols are for the 2.07° array and represent the condition most similar to that of Pokorny and Smith (1997). The data for this condition agree well with those of that study. In the pulse paradigm, thresholds were lowest (highest sensitivity) at the surround luminance (shown by an arrow on the graphs). Thresholds rose as the pulse luminance decreased or increased, forming two arms of a V-shaped function. The arms of the V-shaped function did not vary in shape with stimulus
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size. In the steady-pedestal paradigm, threshold rose monotonically as a function of pedestal luminance. The data sets for the different array sizes were displaced but parallel. For both paradigms, the thresholds decreased as stimulus array size increased. The change in sensitivity was more pronounced for the steady-pedestal than the pulse paradigm. In Pokorny and Smith (1997), the data for the pulse paradigm were described by adapting the characteristic saturation function of the PC-pathway (Kaplan & Shapley, 1986). For a single cell the contrast saturation function is constrained by two parameters, Rmax and Csat; the predicted contrast discrimination, DC, includes a third parameter, the criterion firing rate, l. Since psychophysical data may include the effects of higher order summation, Pokorny and Smith allowed a free vertical scaling parameter. Also, the psychophysics does not have independent access to the cell properties Rmax
Fig. 4. Contrast discrimination thresholds obtained for stimulus arrays between 0.32° and 7.87°, data of observer IY. Other details are as in Fig. 2.
and l. We can abstract only two pieces of information from the data, the slope of the V-shape and the sensitivity at the minimum. Here we present an equation adapted for psychophysics expressed only in Csat, criterion and overall scaling (c.f. Snippe, 1998): logDI = log[(Csat + C )2/{Csat − (KC)(Csat + C )}] + log(KPIS)
Fig. 3. Contrast discrimination thresholds obtained for stimulus arrays between 0.32° and 7.87°, data of observer CS. Other details are as in Fig. 2.
(1)
where C represents the absolute value of the pulse Weber contrast (DI/IS), Csat represents the saturating contrast, KC represents the criterion increment firing rate (comparable to l/Rmax of a single cell) and KP represents the overall scaling constant. The overall scaling constant, KP incorporates threshold sensitivity for the presumed PC-pathway mediated thresholds that may depend on the test square area. The solid lines represent fits of Eq. (1) for the pulse paradigm. The threshold at the surround luminance was omitted from
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the fits. Fits were made for each observer, considering all six array sizes simultaneously. The variable KP was optimized for each array size but the variables Csat and KC were fixed across array size. According to the interpretation of Pokorny and Smith for the pulse paradigm, the thresholds on the arms of the V-shapes are determined in the PC-pathway. The slopes should be dependent upon the contrast gain of cells forming the pathway. The values of Csat were 0.41, 0.40, and 0.67 for observers HK, CS, and IY, respectively, consistent with data measured for primate LGN (Kaplan & Shapley, 1986) and retinal ganglion cells (Lee et al., 1990). For the steady-pedestal paradigm, the data were described by a line of unit slope with a variable scaling factor:
Fig. 5. Contrast discrimination thresholds obtained for the pulse paradigm for surrounds of 2.21° and 2.07° with a foursquare array of 2.07°. The data for the 8° surround are replotted for comparison. The surround retinal illuminance of 115 td is shown by an arrow. (A) Data of observer CS. (B) Data of observer IY.
log DI =log(I)+ log(KMIS)
(2)
where KM represents the vertical scaling parameter for the presumed MC-pathway mediated thresholds. For the steady-pedestal paradigm, the single parameter fit describes the data for the larger array sizes. However, the data for decrement contrasts deviates to higher thresholds for the small array sizes. These decrement data were omitted from the fits shown in the figures. The probable cause of these deviations is spread light (Pokorny & Smith, 1997) that should be greatest for the smallest arrays. Based on the calculations of Shevell and Burroughs (1988), we estimated a threshold increase at 73 td of 0.115 log unit for the 0.32° foursquare array, decreasing to 0.04 log unit for the 2.07° four-square array. Our observers showed a slightly larger effect: 0.19–0.24 log unit for the 0.32° foursquare array decreasing to 0.04–0.07 for the 2.07° four-square array. However the Shevell and Burroughs calculations were for a 2 mm pupil and pupil diameters of our observers (monitored during the course of the experiment) ranged from 5.76 mm to 6.5 mm. Fig. 5 shows data for the pulse paradigm using the 2.07° square array and surround sizes of 2.21° and 2.07°. The 8° surround data are replotted for comparison. The solid lines are fits of Eq. (1) using the optimal values of Csat and KC (Figs. 3 and 4) varying only KP. These conditions were run for comparison with chromatic contrast discrimination. The 2.21° surround provides a 7% border; the 2.07° surround provides only a 7% crosshair separating the four squares. The achromatic data show V-shapes for both surrounds similar in shape to the 8° surround data. For observer CS the 2.21° and 2.07° surround thresholds were slightly less sensitive than the 8° surround data but for observer IY all three data sets overlap. The achromatic data thus show the same phenomenon as the equiluminant chromatic contrast data, consistent with our interpretation that the PC-pathway mediates threshold for the pulse paradigm. We also ran the steady-pedestal paradigm with the small surrounds and, as expected, the data (not shown) differed only slightly in absolute sensitivity.
3.1.1. Area-illuminance functions Area-illuminance functions can be demonstrated by plotting the thresholds as a function of area at a constant Pedestal value. In this analysis we consider only the dimensions of one square of the array since the discrimination task hinged on identification of the one different square. For the pulse paradigm, we calculated the predicted threshold for the condition where the test array was the same illuminance as the surround (pedestal contrast C= 0) from Eq. (1). A similar calculation was made for the steady-pedestal paradigm. Fig. 6 shows the derived values for both paradigms plotted
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as a function of the area of a single square in the four-square array. Data for the three observers are shown in separate panels. Data for the pulse paradigm showed a shallow linear decrease in log threshold with log area. Data for the steady-pedestal paradigm showed a steeper decrease in threshold with log area for small array sizes with an asymptote above one square degree. Early studies of spatial summation, reviewed in Graham (1965) and Baumgardt (1972), phrased the results in terms of Ricco’s law, Piper’s law and Pie´ ron’s law. Above some critical area determined by these laws, threshold is independent of test area. Ricco’s law refers to full summation (AI = K) and occurs for tiny spots less than 10% arc. Piper’s law refers to square root summation (A 0.5I= K); it occurs for diameters greater than 10% and primarily has been reported in the parafovea (Barlow, 1958). At still larger areas, Pie´ ron’s law refers to cube-root summation (A 0.333I= K). The solid lines fit to the steady-pedestal data are derived from a power function similar to that proposed by Graham et al. (1939). This equation was introduced to emphasize the continual decline in slope that is more characteristic of the data than that allowed by combining linear segments of the Ricco, Piper, and Pie´ ron laws. The equation for these fits is: log(DIS)= log(K1)+ K2A K3
(3)
where A is the area of the test square and K1,2,3 are constants. This equation has no interpretation of the constants and they depend on the range of data sampled. The dashed lines fit to the pulse paradigm data are linear fits on the log/log axes given by Eq. (4): log(DIS)= k1log(A +k2)
(4)
where k1 is the slope and k2 is a scaling constant. The best-fitting slopes were − 0.21, −0.14 and − 0.23 for observers HK, CS and IY, respectively.
4. Discussion
Fig. 6. Threshold spatial summation functions for the pulse (squares) and steady-pedestal (circles) paradigms. (A) Data of observer HK. (B) Data of observer CS. (C) Data of observer IY. The dashed lines are linear fits to the data on the log – log axis; the solid lines are from power functions fit to the data (see text for further details).
In this paper we have demonstrated different spatial summation properties for the two paradigms. The steady-pedestal paradigm showed a decrease in log threshold with increase in log area, which could be fit with a power function of area. The pulse paradigm showed a gradual linear decrease on the log–log axes. The former result is consistent with classical studies of spatial summation; the latter result is consistent with data of color matching (Brown, 1952; Yebra et al., 1994). The 2.21° and 2.07° surround data for the pulse paradigm showed V-shapes indicating that it is border contrast that is important in achromatic contrast discrimination just as in equiluminant chromatic contrast discrimination. Overall the data support the conclusion that the two paradigms access different processing
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pathways that we associate with the MC- and PC-pathways. It is of note that the classical studies of areal and temporal summation give functions that we would interpret as consistent with MC-pathway activity (Pokorny & Smith, 1997). The pulse and steady-pedestal paradigms were designed to compare contrast gain accessed psychophysically with contrast gain of single cell data in the retina or lateral geniculate nucleus (LGN). The use of a free vertical scaling factor was incorporated to recognize that the psychophysical sensitivity might include contributions such as averaging or summation at higher cortical levels. A similar point can be made in considering the current study. The sizes of retinal receptive fields in the fovea and parafovea are much smaller than our stimuli for both MC- and PC-pathways (Derrington & Lennie, 1984; Croner & Kaplan, 1995; Lee, 1996). PC-pathway cells show a center size of 3% in the central 10° of the retina while MC-pathway cells are approximately twice that size (Croner & Kaplan, 1995). Obviously the area-illuminance summation we observe psychophysically cannot be related to the dimensions of single cell data. Our data thus indicate a difference between the averaging or summation properties of MCpathway and PC-pathways at higher cortical levels.
4.1. MC-pathway We suggest that area-illuminance summation for the MC-pathway involves probability summation across the area of the test field. A modern investigation of area summation at the fovea (Davila & Geisler, 1991) established that Ricco’s law can reflect spatial summation due to the optical point spread function of the eye while Piper’s law could be explained by probability summation. The majority of studies of foveal summation were performed at absolute threshold. To avoid rod intrusion, the test fields under study were chosen to be less than 1° in diameter. Thus there are few data for larger areas. Fig. 7 shows a comparison of our average data with foveal dark-adapted data of Graham and Bartlett (1939) and Sun, Pokorny, Shevell, and Smith (1997). The average data of these studies were adjusted on the vertical axis for best coincidence with our data in the region where stimulus area overlapped among the studies. The solid line is the fit of Eq. (3) to all three data sets. Our data coincide in shape with the dark-adapted data. Asymptotic sensitivity is approached at a diameter between 1° and 1.41°. Thus the steady-pedestal data agree with classical threshold summation data that have been explained by physical light spread and probability summation across area. The result is also consistent with the transient mechanism of Legge (1978) that was broadband with a roll-off above 1.0 cpd.
4.2. PC-pathway
Fig. 7. Comparison of spatial summation for the steady-pedestal paradigm (the average of the three observers is given by the solid circles) with data for dark-adapted thresholds at the fovea. The data of Graham and Bartlett (1939) are the average of two observers, and are represented by erect triangles. The Sun et al. (1997) results are the average of two observers and are represented by inverted triangles. The Graham and Bartlett data were converted to td with an effective pupil diameter of 5 mm (Le Grand, 1968) and scaled by adding 0.19 to the average data. The Sun et al. data were converted to td and scaled by adding 0.084 to the average data. The solid line is from Eq. (4) fit to the data of all three studies. The value of the parameters k1 to k3 are − 0.005, 0.48, and − 0.21, respectively.
We suggest that area-illuminance summation for the PC-pathway involves probability summation along the test-surround border. In our interpretation of chromatic contrast discrimination we suggested that border elements adapted to the surround determined threshold in the chromatic steady-pedestal paradigm (Smith et al., 2000). A similar interpretation can be applied to the pulse paradigm with achromatic stimuli. The spatial summation function may thus represent probability summation along these border elements. The pulse paradigm bears procedural similarities to simultaneous masking. In these studies use of very low contrast masks (pedestals) gives an initial facilitation near the unmasked contrast threshold (zero pedestal) followed by a rise as mask (pedestal) contrasts exceed threshold. Facilitation can be seen for both achromatic (Legge & Foley, 1980; Foley & Legge, 1981; Foley, 1994) and chromatic patterns (Cole & Kronauer, 1990; Gegenfurtner & Kiper, 1992; Chen, Foley, & Brainard, 2000a,b). We did not use low pedestal contrasts and thus did not measure possible facilitation. Further, for the majority of pulse paradigm conditions, we interpret the minimum threshold at the point of the V-shape to be MC-pathway rather than PC-pathway mediated (Fig. 6). The exception is for the 0.32° four-square
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array. The measured thresholds for all three observers fell above the predicted PC-pathway minimum, consistent with the phenomenon of facilitation. Facilitation is considered a higher order phenomenon (Nachmias & Kocher, 1970; Nachmias & Sansbury, 1974; Foley & Legge, 1981; Pelli, 1985; Foley, 1994). The retinallybased contrast saturation model does not predict such facilitation and thus requires further modification to incorporate higher order effects.
Acknowledgements The research was supported by NEI research grants EY00901 and EY07390. We thank Steven K. Shevell and Hugh Wilson for comments on this project and Linda Glennie for technical assistance. Steven K. Shevell thoughtfully provided an estimate of the equivalent proportion correct for our forced choice paradigm and staircase rule. We also thank our observers HK and IY for their patience and time. Publication was supported by Research to Prevent Blindness.
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Foley, J. M., & Legge, G. E. (1981). Contrast detection and nearthreshold discrimination in human vision. Vision Research, 21, 1041 – 1053. Gegenfurtner, K. R., & Kiper, D. C. (1992). Contrast detection in luminance and chromatic noise. Journal of the Optical Society of America A, 9, 1880 – 1888. Graham, C. H. (1965). Vision and 6isual perception. New York: Wiley. Graham, C. H., & Bartlett, N. R. (1939). The relation of size of stimulus and intensity in the human eye: II. Intensity thresholds for red and violet light. Journal of Experimental Psychology, 24, 574 – 587. Graham, C. H., Brown, R. H., & Mote, F. A. (1939). The relation of size of stimulus and intensity in the human eye: I. Intensity thresholds for white light. Journal of Experimental Psychology, 24, 555 – 573. Ingling, C. R. J. (1978). Luminance and opponent color contributions to visual detection and to temporal and spatial integration: comment. Journal of the Optical Society of America, 68, 1143– 1146. Ingling, C. R. J., & Drum, B. A. (1973). Retinal receptive fields: Correlations between psychophysics and electrophysiology. Vision Research, 13, 1151 – 1163. Kaplan, E., & Shapley, R. M. (1986). The primate retina contains two types of ganglion cells, with high and low contrast sensitivity. Proceedings of the National Academy of Sciences USA, 83, 2755– 2757. King-Smith, P. E., & Carden, D. (1976). Luminance and opponentcolor contributions to visual detection and adaptation and to temporal and spatial integration. Journal of the Optical Society of America, 66, 709 – 717. Krauskopf, J., Williams, D. R., & Heeley, D. W. (1982). Cardinal directions of color space. Vision Research, 22, 1123 – 1131. Le Grand, Y. (1968). Light, colour and 6ision (2nd edn). London: Chapman and Hall. Lee, B. B. (1996). Receptive field structure in the primate retina. Vision Research, 36, 631 – 644. Lee, B. B., Pokorny, J., Smith, V. C., Martin, P. R., & Valberg, A. (1990). Luminance and chromatic modulation sensitivity of macaque ganglion cells and human observers. Journal of the Optical Society of America A, 7, 2223 – 2236. Legge, G. (1978). Sustained and transient mechanisms in human vision: temporal and spatial properties. Vision Research, 18, 69 – 81. Legge, G. E., & Foley, J. M. (1980). Contrast masking in human vision. Journal of the Optical Society of America, 70, 1458– 1471. Nachmias, J., & Kocher, E. C. (1970). Visual detection and discrimination of luminance increments. Journal of the Optical Society of America, 60, 382 – 389. Nachmias, J., & Sansbury, R. V. (1974). Grating contrast: discrimination may be better than detection. Vision Research, 14, 1039– 1042. Nissen, M. J., Pokorny, J., & Smith, V. C. (1979). Chromatic information processing. Journal of Experimental Psychology: Human Perception and Performance, 5, 406 – 419. Pelli, D. G. (1985). Uncertainty explains many aspects of visual contrast detection and discrimination. Journal of the Optical Society of America A, 2, 1508 – 1531. Pokorny, J., & Smith, V. C. (1997). Psychophysical signatures associated with magnocellular and parvocellular pathway contrast gain. Journal of the Optical Society of America A, 14, 2477 – 2486. Shevell, S. K., & Burroughs, T. J. (1988). Light spread and scatter from some common adapting stimuli. Vision Research, 28, 605– 609.
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Smith, V. C., Bowen, R. W., & Pokorny, J. (1984). Threshold temporal integration of chromatic stimuli. Vision Research, 24, 653 – 660. Smith, V. C., Pokorny, J., & Sun, H. (2000). Chromatic contrast discrimination: data and prediction for stimuli varying in L and M cone excitation. Color Research and Application, 25, 105 – 115. Snippe, H. P. (1998). Psychophysical signatures associated with magnocellular and parvocellular pathway contrast gain: comment. Journal of the Optical Society of America A, 15, 2440–2442. Sun, H., Pokorny, J., Shevell, S. K., & Smith, V. C. (1997). Studies of foveal absolute threshold detection. In6estigati6e Ophthalmology and Visual Science (Supplement), 38, S1017. Tolhurst, D. J. (1975). Sustained and transient channels in human vision. Vision Research, 15, 1151 –1155.
Wilson, H. R., & Bergen, J. R. (1979). A four mechanism model for threshold spatial vision. Vision Research, 19, 19 – 32. Wilson, H. R., McFarlane, D. K., & Phillips, G. C. (1983). Spatial frequency tuning of orientation selective units estimated by oblique masking. Vision Research, 23, 873 – 882. Wyszecki, G., & Stiles, W. S. (1982). Color science — concepts and methods, quantitati6e data and formulae (2nd edn). New York: Wiley. Yebra, A., Garcia, J. A., & Romero, J. (1994). Color discrimination data for 2-degrees and 8-degrees and normalized ellipses. Journal Of Optics-Nou6elle Re6ue D Optique, 25, 231 – 242. Zaidi, Q., Shapiro, A., & Hood, D. (1992). The effect of adaptation on the differential sensitivity of the S-cone color system. Vision Research, 32, 1297 – 1318.
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Pulse and steady-pedestal contrast discrimination: effect of spatial parameters Vivianne C. Smith *, Vincent C.W. Sun, Joel Pokorny Visual Sciences Center, The Uni6ersity of Chicago, 940 East 57th Street, Chicago, IL 60637, USA Received 25 September 2000; received in revised form 21 February 2001
Abstract The goal of this study was to establish the spatial summation properties associated with inferred PC- and MC-pathway mediated psychophysical contrast discrimination. Previous work has established two paradigms that reveal characteristic signatures of these pathways. In the pulse paradigm, a four-square array was pulsed briefly, on a constant background. In the steady-pedestal paradigm, the stimulus array was presented continuously as a steady-pedestal within a constant surround. In both paradigms, one square differed from the others, giving the observer a forced choice spatial discrimination task. Area summation functions derived for the pulse paradigm decreased with area, with a slope of − 0.25 on a log– log axis. Area summation functions derived for the steady-pedestal paradigm decreased as a power function of area, approaching an asymptote above one square degree. The latter are consistent with the classical data of threshold spatial summation. © 2001 Elsevier Science Ltd. All rights reserved. Keywords: Contrast discrimination; Magnocellular; Parvocellular; Spatial summation
1. Introduction Pokorny and Smith (1997) introduced two paradigms that were interpreted to represent contrast discrimination mediated by two different retinal pathways. The spatial display was simple, a four-square stimulus array in a larger constant luminance surround as shown in Fig. 1. One paradigm, the pulse paradigm presented a steady, spatially homogeneous background, the trial consisted of a brief presentation of the four-square array at a fixed supra-threshold contrast increment or decrement replacing the background. The four-square stimulus array appeared only during the trial period, with the test square at a higher or a lower retinal illuminance than the other three (upper row of Fig. 1). The second paradigm, the steady-pedestal condition presented the four-square stimulus array continuously as a fixed increment or decrement in the larger constant luminance surround. In this paradigm, only the retinal illuminance of the test square changed during the trial period (lower row of Fig. 1). The trial presentation was * Corresponding author. Fax: + 1-773-702442. E-mail address: [email protected] (V.C. Smith).
identical for both paradigms; all that differed was the inter-trial array and adaptation. The pulse paradigm yielded shallow V-shapes where threshold depended on the contrast between pulse and background. The steady-pedestal paradigm showed monotonic variation of threshold with pedestal luminance, independent of the fixed surround luminance (sample data shown on right of Fig. 1). Temporal summation properties differed for the two paradigms, the steady-pedestal paradigm showed summation with an asymptote above 40 ms while the pulse paradigm showed summation beyond 200 ms. Pokorny and Smith (1997) interpreted the data as indicative of multiple pathway function consistent with parvocellular (PC-) pathway mediation of contrast discrimination thresholds measured in the pulse paradigm with large contrast steps, and magnocellular (MC-) pathway mediation of contrast discrimination thresholds measured in the steady-pedestal paradigm. A third paradigm (the pedestal-D-pedestal paradigm) established a very steep V-shape for small contrast excursions from the pedestal adaptation. The slopes of the V-shapes were consistent with the contrast gain functions measured in primate retinal ganglion (Lee, Pokorny, Smith, Martin, & Valberg, 1990) and
0042-6989/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved. PII: S0042-6989(01)00085-2
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lateral geniculate nucleus (Kaplan & Shapley, 1986) cells. Contrast detection from a uniform (zero contrast) background depended on the temporal parameters; a brief square-wave pulse favored the MC-pathway while a long, slowly ramped pulse favored the PC-pathway. Other researchers have emphasized the importance of parallel pathways in vision (e.g. Ingling, 1978). Increment thresholds for mid- and long-wavelength test lights on a steady white background yield differing spectral sensitivities depending on the spatio-temporal parameters of the test (King-Smith & Carden, 1976). With large, long duration test lights, a bi-lobed function representing the spectral properties of the PC-pathway is observed. With small, brief test lights, a single peaked ‘luminosity’ function representing the non-spectral properties of MC-pathway is observed. Equiluminant chromatic stimuli have been used to access the PC-pathway by many researchers (Nissen, Pokorny, & Smith, 1979; Krauskopf, Williams, & Heeley, 1982; Smith, Bowen, & Pokorny, 1984; Zaidi, Shapiro, & Hood, 1992). The pulse and steady-pedestal paradigms allowed measurement of equiluminant chromatic contrast discrimination (Smith, Pokorny, & Sun, 2000). Chromatic contrast discrimination for both paradigms showed similar V-shaped function. The V-shape was characteristic of PC-pathway function, even with steady adaptation to the pedestal. The chromaticity of the surround determined the position of the least threshold. The data suggested that the pedestal contrast determined the pathway (ON or OFF) while the increment and decrement discrimination steps were within a path-
way, i.e. a red pedestal in a white surround would stimulate an (+ L− M) or ( − M+ L) pathway while a green pedestal on the white surround would stimulate a (+ M− L) or ( − L+ M). The slopes of the chromatic V-shapes were steeper than for achromatic stimuli while the absolute sensitivity was higher, consistent with the physiological data showing steeper contrast response functions for chromatic as compared to achromatic stimuli in the PC-pathway (Lee et al., 1990). Surround widths as small as 7% were sufficient to yield the surround chromaticity-dependent V-shape. These data were interpreted to indicate that contrast signals generated at the test-surround border by cells adapted to the surround determine chromatic contrast discrimination. These chromatic data support the interpretation that the V-shaped function obtained for achromatic contrast discrimination using the pulse paradigm is mediated by the PC-pathway. Parallel pathways have also been distinguished by their spatio-temporal properties (Ingling & Drum, 1973; Tolhurst, 1975). Spatial frequency channels measured with achromatic stimuli (Bodis-Wollner & Hendley, 1979; Wilson & Bergen, 1979; Wilson, McFarlane, & Phillips, 1983) may be differentiated by their temporal response. A systematic study of the effect of temporal duration on spatial frequency channels (Legge, 1978) found broadband transient mechanisms and multiple narrowband sustained mechanisms varying in peak spatial frequency. Today we would associate such mechanisms with influences of MC- and PC-pathway activity.
Fig. 1. Stimulus configuration and sample data for the pulse (upper row) and steady-pedestal (lower row) paradigms. The drawing at left shows the adaptation field; the drawing at center shows the stimulus presentation. The graph at right shows data from Pokorny and Smith (1997).
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Our approach is unique because we attempt to differentiate the pathways by their contrast responsivity. One previous study (Chen, Bedell, & Frishman, 1996) emphasized the contrast variable but they varied the temporal frequency of their test stimulus to distinguish the pathways. In our approach, the test stimulus was identical; only the pre- and post-adaptation displays differed. Our goal in this research was to evaluate spatial summation using the pulse and steady-pedestal paradigms. In a single linear channel, spatial summation and spatial frequency resolution should be linked. Narrowband spatial frequency channels should show minimal spatial summation. When multiple channels are present, we can expect a dissociation between spatial frequency processing and spatial summation. Chromatic discrimination is known to improve with increase in field size over the central 10° of the retina (Brown, 1952; Wyszecki & Stiles, 1982; Yebra, Garcia, & Romero, 1994). This is a much larger area than the classical area-summation function measured foveally (Graham & Bartlett, 1939; Graham, Brown, & Mote, 1939; Davila & Geisler, 1991). The classical data are consistent with summation only by physical light spread or probability summation in the central 1° of the fovea (Davila & Geisler, 1991). We investigated the effect of manipulating spatial parameters on the pulse and steady-pedestal paradigms, using stimulus arrays varying from 0.32° to 7.87°. We maintained the simple center-surround display, while investigating the spatial summation properties of the two pathways by varying the size of the test array. We used a brief 26.67 ms square pulse so that thresholds measured at the surround luminance (zero contrast) would likely to be determined by the MC-pathway (Pokorny & Smith, 1997). We found that spatial summation for the steady-pedestal paradigm (presumed MC-pathway) showed an exponential form approaching an asymptote above 1 square degree, as described in the classical spatial summation literature (reviewed in Graham (1965), Baumgardt (1972)). Spatial summation for the pulse paradigm (presumed PC-pathway) showed summation over the entire range of stimulus areas, but with a shallow slope. Additionally, in order to strengthen the association of the achromatic and chromatic pulse paradigms with PC-pathway function, we reduced the surround size to 2.21° and 2.07° using the a 2.07° square array to establish whether achromatic contrast discrimination with the pulse paradigm depended solely on the presence of contrast at the borders of the test array.
2. Methods
2.1. Equipment The stimuli were generated by a Macintosh PowerPC 9500/132 Computer with a 10-bit Radius Thunder 30/
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1600 video card and were displayed on a 17 in. Radius PressView 17SR color monitor. The display resolution was set at 832×624 and the refresh rate was 75 Hz. The spectral power distributions of the phosphors were measured with an Optronics OL754 spectroradiometer with the detector flush to the screen and illumination of the central 75% of the screen. Phosphor luminance was measured in a similar manner for 1024 levels of input integer value, and a look-up table was constructed to represent relations between voltage integer value and phosphor luminance. The luminance output of the monitor was calibrated by a Minolta LS-100 luminance meter. Screen uniformity was checked at the maximum output. Consistent with the physics of the emitters, there was a roll-off in luminance at the edges of the screen. The central 75% of the screen was used, allowing an error of less than 4%. All stimuli were metameric to the equal energy spectrum. The temporal presentation was a square pulse of 26.7 ms duration (two screen refreshes at a 75 Hz monitor refresh rate). The monitor screen was viewed binocularly at 1 m. The observer sat in a comfortable chair holding the mouse pad and mouse in his/her lap. No head stabilization was used. The screen luminance for adaptation was 12 cd/m2 (approximately 115 trolands (td)) and was constant throughout the experiment. Test stimuli were presented at a series of positive and negative contrasts between 73 and 182 td.
2.1.1. Spatial configuration The maximum display size was an 8°× 8° square, centered on the screen. In the main experiment, we used an 8° surround. The test array consisted of four smaller squares separated by gaps of 0.07°. The height and width of the four-square array was varied between 0.32° and 7.87°. In a subsidiary experiment we reduced the surround to 2.21° and to 2.07°, using the 2.07° four-square array. A central (4.36% ×4.36%) fixation dot provided a fixation target for larger test arrays. For the two smallest test arrays of 0.32° and 0.57°, four fixation dots at 1° on the vertical and horizontal axes provided a fixation target. 2.2. Procedure The pulse and steady-pedestal paradigms were investigated in separate runs. The paradigms differed only in the initial pre-adaptation; all other procedural details were identical. The observer was instructed that one square might appear brighter or darker than the other three and the task was to identify the ‘odd’ square. The observer first adapted for 2 min to a uniform 115 td display that included the fixation target. For the steadypedestal paradigm, there was a further 1 min of adaptation to the four-square array. At the start of a trial, the fixation target disappeared. Each trial presented three
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was reached. The criterion was set in pilot studies to produce an efficient staircase, requiring about 60–70 trials. Once the criterion step size was reached, the staircases continued without further change in step size using a reversal rule. Two successive incorrect identifications led to an increase in test contrast on the following trial; three correct identifications lead to a decrease in test contrast. Eight to ten reversals at the criterion step size were measured for both the increment and the decrement staircases. We calculated the equivalent percent correct on a psychometric function at 0.57 (see Acknowledgements). The average contrast at which the last six reversals occurred was taken as the estimate of the threshold contrast. A 30-min paradigm allowed measurement of increment and decrement thresholds at four or five starting pedestal retinal illuminances. Thus, two sessions were required to obtain full data for one four-square array size for either the pulse or the steadypedestal paradigm. The entire session was repeated and reported data are the average of three increment and three decrement thresholds for each array size and paradigm.
2.3. Obser6ers
Fig. 2. Contrast discrimination thresholds obtained for stimulus arrays between 0.32° and 7.87°, data of observer HK. The surround retinal illuminance was 115 td, shown by an arrow on the abscissa. (A) pulse paradigm. (B) steady-pedestal paradigm.
of the squares at a common retinal illuminance and the test square, selected randomly with equal probability, at a different retinal illuminance. At the trial conclusion, the fixation target reappeared together with a cursor. The observer used the mouse to place the cursor in the stimulus position judged different. A mouse click at this position stored the result and reset the display for the next trial. No feedback was given. Trials followed a double random-alternating staircase. The pedestal retinal illuminance was fixed for each pair of staircases. In one staircase the test square threshold was measured in an increment direction, in the other in a decrement direction. Pilot data established that there were no systematic differences between increment and decrement threshold absolute contrast. At the start of a staircase, an easily discriminable test contrast was present and on succeeding trials the step size was halved until a criterion step of 0.025 log unit
The three observers (HK, female aged 23, CS, male aged 30, and IY, female aged 24) were all normal trichromats as assessed with the Ishihara pseudoisochromatic plates and the Neitz OT anomaloscope. Farnsworth 100-hue error scores were 12 for HK, 4 for CS, and 8 for IY. CS was author Vincent C. Sun. HK and IY were paid observers, and were naive as to the purpose and design of the experiment.
3. Results
3.1. Contrast functions Figs. 2–4 show results for the three observers plotted as log (DI) versus I where DI is the contrast threshold re-expressed in trolands (IDCthr), and I is the fixed surround illuminance (115 td). The upper panel shows data for the pulse paradigm and the lower panel shows data for the steady-pedestal paradigm. The different array sizes are shown by different symbols. The solid symbols are for the 2.07° array and represent the condition most similar to that of Pokorny and Smith (1997). The data for this condition agree well with those of that study. In the pulse paradigm, thresholds were lowest (highest sensitivity) at the surround luminance (shown by an arrow on the graphs). Thresholds rose as the pulse luminance decreased or increased, forming two arms of a V-shaped function. The arms of the V-shaped function did not vary in shape with stimulus
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size. In the steady-pedestal paradigm, threshold rose monotonically as a function of pedestal luminance. The data sets for the different array sizes were displaced but parallel. For both paradigms, the thresholds decreased as stimulus array size increased. The change in sensitivity was more pronounced for the steady-pedestal than the pulse paradigm. In Pokorny and Smith (1997), the data for the pulse paradigm were described by adapting the characteristic saturation function of the PC-pathway (Kaplan & Shapley, 1986). For a single cell the contrast saturation function is constrained by two parameters, Rmax and Csat; the predicted contrast discrimination, DC, includes a third parameter, the criterion firing rate, l. Since psychophysical data may include the effects of higher order summation, Pokorny and Smith allowed a free vertical scaling parameter. Also, the psychophysics does not have independent access to the cell properties Rmax
Fig. 4. Contrast discrimination thresholds obtained for stimulus arrays between 0.32° and 7.87°, data of observer IY. Other details are as in Fig. 2.
and l. We can abstract only two pieces of information from the data, the slope of the V-shape and the sensitivity at the minimum. Here we present an equation adapted for psychophysics expressed only in Csat, criterion and overall scaling (c.f. Snippe, 1998): logDI = log[(Csat + C )2/{Csat − (KC)(Csat + C )}] + log(KPIS)
Fig. 3. Contrast discrimination thresholds obtained for stimulus arrays between 0.32° and 7.87°, data of observer CS. Other details are as in Fig. 2.
(1)
where C represents the absolute value of the pulse Weber contrast (DI/IS), Csat represents the saturating contrast, KC represents the criterion increment firing rate (comparable to l/Rmax of a single cell) and KP represents the overall scaling constant. The overall scaling constant, KP incorporates threshold sensitivity for the presumed PC-pathway mediated thresholds that may depend on the test square area. The solid lines represent fits of Eq. (1) for the pulse paradigm. The threshold at the surround luminance was omitted from
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the fits. Fits were made for each observer, considering all six array sizes simultaneously. The variable KP was optimized for each array size but the variables Csat and KC were fixed across array size. According to the interpretation of Pokorny and Smith for the pulse paradigm, the thresholds on the arms of the V-shapes are determined in the PC-pathway. The slopes should be dependent upon the contrast gain of cells forming the pathway. The values of Csat were 0.41, 0.40, and 0.67 for observers HK, CS, and IY, respectively, consistent with data measured for primate LGN (Kaplan & Shapley, 1986) and retinal ganglion cells (Lee et al., 1990). For the steady-pedestal paradigm, the data were described by a line of unit slope with a variable scaling factor:
Fig. 5. Contrast discrimination thresholds obtained for the pulse paradigm for surrounds of 2.21° and 2.07° with a foursquare array of 2.07°. The data for the 8° surround are replotted for comparison. The surround retinal illuminance of 115 td is shown by an arrow. (A) Data of observer CS. (B) Data of observer IY.
log DI =log(I)+ log(KMIS)
(2)
where KM represents the vertical scaling parameter for the presumed MC-pathway mediated thresholds. For the steady-pedestal paradigm, the single parameter fit describes the data for the larger array sizes. However, the data for decrement contrasts deviates to higher thresholds for the small array sizes. These decrement data were omitted from the fits shown in the figures. The probable cause of these deviations is spread light (Pokorny & Smith, 1997) that should be greatest for the smallest arrays. Based on the calculations of Shevell and Burroughs (1988), we estimated a threshold increase at 73 td of 0.115 log unit for the 0.32° foursquare array, decreasing to 0.04 log unit for the 2.07° four-square array. Our observers showed a slightly larger effect: 0.19–0.24 log unit for the 0.32° foursquare array decreasing to 0.04–0.07 for the 2.07° four-square array. However the Shevell and Burroughs calculations were for a 2 mm pupil and pupil diameters of our observers (monitored during the course of the experiment) ranged from 5.76 mm to 6.5 mm. Fig. 5 shows data for the pulse paradigm using the 2.07° square array and surround sizes of 2.21° and 2.07°. The 8° surround data are replotted for comparison. The solid lines are fits of Eq. (1) using the optimal values of Csat and KC (Figs. 3 and 4) varying only KP. These conditions were run for comparison with chromatic contrast discrimination. The 2.21° surround provides a 7% border; the 2.07° surround provides only a 7% crosshair separating the four squares. The achromatic data show V-shapes for both surrounds similar in shape to the 8° surround data. For observer CS the 2.21° and 2.07° surround thresholds were slightly less sensitive than the 8° surround data but for observer IY all three data sets overlap. The achromatic data thus show the same phenomenon as the equiluminant chromatic contrast data, consistent with our interpretation that the PC-pathway mediates threshold for the pulse paradigm. We also ran the steady-pedestal paradigm with the small surrounds and, as expected, the data (not shown) differed only slightly in absolute sensitivity.
3.1.1. Area-illuminance functions Area-illuminance functions can be demonstrated by plotting the thresholds as a function of area at a constant Pedestal value. In this analysis we consider only the dimensions of one square of the array since the discrimination task hinged on identification of the one different square. For the pulse paradigm, we calculated the predicted threshold for the condition where the test array was the same illuminance as the surround (pedestal contrast C= 0) from Eq. (1). A similar calculation was made for the steady-pedestal paradigm. Fig. 6 shows the derived values for both paradigms plotted
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as a function of the area of a single square in the four-square array. Data for the three observers are shown in separate panels. Data for the pulse paradigm showed a shallow linear decrease in log threshold with log area. Data for the steady-pedestal paradigm showed a steeper decrease in threshold with log area for small array sizes with an asymptote above one square degree. Early studies of spatial summation, reviewed in Graham (1965) and Baumgardt (1972), phrased the results in terms of Ricco’s law, Piper’s law and Pie´ ron’s law. Above some critical area determined by these laws, threshold is independent of test area. Ricco’s law refers to full summation (AI = K) and occurs for tiny spots less than 10% arc. Piper’s law refers to square root summation (A 0.5I= K); it occurs for diameters greater than 10% and primarily has been reported in the parafovea (Barlow, 1958). At still larger areas, Pie´ ron’s law refers to cube-root summation (A 0.333I= K). The solid lines fit to the steady-pedestal data are derived from a power function similar to that proposed by Graham et al. (1939). This equation was introduced to emphasize the continual decline in slope that is more characteristic of the data than that allowed by combining linear segments of the Ricco, Piper, and Pie´ ron laws. The equation for these fits is: log(DIS)= log(K1)+ K2A K3
(3)
where A is the area of the test square and K1,2,3 are constants. This equation has no interpretation of the constants and they depend on the range of data sampled. The dashed lines fit to the pulse paradigm data are linear fits on the log/log axes given by Eq. (4): log(DIS)= k1log(A +k2)
(4)
where k1 is the slope and k2 is a scaling constant. The best-fitting slopes were − 0.21, −0.14 and − 0.23 for observers HK, CS and IY, respectively.
4. Discussion
Fig. 6. Threshold spatial summation functions for the pulse (squares) and steady-pedestal (circles) paradigms. (A) Data of observer HK. (B) Data of observer CS. (C) Data of observer IY. The dashed lines are linear fits to the data on the log – log axis; the solid lines are from power functions fit to the data (see text for further details).
In this paper we have demonstrated different spatial summation properties for the two paradigms. The steady-pedestal paradigm showed a decrease in log threshold with increase in log area, which could be fit with a power function of area. The pulse paradigm showed a gradual linear decrease on the log–log axes. The former result is consistent with classical studies of spatial summation; the latter result is consistent with data of color matching (Brown, 1952; Yebra et al., 1994). The 2.21° and 2.07° surround data for the pulse paradigm showed V-shapes indicating that it is border contrast that is important in achromatic contrast discrimination just as in equiluminant chromatic contrast discrimination. Overall the data support the conclusion that the two paradigms access different processing
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pathways that we associate with the MC- and PC-pathways. It is of note that the classical studies of areal and temporal summation give functions that we would interpret as consistent with MC-pathway activity (Pokorny & Smith, 1997). The pulse and steady-pedestal paradigms were designed to compare contrast gain accessed psychophysically with contrast gain of single cell data in the retina or lateral geniculate nucleus (LGN). The use of a free vertical scaling factor was incorporated to recognize that the psychophysical sensitivity might include contributions such as averaging or summation at higher cortical levels. A similar point can be made in considering the current study. The sizes of retinal receptive fields in the fovea and parafovea are much smaller than our stimuli for both MC- and PC-pathways (Derrington & Lennie, 1984; Croner & Kaplan, 1995; Lee, 1996). PC-pathway cells show a center size of 3% in the central 10° of the retina while MC-pathway cells are approximately twice that size (Croner & Kaplan, 1995). Obviously the area-illuminance summation we observe psychophysically cannot be related to the dimensions of single cell data. Our data thus indicate a difference between the averaging or summation properties of MCpathway and PC-pathways at higher cortical levels.
4.1. MC-pathway We suggest that area-illuminance summation for the MC-pathway involves probability summation across the area of the test field. A modern investigation of area summation at the fovea (Davila & Geisler, 1991) established that Ricco’s law can reflect spatial summation due to the optical point spread function of the eye while Piper’s law could be explained by probability summation. The majority of studies of foveal summation were performed at absolute threshold. To avoid rod intrusion, the test fields under study were chosen to be less than 1° in diameter. Thus there are few data for larger areas. Fig. 7 shows a comparison of our average data with foveal dark-adapted data of Graham and Bartlett (1939) and Sun, Pokorny, Shevell, and Smith (1997). The average data of these studies were adjusted on the vertical axis for best coincidence with our data in the region where stimulus area overlapped among the studies. The solid line is the fit of Eq. (3) to all three data sets. Our data coincide in shape with the dark-adapted data. Asymptotic sensitivity is approached at a diameter between 1° and 1.41°. Thus the steady-pedestal data agree with classical threshold summation data that have been explained by physical light spread and probability summation across area. The result is also consistent with the transient mechanism of Legge (1978) that was broadband with a roll-off above 1.0 cpd.
4.2. PC-pathway
Fig. 7. Comparison of spatial summation for the steady-pedestal paradigm (the average of the three observers is given by the solid circles) with data for dark-adapted thresholds at the fovea. The data of Graham and Bartlett (1939) are the average of two observers, and are represented by erect triangles. The Sun et al. (1997) results are the average of two observers and are represented by inverted triangles. The Graham and Bartlett data were converted to td with an effective pupil diameter of 5 mm (Le Grand, 1968) and scaled by adding 0.19 to the average data. The Sun et al. data were converted to td and scaled by adding 0.084 to the average data. The solid line is from Eq. (4) fit to the data of all three studies. The value of the parameters k1 to k3 are − 0.005, 0.48, and − 0.21, respectively.
We suggest that area-illuminance summation for the PC-pathway involves probability summation along the test-surround border. In our interpretation of chromatic contrast discrimination we suggested that border elements adapted to the surround determined threshold in the chromatic steady-pedestal paradigm (Smith et al., 2000). A similar interpretation can be applied to the pulse paradigm with achromatic stimuli. The spatial summation function may thus represent probability summation along these border elements. The pulse paradigm bears procedural similarities to simultaneous masking. In these studies use of very low contrast masks (pedestals) gives an initial facilitation near the unmasked contrast threshold (zero pedestal) followed by a rise as mask (pedestal) contrasts exceed threshold. Facilitation can be seen for both achromatic (Legge & Foley, 1980; Foley & Legge, 1981; Foley, 1994) and chromatic patterns (Cole & Kronauer, 1990; Gegenfurtner & Kiper, 1992; Chen, Foley, & Brainard, 2000a,b). We did not use low pedestal contrasts and thus did not measure possible facilitation. Further, for the majority of pulse paradigm conditions, we interpret the minimum threshold at the point of the V-shape to be MC-pathway rather than PC-pathway mediated (Fig. 6). The exception is for the 0.32° four-square
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array. The measured thresholds for all three observers fell above the predicted PC-pathway minimum, consistent with the phenomenon of facilitation. Facilitation is considered a higher order phenomenon (Nachmias & Kocher, 1970; Nachmias & Sansbury, 1974; Foley & Legge, 1981; Pelli, 1985; Foley, 1994). The retinallybased contrast saturation model does not predict such facilitation and thus requires further modification to incorporate higher order effects.
Acknowledgements The research was supported by NEI research grants EY00901 and EY07390. We thank Steven K. Shevell and Hugh Wilson for comments on this project and Linda Glennie for technical assistance. Steven K. Shevell thoughtfully provided an estimate of the equivalent proportion correct for our forced choice paradigm and staircase rule. We also thank our observers HK and IY for their patience and time. Publication was supported by Research to Prevent Blindness.
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