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Remote facilitation in the Fourier domain
Vision Research 47 (2007) 1112–1119 www.elsevier.com/locate/visres
Remote facilitation in the Fourier domain Tim S. Meese ¤, David J. Holmes, Kirsten L. Challinor School of Life and Health Sciences, Aston University, Birmingham B47ET, UK Received 27 September 2006; received in revised form 4 November 2006
Abstract To explore spatial interactions between visual mechanisms in the Fourier domain we measured detection thresholds for vertical and horizontal sine-wave gratings (4.4 deg diameter) over a range of spatial frequencies (0.5–23 c/deg) in the presence of grating and plaid masks with component contrasts of 8%, orientations of §45° and a spatial frequency of 1 c/deg. The mask suppressed the target grating over a range of §1 octave, and the plaid produced more suppression than the grating, consistent with summation of mask components in a broadly tuned contrast gain pool. At greater diVerences in spatial frequency (»3 octaves), the plaid and grating masks both produced about 3 dB of facilitation (they reduced detection thresholds by a factor of about F2). At yet further distances (»4 octaves) the masks had no eVect. The facilitation cannot be attributed to a reduction of uncertainty by the mask because (a) it occurs for mask components that have very diVerent spatial frequencies and orientations from the test and (b) the large stimulus size and central Wxation point mean there was no spatial uncertainty that could be reduced. We suggest the results are due to long-range sensory interactions (in the Fourier domain) between mask and test-channels. The eVects could be due to either direct facilitation or disinhibition. © 2006 Elsevier Ltd. All rights reserved. Keywords: Contrast gain control; Psychophysics; Attention; Masking; Human vision
1. Introduction Masking is the phenomenon whereby the presence of one stimulus (the mask) impedes the detectability or response to a second stimulus (the test, or target), and it is usually attributed to suppression between mask and test mechanisms (see Meese & Holmes, 2007 for a recent short review). Facilitation is said to occur when the mask enhances the detectability or response to the test stimulus. At contrast detection threshold, facilitation has been found between patches of mask and test grating that diVer in spatial position (Chen & Tyler, 2001; Huang, Hess, & Dakin, 2006; Petrov, Verghese, & McKee, 2006; Polat & Sagi, 1993; Solomon & Morgan, 2000; Solomon, Watson, & Morgan, 1999; Williams & Hess, 1998), spatial frequency (Georgeson & Georgeson, 1987; Stromeyer & Klein, 1974; Tolhurst & BarWeld, 1978), orientation (Meese & Holmes, 2007; Meese, Summers, Holmes, & Wallis, 2007; Zenger & Sagi, *
Corresponding author. Fax: +44 121 333 4220. E-mail address: [email protected] (T.S. Meese).
0042-6989/$ - see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2006.11.010
1996) and combinations of two (Chen & Tyler, 2002; Meese et al., 2007; Yu, Klein, & Levi, 2002) or three of these parameters (Meese & Hess, 2004; Meese et al., 2007). However, most of these studies have concentrated on a fairly narrow range of spatial frequencies and so the full extent of interactions in the Fourier domain is not known. To build a more complete picture of these interactions we report masking experiments for a greater range of diVerences between mask and test spatial frequency than has been done in most previous studies. In particular, we were interested in conditions where we anticipated that the test grating would be detected by a mechanism that was not excited by the mask. 2. Methods 2.1. Equipment Stimuli were displayed on a Sony Trinitron Multiscan monitor with a frame rate of 120 Hz using a VSG2/3 stimulus generator operating in pseudo 12-bit mode and controlled by a PC. Mean luminance of the central display region was 65 cd/m2. The display was gamma corrected to ensure linearity
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over the full contrast range, and a frame interleaving technique (60 Hz per image) allowed the contrasts of the mask (grating or plaid) and test grating to be varied independently using lookup tables. A chin- and head-rest were used to help observers hold Wxation, and viewing was binocular.
2.2. Observers Four observers performed the main experiment. These were DJH (one of the authors) and three volunteers. Two of these were psychophysics graduate students (ADP & RJS) and one was a graduate student from another scientiWc discipline (JFT). The facilitation that we found for DJH was unexpected, and the other three observers were not made aware of this Wnding. To become practiced at the task and familiar with the stimuli, DJH performed three complete experimental runs (»10,800 trials) before formal data collection began. The other three observers performed a sub-sample of conditions and one complete run (»1200 trials) as practice. For all observers results are means and standard errors from Wve experimental runs. A series of further experiments designed as controls and to test the generality of our Wndings (described in Section 3) was performed by DJH only.
2.3. Stimuli All stimuli were stationary sine-wave gratings or two-component plaids the were windowed by a circular raised-cosine envelope. The central plateau of this envelope was 4.1° in diameter and the half-height, full-width of the envelope was 4.4°. The gratings were in sine-phase with a central dark Wxation point (2 pixels square) that was visible throughout the experiment. The spatial frequency of the mask was always 1 c/deg. The spatial frequency of the test was varied over the range 0.5–23 c/deg. There were two types of mask: a grating mask had an orientation of ¡45° (left oblique) and a plaid mask had component orientations of §45°. The orientation of the test grating was typically vertical, though in one experiment it was horizontal and in another it varied between vertical and ¡45°. Examples of 1 c/deg grating and plaid masks and a 5.7 c/deg test grating are shown in Fig. 1. Stimulus contrast is expressed as the Michelson contrast of the carrier in percent. In most experiments the masks (both plaids and gratings) had component contrasts of 8%. Because of the frame interleaving (see above) this was achieved by alternating between 16% in the mask frame and 0% in the test frame. Thus, to generate a plaid where each component had a contrast of 8% in the time averaged image, the overall contrast of the plaid in the mask frame was 32%.
Fig. 2. Threshold elevation (20 times the log10 ratio of detection thresholds with and without the mask) for grating and plaid masks (diVerent symbols) as functions of spatial frequency (SF). The spatial frequency of the mask was 1 c/deg. Error bars (in this and all other Wgures) show §1 SE of the threshold elevation distribution (n D 5) at each point. This incorporates the error measures for both the masked and unmasked thresholds. This Wgure represents results from about 18,000 trials. the correctness of response. The two intervals (100 ms each) were marked by short tones at their onset. The duration between the oVset of the Wrst interval and the onset of the second interval was 500 ms. A ‘three-down, one-up’ randomly interleaved staircase procedure was used to control the magnitude of the target contrast in logarithmic steps. A pair of interleaved staircases were used for each condition and terminated after 12 reversals each. The staircases were used only to determine stimulus placement. Threshold and its standard error (SE) were estimated using probit analysis (Finney, 1971) to calculate the 75% correct point on the psychometric function and its standard error (SE). This gave estimates based on about 100 trials for each experimental run. In the rare cases where the estimated SE was greater than 3 dB, these data were rejected and the experimental session was rerun. Experimental trials were interleaved across mask type (no mask, grating mask and plaid mask) and blocked across test spatial frequency. Threshold elevation is expressed in dB, equal to 20 times the log10 ratio of the detection thresholds with and without the mask. This was derived from approximately 1000 trials for each point (500 trials with the mask and 500 trials without the mask).
2.4. Procedure A temporal two-interval forced-choice (2IFC) technique was used where observers indicated which of the two intervals contained the target using one of two mouse buttons. The computer determined the temporal interval that contained the target randomly and auditory feedback was used to indicate
3. Results and discussion Results are shown for DJH in Fig. 2. When the test grating has a similar spatial frequency to the mask (1 c/deg),
Fig. 1. High contrast examples of stimuli used in the experiments. (A) 1 c/deg plaid mask, (B) 1 c/deg grating mask, and (C) 5.7 c/deg test grating. Note that the grating and plaid masks have the same component contrast (8% in most experiments) and therefore diVerent overall contrasts (the Michelson contrast of the plaid is twice that of the grating).
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Mask grating (-45°) Mask plaid (±45°) Mask component contrast = 8%
Threshold elevation (dB)
Mask SF
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ADP
Vertical test Horizontal test
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Vertical test (Fig 2) Mask component contrast = 8%
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DJH 1
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SF of vertical test grating (c/deg)
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Threshold elevation (dB)
Mask plaid
Mask SF
Fig. 4. EVects of practice and test orientation on masking by a plaid for DJH. Open symbols are for the same vertical test grating. The circular symbols are replotted from Fig. 2 and are for experimental sessions performed before those for the square symbols. This Wgure represents results from about 30,000 trials.
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0
JFT -6
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6 0
RJS -6 1
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SF of vertical test grating (c/deg) Fig. 3. The same as Fig. 2, but for three diVerent observers and fewer test spatial frequencies. This Wgure represents results from about 6000 trials for each observer.
threshold elevation occurs and is much greater for the plaid mask than for the grating mask. This has been found before when plaid and grating masks had the same spatial frequency as the test (Derrington & Henning, 1989). At higher test spatial frequencies (»5.7 c/deg) masking from both types of mask gives way to a region of facilitation of about 3 dB. The eVect is tuned, since it diminishes at higher spatial frequencies. The same experiment was performed on three other observers but for a more restricted set of test spatial frequencies (Fig. 3). The main eVects are replicated by all three observers: at a test spatial frequency of 1 c/deg, the plaid produces considerably more masking than does the grating, but at higher test spatial frequencies (»4 to 8 c/deg) both masks produce small levels of facilitation (»3 dB). Taken with the results from DJH, there is a suggestion that facilitation is stronger for the plaid than for the grating, though the eVect is small.
Fig. 4 shows further results for DJH who repeated the experiment using only the plaid mask, but for vertical and horizontal orientations of the test grating measured in diVerent experimental blocks (square symbols). Masking is less for the vertical grating than for the horizontal grating. However, the open circular symbols, replotted from the earlier experimental sessions in Fig. 2, show that this diVerence is probably due to a decrease in masking with practice for the vertical condition. Zenger and Sagi (1996) and Dorais and Sagi (1997) found similar orientation-speciWc eVects of practice for the cross-orientation masking measured in their experiments. The level of facilitation is the same for both orientations of the test grating and unlike masking, does not change with practice, at least for this observer. However, the main reason for repeating the experiment with horizontal gratings was to test a concern about adjacent pixel nonlinearity. This is a property of CRT raster monitors (Robson, 1999) and can have the eVect of reducing the local mean luminance of vertical high spatial frequency gratings. However, the similarity between the results for horizontal and vertical gratings (square symbols) at high spatial frequencies indicates that this is not a factor here. Next, we investigated whether the facilitation was speciWc to the 45° orientation diVerence between the mask and test components used so far. Threshold elevation was measured for a two-octave range of Wve test spatial frequencies at each of 10 diVerent test orientations (0–45° in 5° steps) as shown in Fig. 5A. The mask was always a 1 c/deg grating with an orientation of ¡45° and a contrast of 8%. In all cases we found masking at the lower spatial frequencies and facilitation of about 3 dB at the higher spatial frequencies. The spatial frequency at which masking gives way to facilitation (determined by linear interpolation of the masking functions) is shown in Fig. 5B. As the mask and test orientations become more similar, the region of facilitation moves closer to the mask spatial frequency. When the mask and test have the same orientation, facilitation occurs for
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spatial frequency diVerences as small as one octave.1 This is consistent with previous work that has found facilitation from masks with the same orientation as the test grating and contrasts well above their own detection threshold (e.g. Nachmias & Weber, 1975; Georgeson & Georgeson, 1987; Stromeyer & Klein, 1974; Tolhurst & BarWeld, 1978). Thus, our study here extends the results of previous work by showing that facilitation can be found for a wider range of orientation and spatial frequency diVerences than had previously been thought. Whether the results in Fig. 5 represent a single process that operates over a continuum in Fourier space, or two or more distinct processes that operate in diVerent regions, is not clear. Finally, we investigated the eVect of mask contrast on facilitation for a test spatial frequency of 5.7 c/deg. For component contrasts of 12%, 14%, 16% and 24%, the level of facilitation was the same for grating and plaid masks and was no greater than that seen in the previous experiments (»3 dB). For a component contrast of 8% we conWrmed that facilitation was greater for the plaid than for the grating (see Figs. 2 and 3). This suggests a facilitatory process that saturates at an overall mask contrast of around 12%, at least for DJH. 4. General discussion We have presented evidence for facilitation from 1 c/deg mask components on test gratings around 2.5 octaves higher in spatial frequency and with orientation diVerences of up to 45°. These eVects would have been missed in several previous masking studies because those that have used test spatial frequencies in the range 4–8 c/deg have not typically used masks as low as 1 c/deg (Daugman, 1984; Derrington & Henning, 1989; Harvey & Doan, 1990; Wilson, McFarlane, & Phillips, 1983; though see Bowen & Wilson, 1994). 4.1. A luminance artefact? Before discussing possible causes of facilitation we Wrst consider a possible artefact. Our sine-phase grating and plaid masks were presented simultaneously with the test stimulus, both for 100 ms. Thus, there were ‘dark’ regions in the image where the local luminance was less than the mean luminance of 65 cd/m2 by c%, where c is the overall contrast of the mask. Therefore, the physical contrast of a high frequency test grating in the ‘dark’ regions would approach a contrast that is a factor of 100/(100 ¡ c) higher than its nominal value. If this were the eVective contrast of the test grating available to the detection process (Bowen & Wilson, 1994), then when expressed relative to mean luminance 1 In this experiment the orientations of the mask and test gratings were the same and the contrast of the mask was 8%. It is well known that when the mask has much lower contrast—around its own detection threshold— facilitation occurs when the mask and test have the same spatial frequency and orientation (e.g. Legge & Foley, 1980).
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(as it was in the experiments) we should expect facilitation of »0.72 and »1.5 dB for c D 8%, and c D 16%, respectively. However, these artefacts are notably less than the maximum experimental eVects for the grating mask (c D 8%) in Figs. 2, 3 and 5, and the plaid masks (c D 16%) in Fig. 4, where facilitation typically reached »3 dB. Furthermore, retinal inhomogeneity (Pointer & Hess, 1989) and a dark adaptation process that takes about 150 ms to saturate (Bowen & Wilson, 1994; Crawford, 1947; Kingdom & Whittle, 1996) are both likely to decrease the size of the eVects possible through this route. Finally, if this were a substantial contributing factor to the facilitation in our experiments, then facilitation should have increased markedly with mask contrast. It did not: the empirical eVects saturated at a contrast of about 12%. 4.2. Three causes of facilitation As we outlined in Section 1, facilitatory eVects have been found in other types of masking experiment, but there is disagreement about their cause. Three candidate processes have been proposed: (i) within-channel excitation from the mask (Legge & Foley, 1980; Solomon et al., 1999; Williams & Hess, 1998; Zenger & Sagi, 1996); (ii) reduction of uncertainty by the mask (Petrov et al., 2006; Williams & Hess, 1998) and (iii) sensory interactions between mask and test mechanisms (Chen & Tyler, 2001, 2002; Meese et al., 2007; Polat & Sagi, 1993). The Wrst account requires that the mask and test both fall within the receptive Weld of a common mechanism with an accelerating output nonlinearity or hard threshold. This seems plausible in the situation where a test patch is placed between two co-oriented Xankers (Solomon et al., 1999) or is superimposed and has a similar spatial frequency and orientation to the mask (Zenger & Sagi, 1996), but is much less likely when the mask and test diVer substantially in spatial frequency and orientation. This ‘within-channel’ hypothesis can be easily tested because in general, the linearizing eVects of excitation by the mask should reduce the slope of the psychometric function to a Weibull » 1.3 (Bird, Henning, & Wichmann, 2002; Georgeson & Meese, 2004; Meese, Georgeson, & Baker, 2006; Pelli, 1985, 1987). However, the slope does not become this shallow for superimposed patches of mask and test grating with orthogonal orientations (Baker & Meese, 2006; Georgeson & Meese, 2004; Meese & Holmes, 2007) even though these stimuli can produce facilitation (Baker & Meese, 2006; Foley & Chen, 1997; Meese & Holmes, 2007; Meese et al., 2007). On the other hand, Petrov et al. (2006) found that Xanking patches do reduce the slope of the psychometric function for a central test patch. This might be taken to support the within-channel account of facilitation (Solomon & Morgan, 2000), but Petrov et al. also found the same eVect for a low contrast ring surrounding the target. Although withinchannel eVects could occur for this conWguration (Petrov et al. used a cosine-phase test stimulus), this seems unlikely, and other possibilities should be considered. The uncertainty hypothesis also predicts that the mask will reduce the slope of the psychometric function (Pelli, 1985; Tyler & Chen, 2000),
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Fig. 5. Masking and facilitation for a range of orientation diVerences between mask and test gratings. (A) Each plot shows a masking function for the orientation diVerence in the inset. Note that the Wve test spatial frequencies are not the same in each plot. (B) The diVerence between mask and test spatial frequencies (in octaves) for which masking gives way to facilitation, as a function of the orientation diVerence between mask and test gratings. Note that the results for an orientation diVerence of 15° are omitted in this panel because of the ambiguity in the masking function (A). This Wgure represents results from about 45,000 trials.
(though not necessarily as low as » 1.3), and so this result has been taken to support the uncertainty hypothesis for rings and Xanker masks (Petrov et al., 2006). However, the situation is not straightforward. Huang et al. (2006) found that facilitation is abolished when the Xankers are presented to a diVerent eye from the test, and Meese and Hess (2004) found a similar result for cross-oriented annular masks. Furthermore, Huang et al. decoupled facilitation from a reduction in the slope of the psychometric function: their Xankers reduced the psychometric slope regardless of whether they were presented to the same or diVerent eyes from the test. In its simplest form, the third explanation of facilitation (sensory interactions) proposes that the mask increases the gain of the detecting mechanism, and this does not change the slope of the psychometric function (e.g. Dao, Lu, & Dosher, 2006). At Wrst glance this seems inconsistent with the experimental evidence that the psychometric slope is reduced by facilitation (Huang et al., 2006; Petrov et al., 2006). However, this eVect could arise for other reasons. For example, the psychometric function would ‘blur’ if the mask caused it to be nonstationary. This might happen if the mask caused Xuctuations in the observer’s attention or if the interaction between the mask and test Xuctuated owing to noise. 4.3. The slope of the psychometric function As outlined above, the slope of the psychometric function can provide valuable supplementary information in experiments on masking and facilitation. The experiments here were performed circa 1998, before we routinely saved those data, but we have performed similar (unpublished)
experiments since, in which vertical or horizontal test gratings were detected in the presence of plaids or oblique gratings. Those experiments included conditions in which the test and mask both had component spatial frequencies of 1 c/deg. Those conditions are of interest because we wondered whether the masking at low spatial frequencies (Figs. 2–4) might have involved excitation of the test mechanism by the mask (Phillips & Wilson, 1984; Wilson et al., 1983). In a ‘transient’ condition, both mask and test were temporally modulated by a single cycle of a 15 Hz square-wave pulse, the mask contrast was 40%, the orientation diVerence between mask and test was 40°, the observer was DJH and all conditions were blocked. In this case, threshold elevation was 16.6 dB and the psychometric functions had slopes2 of D 3.0 and D 3.4 with and without a mask, respectively. These estimates contrast with the much shallower slope of D 1.5 when the mask had the same orientation as the test: a result consistent with linearization of the test mechanism by the mask. In another condition the mask was a plaid (§45°) with component contrasts of 11% and stimulus duration was 100 ms (similar conditions to those used here). Threshold elevation was 15.5 and 18 dB for DJH 2 The slope of the psychometric function was estimated using probit analysis, assuming a cumulative log-normal form (approximated by a Wfth-order polynomial). The slope of this curve () is expressed in dB and was estimated independently for each experimental session (typically 100 trials each). Estimates of were then averaged across multiple sessions (typically 4 or 5) before converting to the more familiar Weibull using the approximation D 10.3/. This approximation was derived by performing a least squares Wt of a Weibull function to the cumulative log-normal over a range of §3.
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and TSM, respectively. Correspondingly, the slopes with a mask were D 3.0 and D 3.6, and without a mask were D 3.4 and D 3.3. Therefore, despite considerable levels of masking (up to a factor of »8) the slope of the psychometric function remained steep when the diVerence between mask and test orientations was 40° or greater.3 Thus, assuming that nonlinear contrast transduction is at least part of the reason for the steep psychometric function ( » 3.5) at detection threshold (Kontsevich & Tyler, 1999; Legge & Foley, 1980; Legge, Kersten, & Burgess, 1987; Wilson, 1980), this analysis implies that the masking was not due to excitation of a broadband test mechanism by the mask (Phillips & Wilson, 1984), but is consistent with a suppressive inXuence from the mask on the test mechanism (Foley, 1994; Meese & Hess, 2004). It seems very likely that the same it true of the masking in Figs. 2–4 here. We have not measured the slope of the psychometric function under conditions similar to those that have produced facilitation in the experiments here. However, we did record the slopes in cross-oriented masking experiments in which similar levels of facilitation (»3 dB) have been found (Baker, Meese, & Summers, 2007; Meese & Holmes, 2007; Meese et al., 2007). Our preliminary analysis suggests that this type of facilitation is associated with a modest decrease in the slope of the psychometric function, though there is much variability across observers and conditions. We are presently investigating this issue further. 4.4. What caused the facilitation here? We address what caused the facilitation seen in the experiments here by Wrst considering the uncertainty hypothesis in the context of the Wve dimensions of: temporal location, spatial location, orientation, spatial frequency, and spatial phase. Regardless of whether the mask was present, both 2IFC intervals were marked by auditory beeps and so it is unlikely that there was an appreciable reduction of temporal uncertainty by the mask. A central Wxation point was presented continuously and the test gratings had a large spatial extent of 4.4 deg. Thus, observers were well cued to the location of the stimulus on the monitor. Unlike the mask, the Wxation point did not indicate the spatial extent of the stimulus, but we think this is unlikely to be important for two reasons. First, ‘no-mask’ and ‘mask’ trials were randomly interleaved on a trial-by-trial basis meaning that observers were repeatedly reminded of the spatial extent of the target (because the mask and target were the same size). Second, the contribution to detection is less towards the grating’s extremities because sensitivity declines with distance from the Wxation point at a rate of about 0.5 deg per cycle (Foley, Varadharajan, Koh, & Farias, 2007; Pointer & Hess, 1989; Robson & Graham,
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1981). For example, for the stimulus in Fig. 1C, sensitivity to the outer region of the stimulus is about half that to the centre. In the main conWgurations where facilitation was measured, the grating mask provided no cue to test orientation and neither type of mask provided a cue to test spatial frequency. Furthermore, the central Wxation point is expected to have reduced phase uncertainty (the target and masks were always in sine-phase) to an extent at least equal to that available from the mask. In sum, it is very unlikely that the masks reduced either spatio-temporal uncertainty or uncertainty in the Fourier domain for the test gratings that exhibited facilitation here. But this does not rule out the involvement of uncertainty in other contexts (e.g. Tjan & Nandy, 2006). When uncertainty is increased experimentally it raises contrast detection and discrimination thresholds and increases the slope of the psychometric function at and above detection threshold (Meese, Hess, & Williams, 2001; Shani & Sagi, 2005). It remains possible that the facilitation produced by Xankers and rings also involves a reduction of uncertainty (Petrov et al., 2006). The facilitation found here is also inconsistent with subthreshold stimulation of the test-channel by the mask because the eVects occur at orientation and spatial frequency diVerences that are far too great to stimulate a single mechanism (Foley, 1994; Holmes & Meese, 2004), and psychometric functions are not linearized at these distances (Georgeson & Meese, 2004; Meese & Holmes, 2007). Furthermore, the Wnding that the spatial frequency at which facilitation occurred increased as the diVerence between mask and test orientation increased is also inconsistent with that account (Daugman, 1984). (Also see the previous subsection.) The remaining explanation of facilitation is that of sensory interactions, and this seems the most likely account for the results here. There are at least two ways in which this could occur. First there could be a pool of mechanisms that provides direct modulatory facilitation of the activity in the test mechanism. In that case, it is plausible that the facilitatory pool overlaps with the well-known suppressive pool (Heeger, 1992), but is hidden by suppression (Meese & Holmes, 2007) over much of its range. Second, it could be that the mask suppresses an intermediate mechanism, which causes it to release its standing level of suppression from the target mechanism. Similar proposals have been made for the facilitation (De Valois, 1977; Greenlee & Magnussen, 1988; Tolhurst & BarWeld, 1978) and hallucinated contours (Georgeson, 1980) that are experienced at remote spatial frequencies and orientations during and after adaptation. Acknowledgments
3 In fact, a more complete analysis (to be presented elsewhere) shows that there is very little change in the slope of the psychometric function for orientation diVerences as small as 20° when mask and test spatial frequency are both 1 or 3 c/deg.
This work was supported partially by a grant from the Engineering and Physical Sciences Research Council (GR/ S74515/01) awarded to Tim Meese and Mark Georgeson.
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Some of this work Wrst appeared in abstract form in Holmes and Meese (1999). We thank Mark Georgeson for discussion about potential causes of facilitation. We also thank two anonymous referees for their thoughtful comments. References Baker, D. H., & Meese, T. S. (2006). Cross-orientation suppression occurs before binocular summation: evidence from masking and adaptation. Journal of Vision, 6, 821a. Baker, D. H., Meese, T. S., & Summers, R. J. (2007). Psychophysical evidence for two routes to suppression before binocular summation of signals in human vision. Neuroscience under review. Bird, C. M., Henning, G. B., & Wichmann, F. A. (2002). Contrast discrimination with sinusoidal gratings of diVerent spatial frequency. Journal of the Optical Society of America A, 19, 1267–1273. Bowen, R. W., & Wilson, H. R. (1994). A two-process analysis of pattern masking. Vision Research, 34, 645–657. Chen, C.-C., & Tyler, C. W. (2001). Lateral sensitivity modulation explains the Xanker eVect in contrast discrimination. Proceedings of the Royal Society B, 268, 509–516. Chen, C. C., & Tyler, C. W. (2002). Lateral modulation of contrast discrimination: Xanker orientation eVects. Journal of Vision, 2, 520–530. Crawford, B. H. (1947). Visual adaptation in relation to brief conditioning stimuli. Proceedings of the Royal Society B, 134, 283–302. Dao, D. Y., Lu, Z.-L., & Dosher, B. A. (2006). Adaptation to sine-wave gratings selectively reduces the contrast gain of the adapted stimuli. Journal of Vision, 6, 739–759. Daugman, J. G. (1984). Spatial visual channels in the Fourier plane. Vision Research, 9, 891–910. Derrington, A. M., & Henning, G. B. (1989). Some observations on the masking eVects of two-dimensional stimuli. Vision Research, 29, 241–246. De Valois, K. K. (1977). Spatial frequency adaptation can enhance contrast sensitivity. Vision Research, 23, 249–256. Dorais, A., & Sagi, D. (1997). Contrast masking eVects change with practice. Vision Research, 37, 1725–1733. Finney, D. J. (1971). Probit analysis (3rd ed.). London: Cambridge University Press. Foley, J. (1994). Human luminance pattern-vision mechanisms: masking experiments require a new model. Journal of the Optical Society of America A, 11, 1710–1719. Foley, J., & Chen, C. (1997). Analysis of the eVect of pattern adaptation on pattern pedestal eVects: a two-process model. Vision Research, 37, 2779–2788. Foley, J. M., Varadharajan, S., Koh, C. C., & Farias, C. Q. (2007). Detection of gabor patterns of diVerent sizes, shapes, phases and eccentricities. Vision Research, 47, 85–107. Georgeson, M. A. (1980). The perceived spatial frequency, contrast, and orientation of illusory gratings. Perception, 9, 695–712. Georgeson, M. A., & Georgeson, J. M. (1987). Facilitation and masking of brieXy presented gratings—time-course and contrast dependence. Vision Research, 27, 369–379. Georgeson, M. A., & Meese, T. S. (2004). Contrast discrimination and pattern masking: contrast gain control with Wxed additive noise. Perception, 33, 754–755. Greenlee, M. W., & Magnussen, S. (1988). Interactions among spatial-frequency and orientation channels adapted concurrently. Vision Research, 28, 1303–1310. Harvey, L. O., & Doan, V. V. (1990). Visual masking at diVerent polar angles in the two-dimensional Fourier plane. Journal of the Optical Society of America A, 7, 116–127. Heeger, D. (1992). Normalization of cell responses in cat striate cortex. Visual Neuroscience, 9, 181–197. Holmes, D. J., & Meese, T. S. (1999). Simultaneous masking by plaids and gratings: threshold elevation and threshold facilitation. Perception, 28(Suppl.), 88.
Holmes, D. J., & Meese, T. S. (2004). Grating and plaid masks indicate linear summation in a contrast gain pool. Journal of Vision, 4, 1080– 1089. Huang, P. C., Hess, R. F., & Dakin, S. C. (2006). Flank facilitation and contour integration: diVerent sites. Vision Research, 46, 3699–3706. Kingdom, F. A. A., & Whittle, P. (1996). Contrast discrimination at high contrasts reveals the inXuence of local light adaptation. Vision Research, 36, 817–829. Kontsevich, L. L., & Tyler, C. W. (1999). Nonlinearities of near-threshold contrast transduction. Vision Research, 39, 1869–1880. Legge, G., & Foley, J. (1980). Contrast masking in human vision. Journal of the Optical Society of America A, 70, 1458–1471. Legge, G. E., Kersten, D., & Burgess, A. E. (1987). Contrast discrimination in noise. Journal of the Optical Society of America A, 4, 391–404. Meese, T. S., & Holmes, D. J. (2007). Spatial and temporal dependencies of cross-orientation suppression in human vision. Proceedings of the Royal Society B, 274, 127–136. Meese, T. S., Georgeson, M. A., & Baker, D. H. (2006). Binocular contrast vision at and above threshold. Journal of Vision, 6, 1224–1243. Meese, T. S., & Hess, R. F. (2004). Low spatial frequencies are suppressively masked across spatial scale, orientation, Weld position, and eye of origin. Journal of Vision, 4, 843–859. Meese, T. S., Hess, R. F., & Williams, C. B. W. (2001). Spatial coherence does not aVect contrast discrimination for multiple Gabor stimuli. Perception, 30, 1411–1422. Meese, T.S., Summers, R.J., Holmes, D.J., & Wallis, S.A. (2007). Contextual modulation involves suppression and facilitation from the centre and the surround. Journal of Vision, in press. Nachmias, J., & Weber, A. (1975). Discrimination of simple and complex gratings. Vision Research, 15, 217–223. Pelli, D. G. (1985). Uncertainty explains many aspects of visual contrast detection and discrimination. Journal of the Optical Society of America A, 2, 1508–1532. Pelli, D. G. (1987). On the relation between summation and facilitation. Vision Research, 27, 119–123. Petrov, Y., Verghese, & McKee (2006). Collinear facilitation is largely uncertainty reduction. Journal of Vision, 6, 170–178. Phillips, G. C., & Wilson, H. R. (1984). Orientation bandwidths of spatial mechanisms measured by masking. Journal of the Optical Society of America A, 1, 226–232. Pointer, J. S., & Hess, R. F. (1989). The contrast sensitivity gradient across the human visual-Weld—with emphasis on the low spatial-frequency range. Vision Research, 29(9), 1133–1151. Polat, U., & Sagi, D. (1993). Lateral interactions between spatial channels: suppression and facilitation revealed by lateral masking experiments. Vision Research, 33, 993–999. Robson, T. (1999). In R. H. S. Carpenter & J. G. Robson (Eds.), Vision Research: A Practical Guide to Laboratory Methods (pp. 81–105). Oxford: Oxford University Press. Robson, J. G., & Graham, N. (1981). Probability summation and regional variation in contrast sensitivity across the visual-Weld. Vision Research, 21(3), 409–418. Shani, R., & Sagi, D. (2005). Eccentricity eVects on lateral interactions. Vision Research, 45, 2009–2024. Solomon, J. A., & Morgan, M. J. (2000). Facilitation from collinear Xanks is cancelled by non-collinear Xanks. Vision Research, 40, 279– 286. Solomon, J. A., Watson, A. B., & Morgan, M. J. (1999). Transducer model produces facilitation from opposite-sign Xanks. Vision Research, 39, 987–992. Stromeyer, C. F., & Klein, S. A. (1974). Spatial frequency channels in human vision as asymmetric (edge) mechanisms. Vision Research, 14, 1409–1420. Tjan, B. S., & Nandy, A. S. (2006). ClassiWcation images with uncertainty. Journal of Vision, 6, 387–413. Tolhurst, D. J., & BarWeld, L. P. (1978). Interactions between spatial-frequency channels. Vision Research, 18, 951–958.
T.S. Meese et al. / Vision Research 47 (2007) 1112–1119 Tyler, C. W., & Chen, C. C. (2000). Signal detection theory in the 2AFC paradigm: attention, channel uncertainty and probability summation. Vision Research, 40, 3121–3144. Williams, C. B., & Hess, R. F. (1998). Relationship between facilitation at threshold and suprathreshold contour integration. Journal of the Optical Society of America A, 15, 2046–2051. Wilson, H. R. (1980). A transducer function for threshold and suprathreshold human-vision. Biological Cybernetics, 38, 171–178.
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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. Yu, C., Klein, S. A., & Levi, D. M. (2002). Facilitation of contrast detection by cross-oriented surround stimuli and its psychophysical mechanism. Journal of Vision, 2, 243–255. Zenger, B., & Sagi, D. (1996). Isolating excitatory and inhibitory nonlinear spatial interactions involved in contrast detection. Vision Research, 36, 2497–2513.
Remote facilitation in the Fourier domain Tim S. Meese ¤, David J. Holmes, Kirsten L. Challinor School of Life and Health Sciences, Aston University, Birmingham B47ET, UK Received 27 September 2006; received in revised form 4 November 2006
Abstract To explore spatial interactions between visual mechanisms in the Fourier domain we measured detection thresholds for vertical and horizontal sine-wave gratings (4.4 deg diameter) over a range of spatial frequencies (0.5–23 c/deg) in the presence of grating and plaid masks with component contrasts of 8%, orientations of §45° and a spatial frequency of 1 c/deg. The mask suppressed the target grating over a range of §1 octave, and the plaid produced more suppression than the grating, consistent with summation of mask components in a broadly tuned contrast gain pool. At greater diVerences in spatial frequency (»3 octaves), the plaid and grating masks both produced about 3 dB of facilitation (they reduced detection thresholds by a factor of about F2). At yet further distances (»4 octaves) the masks had no eVect. The facilitation cannot be attributed to a reduction of uncertainty by the mask because (a) it occurs for mask components that have very diVerent spatial frequencies and orientations from the test and (b) the large stimulus size and central Wxation point mean there was no spatial uncertainty that could be reduced. We suggest the results are due to long-range sensory interactions (in the Fourier domain) between mask and test-channels. The eVects could be due to either direct facilitation or disinhibition. © 2006 Elsevier Ltd. All rights reserved. Keywords: Contrast gain control; Psychophysics; Attention; Masking; Human vision
1. Introduction Masking is the phenomenon whereby the presence of one stimulus (the mask) impedes the detectability or response to a second stimulus (the test, or target), and it is usually attributed to suppression between mask and test mechanisms (see Meese & Holmes, 2007 for a recent short review). Facilitation is said to occur when the mask enhances the detectability or response to the test stimulus. At contrast detection threshold, facilitation has been found between patches of mask and test grating that diVer in spatial position (Chen & Tyler, 2001; Huang, Hess, & Dakin, 2006; Petrov, Verghese, & McKee, 2006; Polat & Sagi, 1993; Solomon & Morgan, 2000; Solomon, Watson, & Morgan, 1999; Williams & Hess, 1998), spatial frequency (Georgeson & Georgeson, 1987; Stromeyer & Klein, 1974; Tolhurst & BarWeld, 1978), orientation (Meese & Holmes, 2007; Meese, Summers, Holmes, & Wallis, 2007; Zenger & Sagi, *
Corresponding author. Fax: +44 121 333 4220. E-mail address: [email protected] (T.S. Meese).
0042-6989/$ - see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2006.11.010
1996) and combinations of two (Chen & Tyler, 2002; Meese et al., 2007; Yu, Klein, & Levi, 2002) or three of these parameters (Meese & Hess, 2004; Meese et al., 2007). However, most of these studies have concentrated on a fairly narrow range of spatial frequencies and so the full extent of interactions in the Fourier domain is not known. To build a more complete picture of these interactions we report masking experiments for a greater range of diVerences between mask and test spatial frequency than has been done in most previous studies. In particular, we were interested in conditions where we anticipated that the test grating would be detected by a mechanism that was not excited by the mask. 2. Methods 2.1. Equipment Stimuli were displayed on a Sony Trinitron Multiscan monitor with a frame rate of 120 Hz using a VSG2/3 stimulus generator operating in pseudo 12-bit mode and controlled by a PC. Mean luminance of the central display region was 65 cd/m2. The display was gamma corrected to ensure linearity
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over the full contrast range, and a frame interleaving technique (60 Hz per image) allowed the contrasts of the mask (grating or plaid) and test grating to be varied independently using lookup tables. A chin- and head-rest were used to help observers hold Wxation, and viewing was binocular.
2.2. Observers Four observers performed the main experiment. These were DJH (one of the authors) and three volunteers. Two of these were psychophysics graduate students (ADP & RJS) and one was a graduate student from another scientiWc discipline (JFT). The facilitation that we found for DJH was unexpected, and the other three observers were not made aware of this Wnding. To become practiced at the task and familiar with the stimuli, DJH performed three complete experimental runs (»10,800 trials) before formal data collection began. The other three observers performed a sub-sample of conditions and one complete run (»1200 trials) as practice. For all observers results are means and standard errors from Wve experimental runs. A series of further experiments designed as controls and to test the generality of our Wndings (described in Section 3) was performed by DJH only.
2.3. Stimuli All stimuli were stationary sine-wave gratings or two-component plaids the were windowed by a circular raised-cosine envelope. The central plateau of this envelope was 4.1° in diameter and the half-height, full-width of the envelope was 4.4°. The gratings were in sine-phase with a central dark Wxation point (2 pixels square) that was visible throughout the experiment. The spatial frequency of the mask was always 1 c/deg. The spatial frequency of the test was varied over the range 0.5–23 c/deg. There were two types of mask: a grating mask had an orientation of ¡45° (left oblique) and a plaid mask had component orientations of §45°. The orientation of the test grating was typically vertical, though in one experiment it was horizontal and in another it varied between vertical and ¡45°. Examples of 1 c/deg grating and plaid masks and a 5.7 c/deg test grating are shown in Fig. 1. Stimulus contrast is expressed as the Michelson contrast of the carrier in percent. In most experiments the masks (both plaids and gratings) had component contrasts of 8%. Because of the frame interleaving (see above) this was achieved by alternating between 16% in the mask frame and 0% in the test frame. Thus, to generate a plaid where each component had a contrast of 8% in the time averaged image, the overall contrast of the plaid in the mask frame was 32%.
Fig. 2. Threshold elevation (20 times the log10 ratio of detection thresholds with and without the mask) for grating and plaid masks (diVerent symbols) as functions of spatial frequency (SF). The spatial frequency of the mask was 1 c/deg. Error bars (in this and all other Wgures) show §1 SE of the threshold elevation distribution (n D 5) at each point. This incorporates the error measures for both the masked and unmasked thresholds. This Wgure represents results from about 18,000 trials. the correctness of response. The two intervals (100 ms each) were marked by short tones at their onset. The duration between the oVset of the Wrst interval and the onset of the second interval was 500 ms. A ‘three-down, one-up’ randomly interleaved staircase procedure was used to control the magnitude of the target contrast in logarithmic steps. A pair of interleaved staircases were used for each condition and terminated after 12 reversals each. The staircases were used only to determine stimulus placement. Threshold and its standard error (SE) were estimated using probit analysis (Finney, 1971) to calculate the 75% correct point on the psychometric function and its standard error (SE). This gave estimates based on about 100 trials for each experimental run. In the rare cases where the estimated SE was greater than 3 dB, these data were rejected and the experimental session was rerun. Experimental trials were interleaved across mask type (no mask, grating mask and plaid mask) and blocked across test spatial frequency. Threshold elevation is expressed in dB, equal to 20 times the log10 ratio of the detection thresholds with and without the mask. This was derived from approximately 1000 trials for each point (500 trials with the mask and 500 trials without the mask).
2.4. Procedure A temporal two-interval forced-choice (2IFC) technique was used where observers indicated which of the two intervals contained the target using one of two mouse buttons. The computer determined the temporal interval that contained the target randomly and auditory feedback was used to indicate
3. Results and discussion Results are shown for DJH in Fig. 2. When the test grating has a similar spatial frequency to the mask (1 c/deg),
Fig. 1. High contrast examples of stimuli used in the experiments. (A) 1 c/deg plaid mask, (B) 1 c/deg grating mask, and (C) 5.7 c/deg test grating. Note that the grating and plaid masks have the same component contrast (8% in most experiments) and therefore diVerent overall contrasts (the Michelson contrast of the plaid is twice that of the grating).
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12
18
Mask grating (-45°) Mask plaid (±45°) Mask component contrast = 8%
Threshold elevation (dB)
Mask SF
18
6
0 -6
ADP
Vertical test Horizontal test
12
Vertical test (Fig 2) Mask component contrast = 8%
6 0 -6
DJH 1
3
10
SF of vertical test grating (c/deg)
18
Threshold elevation (dB)
Mask plaid
Mask SF
Fig. 4. EVects of practice and test orientation on masking by a plaid for DJH. Open symbols are for the same vertical test grating. The circular symbols are replotted from Fig. 2 and are for experimental sessions performed before those for the square symbols. This Wgure represents results from about 30,000 trials.
12
6
0
JFT -6
18 12
6 0
RJS -6 1
3
10
SF of vertical test grating (c/deg) Fig. 3. The same as Fig. 2, but for three diVerent observers and fewer test spatial frequencies. This Wgure represents results from about 6000 trials for each observer.
threshold elevation occurs and is much greater for the plaid mask than for the grating mask. This has been found before when plaid and grating masks had the same spatial frequency as the test (Derrington & Henning, 1989). At higher test spatial frequencies (»5.7 c/deg) masking from both types of mask gives way to a region of facilitation of about 3 dB. The eVect is tuned, since it diminishes at higher spatial frequencies. The same experiment was performed on three other observers but for a more restricted set of test spatial frequencies (Fig. 3). The main eVects are replicated by all three observers: at a test spatial frequency of 1 c/deg, the plaid produces considerably more masking than does the grating, but at higher test spatial frequencies (»4 to 8 c/deg) both masks produce small levels of facilitation (»3 dB). Taken with the results from DJH, there is a suggestion that facilitation is stronger for the plaid than for the grating, though the eVect is small.
Fig. 4 shows further results for DJH who repeated the experiment using only the plaid mask, but for vertical and horizontal orientations of the test grating measured in diVerent experimental blocks (square symbols). Masking is less for the vertical grating than for the horizontal grating. However, the open circular symbols, replotted from the earlier experimental sessions in Fig. 2, show that this diVerence is probably due to a decrease in masking with practice for the vertical condition. Zenger and Sagi (1996) and Dorais and Sagi (1997) found similar orientation-speciWc eVects of practice for the cross-orientation masking measured in their experiments. The level of facilitation is the same for both orientations of the test grating and unlike masking, does not change with practice, at least for this observer. However, the main reason for repeating the experiment with horizontal gratings was to test a concern about adjacent pixel nonlinearity. This is a property of CRT raster monitors (Robson, 1999) and can have the eVect of reducing the local mean luminance of vertical high spatial frequency gratings. However, the similarity between the results for horizontal and vertical gratings (square symbols) at high spatial frequencies indicates that this is not a factor here. Next, we investigated whether the facilitation was speciWc to the 45° orientation diVerence between the mask and test components used so far. Threshold elevation was measured for a two-octave range of Wve test spatial frequencies at each of 10 diVerent test orientations (0–45° in 5° steps) as shown in Fig. 5A. The mask was always a 1 c/deg grating with an orientation of ¡45° and a contrast of 8%. In all cases we found masking at the lower spatial frequencies and facilitation of about 3 dB at the higher spatial frequencies. The spatial frequency at which masking gives way to facilitation (determined by linear interpolation of the masking functions) is shown in Fig. 5B. As the mask and test orientations become more similar, the region of facilitation moves closer to the mask spatial frequency. When the mask and test have the same orientation, facilitation occurs for
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spatial frequency diVerences as small as one octave.1 This is consistent with previous work that has found facilitation from masks with the same orientation as the test grating and contrasts well above their own detection threshold (e.g. Nachmias & Weber, 1975; Georgeson & Georgeson, 1987; Stromeyer & Klein, 1974; Tolhurst & BarWeld, 1978). Thus, our study here extends the results of previous work by showing that facilitation can be found for a wider range of orientation and spatial frequency diVerences than had previously been thought. Whether the results in Fig. 5 represent a single process that operates over a continuum in Fourier space, or two or more distinct processes that operate in diVerent regions, is not clear. Finally, we investigated the eVect of mask contrast on facilitation for a test spatial frequency of 5.7 c/deg. For component contrasts of 12%, 14%, 16% and 24%, the level of facilitation was the same for grating and plaid masks and was no greater than that seen in the previous experiments (»3 dB). For a component contrast of 8% we conWrmed that facilitation was greater for the plaid than for the grating (see Figs. 2 and 3). This suggests a facilitatory process that saturates at an overall mask contrast of around 12%, at least for DJH. 4. General discussion We have presented evidence for facilitation from 1 c/deg mask components on test gratings around 2.5 octaves higher in spatial frequency and with orientation diVerences of up to 45°. These eVects would have been missed in several previous masking studies because those that have used test spatial frequencies in the range 4–8 c/deg have not typically used masks as low as 1 c/deg (Daugman, 1984; Derrington & Henning, 1989; Harvey & Doan, 1990; Wilson, McFarlane, & Phillips, 1983; though see Bowen & Wilson, 1994). 4.1. A luminance artefact? Before discussing possible causes of facilitation we Wrst consider a possible artefact. Our sine-phase grating and plaid masks were presented simultaneously with the test stimulus, both for 100 ms. Thus, there were ‘dark’ regions in the image where the local luminance was less than the mean luminance of 65 cd/m2 by c%, where c is the overall contrast of the mask. Therefore, the physical contrast of a high frequency test grating in the ‘dark’ regions would approach a contrast that is a factor of 100/(100 ¡ c) higher than its nominal value. If this were the eVective contrast of the test grating available to the detection process (Bowen & Wilson, 1994), then when expressed relative to mean luminance 1 In this experiment the orientations of the mask and test gratings were the same and the contrast of the mask was 8%. It is well known that when the mask has much lower contrast—around its own detection threshold— facilitation occurs when the mask and test have the same spatial frequency and orientation (e.g. Legge & Foley, 1980).
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(as it was in the experiments) we should expect facilitation of »0.72 and »1.5 dB for c D 8%, and c D 16%, respectively. However, these artefacts are notably less than the maximum experimental eVects for the grating mask (c D 8%) in Figs. 2, 3 and 5, and the plaid masks (c D 16%) in Fig. 4, where facilitation typically reached »3 dB. Furthermore, retinal inhomogeneity (Pointer & Hess, 1989) and a dark adaptation process that takes about 150 ms to saturate (Bowen & Wilson, 1994; Crawford, 1947; Kingdom & Whittle, 1996) are both likely to decrease the size of the eVects possible through this route. Finally, if this were a substantial contributing factor to the facilitation in our experiments, then facilitation should have increased markedly with mask contrast. It did not: the empirical eVects saturated at a contrast of about 12%. 4.2. Three causes of facilitation As we outlined in Section 1, facilitatory eVects have been found in other types of masking experiment, but there is disagreement about their cause. Three candidate processes have been proposed: (i) within-channel excitation from the mask (Legge & Foley, 1980; Solomon et al., 1999; Williams & Hess, 1998; Zenger & Sagi, 1996); (ii) reduction of uncertainty by the mask (Petrov et al., 2006; Williams & Hess, 1998) and (iii) sensory interactions between mask and test mechanisms (Chen & Tyler, 2001, 2002; Meese et al., 2007; Polat & Sagi, 1993). The Wrst account requires that the mask and test both fall within the receptive Weld of a common mechanism with an accelerating output nonlinearity or hard threshold. This seems plausible in the situation where a test patch is placed between two co-oriented Xankers (Solomon et al., 1999) or is superimposed and has a similar spatial frequency and orientation to the mask (Zenger & Sagi, 1996), but is much less likely when the mask and test diVer substantially in spatial frequency and orientation. This ‘within-channel’ hypothesis can be easily tested because in general, the linearizing eVects of excitation by the mask should reduce the slope of the psychometric function to a Weibull » 1.3 (Bird, Henning, & Wichmann, 2002; Georgeson & Meese, 2004; Meese, Georgeson, & Baker, 2006; Pelli, 1985, 1987). However, the slope does not become this shallow for superimposed patches of mask and test grating with orthogonal orientations (Baker & Meese, 2006; Georgeson & Meese, 2004; Meese & Holmes, 2007) even though these stimuli can produce facilitation (Baker & Meese, 2006; Foley & Chen, 1997; Meese & Holmes, 2007; Meese et al., 2007). On the other hand, Petrov et al. (2006) found that Xanking patches do reduce the slope of the psychometric function for a central test patch. This might be taken to support the within-channel account of facilitation (Solomon & Morgan, 2000), but Petrov et al. also found the same eVect for a low contrast ring surrounding the target. Although withinchannel eVects could occur for this conWguration (Petrov et al. used a cosine-phase test stimulus), this seems unlikely, and other possibilities should be considered. The uncertainty hypothesis also predicts that the mask will reduce the slope of the psychometric function (Pelli, 1985; Tyler & Chen, 2000),
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Fig. 5. Masking and facilitation for a range of orientation diVerences between mask and test gratings. (A) Each plot shows a masking function for the orientation diVerence in the inset. Note that the Wve test spatial frequencies are not the same in each plot. (B) The diVerence between mask and test spatial frequencies (in octaves) for which masking gives way to facilitation, as a function of the orientation diVerence between mask and test gratings. Note that the results for an orientation diVerence of 15° are omitted in this panel because of the ambiguity in the masking function (A). This Wgure represents results from about 45,000 trials.
(though not necessarily as low as » 1.3), and so this result has been taken to support the uncertainty hypothesis for rings and Xanker masks (Petrov et al., 2006). However, the situation is not straightforward. Huang et al. (2006) found that facilitation is abolished when the Xankers are presented to a diVerent eye from the test, and Meese and Hess (2004) found a similar result for cross-oriented annular masks. Furthermore, Huang et al. decoupled facilitation from a reduction in the slope of the psychometric function: their Xankers reduced the psychometric slope regardless of whether they were presented to the same or diVerent eyes from the test. In its simplest form, the third explanation of facilitation (sensory interactions) proposes that the mask increases the gain of the detecting mechanism, and this does not change the slope of the psychometric function (e.g. Dao, Lu, & Dosher, 2006). At Wrst glance this seems inconsistent with the experimental evidence that the psychometric slope is reduced by facilitation (Huang et al., 2006; Petrov et al., 2006). However, this eVect could arise for other reasons. For example, the psychometric function would ‘blur’ if the mask caused it to be nonstationary. This might happen if the mask caused Xuctuations in the observer’s attention or if the interaction between the mask and test Xuctuated owing to noise. 4.3. The slope of the psychometric function As outlined above, the slope of the psychometric function can provide valuable supplementary information in experiments on masking and facilitation. The experiments here were performed circa 1998, before we routinely saved those data, but we have performed similar (unpublished)
experiments since, in which vertical or horizontal test gratings were detected in the presence of plaids or oblique gratings. Those experiments included conditions in which the test and mask both had component spatial frequencies of 1 c/deg. Those conditions are of interest because we wondered whether the masking at low spatial frequencies (Figs. 2–4) might have involved excitation of the test mechanism by the mask (Phillips & Wilson, 1984; Wilson et al., 1983). In a ‘transient’ condition, both mask and test were temporally modulated by a single cycle of a 15 Hz square-wave pulse, the mask contrast was 40%, the orientation diVerence between mask and test was 40°, the observer was DJH and all conditions were blocked. In this case, threshold elevation was 16.6 dB and the psychometric functions had slopes2 of D 3.0 and D 3.4 with and without a mask, respectively. These estimates contrast with the much shallower slope of D 1.5 when the mask had the same orientation as the test: a result consistent with linearization of the test mechanism by the mask. In another condition the mask was a plaid (§45°) with component contrasts of 11% and stimulus duration was 100 ms (similar conditions to those used here). Threshold elevation was 15.5 and 18 dB for DJH 2 The slope of the psychometric function was estimated using probit analysis, assuming a cumulative log-normal form (approximated by a Wfth-order polynomial). The slope of this curve () is expressed in dB and was estimated independently for each experimental session (typically 100 trials each). Estimates of were then averaged across multiple sessions (typically 4 or 5) before converting to the more familiar Weibull using the approximation D 10.3/. This approximation was derived by performing a least squares Wt of a Weibull function to the cumulative log-normal over a range of §3.
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and TSM, respectively. Correspondingly, the slopes with a mask were D 3.0 and D 3.6, and without a mask were D 3.4 and D 3.3. Therefore, despite considerable levels of masking (up to a factor of »8) the slope of the psychometric function remained steep when the diVerence between mask and test orientations was 40° or greater.3 Thus, assuming that nonlinear contrast transduction is at least part of the reason for the steep psychometric function ( » 3.5) at detection threshold (Kontsevich & Tyler, 1999; Legge & Foley, 1980; Legge, Kersten, & Burgess, 1987; Wilson, 1980), this analysis implies that the masking was not due to excitation of a broadband test mechanism by the mask (Phillips & Wilson, 1984), but is consistent with a suppressive inXuence from the mask on the test mechanism (Foley, 1994; Meese & Hess, 2004). It seems very likely that the same it true of the masking in Figs. 2–4 here. We have not measured the slope of the psychometric function under conditions similar to those that have produced facilitation in the experiments here. However, we did record the slopes in cross-oriented masking experiments in which similar levels of facilitation (»3 dB) have been found (Baker, Meese, & Summers, 2007; Meese & Holmes, 2007; Meese et al., 2007). Our preliminary analysis suggests that this type of facilitation is associated with a modest decrease in the slope of the psychometric function, though there is much variability across observers and conditions. We are presently investigating this issue further. 4.4. What caused the facilitation here? We address what caused the facilitation seen in the experiments here by Wrst considering the uncertainty hypothesis in the context of the Wve dimensions of: temporal location, spatial location, orientation, spatial frequency, and spatial phase. Regardless of whether the mask was present, both 2IFC intervals were marked by auditory beeps and so it is unlikely that there was an appreciable reduction of temporal uncertainty by the mask. A central Wxation point was presented continuously and the test gratings had a large spatial extent of 4.4 deg. Thus, observers were well cued to the location of the stimulus on the monitor. Unlike the mask, the Wxation point did not indicate the spatial extent of the stimulus, but we think this is unlikely to be important for two reasons. First, ‘no-mask’ and ‘mask’ trials were randomly interleaved on a trial-by-trial basis meaning that observers were repeatedly reminded of the spatial extent of the target (because the mask and target were the same size). Second, the contribution to detection is less towards the grating’s extremities because sensitivity declines with distance from the Wxation point at a rate of about 0.5 deg per cycle (Foley, Varadharajan, Koh, & Farias, 2007; Pointer & Hess, 1989; Robson & Graham,
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1981). For example, for the stimulus in Fig. 1C, sensitivity to the outer region of the stimulus is about half that to the centre. In the main conWgurations where facilitation was measured, the grating mask provided no cue to test orientation and neither type of mask provided a cue to test spatial frequency. Furthermore, the central Wxation point is expected to have reduced phase uncertainty (the target and masks were always in sine-phase) to an extent at least equal to that available from the mask. In sum, it is very unlikely that the masks reduced either spatio-temporal uncertainty or uncertainty in the Fourier domain for the test gratings that exhibited facilitation here. But this does not rule out the involvement of uncertainty in other contexts (e.g. Tjan & Nandy, 2006). When uncertainty is increased experimentally it raises contrast detection and discrimination thresholds and increases the slope of the psychometric function at and above detection threshold (Meese, Hess, & Williams, 2001; Shani & Sagi, 2005). It remains possible that the facilitation produced by Xankers and rings also involves a reduction of uncertainty (Petrov et al., 2006). The facilitation found here is also inconsistent with subthreshold stimulation of the test-channel by the mask because the eVects occur at orientation and spatial frequency diVerences that are far too great to stimulate a single mechanism (Foley, 1994; Holmes & Meese, 2004), and psychometric functions are not linearized at these distances (Georgeson & Meese, 2004; Meese & Holmes, 2007). Furthermore, the Wnding that the spatial frequency at which facilitation occurred increased as the diVerence between mask and test orientation increased is also inconsistent with that account (Daugman, 1984). (Also see the previous subsection.) The remaining explanation of facilitation is that of sensory interactions, and this seems the most likely account for the results here. There are at least two ways in which this could occur. First there could be a pool of mechanisms that provides direct modulatory facilitation of the activity in the test mechanism. In that case, it is plausible that the facilitatory pool overlaps with the well-known suppressive pool (Heeger, 1992), but is hidden by suppression (Meese & Holmes, 2007) over much of its range. Second, it could be that the mask suppresses an intermediate mechanism, which causes it to release its standing level of suppression from the target mechanism. Similar proposals have been made for the facilitation (De Valois, 1977; Greenlee & Magnussen, 1988; Tolhurst & BarWeld, 1978) and hallucinated contours (Georgeson, 1980) that are experienced at remote spatial frequencies and orientations during and after adaptation. Acknowledgments
3 In fact, a more complete analysis (to be presented elsewhere) shows that there is very little change in the slope of the psychometric function for orientation diVerences as small as 20° when mask and test spatial frequency are both 1 or 3 c/deg.
This work was supported partially by a grant from the Engineering and Physical Sciences Research Council (GR/ S74515/01) awarded to Tim Meese and Mark Georgeson.
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Some of this work Wrst appeared in abstract form in Holmes and Meese (1999). We thank Mark Georgeson for discussion about potential causes of facilitation. We also thank two anonymous referees for their thoughtful comments. References Baker, D. H., & Meese, T. S. (2006). Cross-orientation suppression occurs before binocular summation: evidence from masking and adaptation. Journal of Vision, 6, 821a. Baker, D. H., Meese, T. S., & Summers, R. J. (2007). Psychophysical evidence for two routes to suppression before binocular summation of signals in human vision. Neuroscience under review. Bird, C. M., Henning, G. B., & Wichmann, F. A. (2002). Contrast discrimination with sinusoidal gratings of diVerent spatial frequency. Journal of the Optical Society of America A, 19, 1267–1273. Bowen, R. W., & Wilson, H. R. (1994). A two-process analysis of pattern masking. Vision Research, 34, 645–657. Chen, C.-C., & Tyler, C. W. (2001). Lateral sensitivity modulation explains the Xanker eVect in contrast discrimination. Proceedings of the Royal Society B, 268, 509–516. Chen, C. C., & Tyler, C. W. (2002). Lateral modulation of contrast discrimination: Xanker orientation eVects. Journal of Vision, 2, 520–530. Crawford, B. H. (1947). Visual adaptation in relation to brief conditioning stimuli. Proceedings of the Royal Society B, 134, 283–302. Dao, D. Y., Lu, Z.-L., & Dosher, B. A. (2006). Adaptation to sine-wave gratings selectively reduces the contrast gain of the adapted stimuli. Journal of Vision, 6, 739–759. Daugman, J. G. (1984). Spatial visual channels in the Fourier plane. Vision Research, 9, 891–910. Derrington, A. M., & Henning, G. B. (1989). Some observations on the masking eVects of two-dimensional stimuli. Vision Research, 29, 241–246. De Valois, K. K. (1977). Spatial frequency adaptation can enhance contrast sensitivity. Vision Research, 23, 249–256. Dorais, A., & Sagi, D. (1997). Contrast masking eVects change with practice. Vision Research, 37, 1725–1733. Finney, D. J. (1971). Probit analysis (3rd ed.). London: Cambridge University Press. Foley, J. (1994). Human luminance pattern-vision mechanisms: masking experiments require a new model. Journal of the Optical Society of America A, 11, 1710–1719. Foley, J., & Chen, C. (1997). Analysis of the eVect of pattern adaptation on pattern pedestal eVects: a two-process model. Vision Research, 37, 2779–2788. Foley, J. M., Varadharajan, S., Koh, C. C., & Farias, C. Q. (2007). Detection of gabor patterns of diVerent sizes, shapes, phases and eccentricities. Vision Research, 47, 85–107. Georgeson, M. A. (1980). The perceived spatial frequency, contrast, and orientation of illusory gratings. Perception, 9, 695–712. Georgeson, M. A., & Georgeson, J. M. (1987). Facilitation and masking of brieXy presented gratings—time-course and contrast dependence. Vision Research, 27, 369–379. Georgeson, M. A., & Meese, T. S. (2004). Contrast discrimination and pattern masking: contrast gain control with Wxed additive noise. Perception, 33, 754–755. Greenlee, M. W., & Magnussen, S. (1988). Interactions among spatial-frequency and orientation channels adapted concurrently. Vision Research, 28, 1303–1310. Harvey, L. O., & Doan, V. V. (1990). Visual masking at diVerent polar angles in the two-dimensional Fourier plane. Journal of the Optical Society of America A, 7, 116–127. Heeger, D. (1992). Normalization of cell responses in cat striate cortex. Visual Neuroscience, 9, 181–197. Holmes, D. J., & Meese, T. S. (1999). Simultaneous masking by plaids and gratings: threshold elevation and threshold facilitation. Perception, 28(Suppl.), 88.
Holmes, D. J., & Meese, T. S. (2004). Grating and plaid masks indicate linear summation in a contrast gain pool. Journal of Vision, 4, 1080– 1089. Huang, P. C., Hess, R. F., & Dakin, S. C. (2006). Flank facilitation and contour integration: diVerent sites. Vision Research, 46, 3699–3706. Kingdom, F. A. A., & Whittle, P. (1996). Contrast discrimination at high contrasts reveals the inXuence of local light adaptation. Vision Research, 36, 817–829. Kontsevich, L. L., & Tyler, C. W. (1999). Nonlinearities of near-threshold contrast transduction. Vision Research, 39, 1869–1880. Legge, G., & Foley, J. (1980). Contrast masking in human vision. Journal of the Optical Society of America A, 70, 1458–1471. Legge, G. E., Kersten, D., & Burgess, A. E. (1987). Contrast discrimination in noise. Journal of the Optical Society of America A, 4, 391–404. Meese, T. S., & Holmes, D. J. (2007). Spatial and temporal dependencies of cross-orientation suppression in human vision. Proceedings of the Royal Society B, 274, 127–136. Meese, T. S., Georgeson, M. A., & Baker, D. H. (2006). Binocular contrast vision at and above threshold. Journal of Vision, 6, 1224–1243. Meese, T. S., & Hess, R. F. (2004). Low spatial frequencies are suppressively masked across spatial scale, orientation, Weld position, and eye of origin. Journal of Vision, 4, 843–859. Meese, T. S., Hess, R. F., & Williams, C. B. W. (2001). Spatial coherence does not aVect contrast discrimination for multiple Gabor stimuli. Perception, 30, 1411–1422. Meese, T.S., Summers, R.J., Holmes, D.J., & Wallis, S.A. (2007). Contextual modulation involves suppression and facilitation from the centre and the surround. Journal of Vision, in press. Nachmias, J., & Weber, A. (1975). Discrimination of simple and complex gratings. Vision Research, 15, 217–223. Pelli, D. G. (1985). Uncertainty explains many aspects of visual contrast detection and discrimination. Journal of the Optical Society of America A, 2, 1508–1532. Pelli, D. G. (1987). On the relation between summation and facilitation. Vision Research, 27, 119–123. Petrov, Y., Verghese, & McKee (2006). Collinear facilitation is largely uncertainty reduction. Journal of Vision, 6, 170–178. Phillips, G. C., & Wilson, H. R. (1984). Orientation bandwidths of spatial mechanisms measured by masking. Journal of the Optical Society of America A, 1, 226–232. Pointer, J. S., & Hess, R. F. (1989). The contrast sensitivity gradient across the human visual-Weld—with emphasis on the low spatial-frequency range. Vision Research, 29(9), 1133–1151. Polat, U., & Sagi, D. (1993). Lateral interactions between spatial channels: suppression and facilitation revealed by lateral masking experiments. Vision Research, 33, 993–999. Robson, T. (1999). In R. H. S. Carpenter & J. G. Robson (Eds.), Vision Research: A Practical Guide to Laboratory Methods (pp. 81–105). Oxford: Oxford University Press. Robson, J. G., & Graham, N. (1981). Probability summation and regional variation in contrast sensitivity across the visual-Weld. Vision Research, 21(3), 409–418. Shani, R., & Sagi, D. (2005). Eccentricity eVects on lateral interactions. Vision Research, 45, 2009–2024. Solomon, J. A., & Morgan, M. J. (2000). Facilitation from collinear Xanks is cancelled by non-collinear Xanks. Vision Research, 40, 279– 286. Solomon, J. A., Watson, A. B., & Morgan, M. J. (1999). Transducer model produces facilitation from opposite-sign Xanks. Vision Research, 39, 987–992. Stromeyer, C. F., & Klein, S. A. (1974). Spatial frequency channels in human vision as asymmetric (edge) mechanisms. Vision Research, 14, 1409–1420. Tjan, B. S., & Nandy, A. S. (2006). ClassiWcation images with uncertainty. Journal of Vision, 6, 387–413. Tolhurst, D. J., & BarWeld, L. P. (1978). Interactions between spatial-frequency channels. Vision Research, 18, 951–958.
T.S. Meese et al. / Vision Research 47 (2007) 1112–1119 Tyler, C. W., & Chen, C. C. (2000). Signal detection theory in the 2AFC paradigm: attention, channel uncertainty and probability summation. Vision Research, 40, 3121–3144. Williams, C. B., & Hess, R. F. (1998). Relationship between facilitation at threshold and suprathreshold contour integration. Journal of the Optical Society of America A, 15, 2046–2051. Wilson, H. R. (1980). A transducer function for threshold and suprathreshold human-vision. Biological Cybernetics, 38, 171–178.
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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. Yu, C., Klein, S. A., & Levi, D. M. (2002). Facilitation of contrast detection by cross-oriented surround stimuli and its psychophysical mechanism. Journal of Vision, 2, 243–255. Zenger, B., & Sagi, D. (1996). Isolating excitatory and inhibitory nonlinear spatial interactions involved in contrast detection. Vision Research, 36, 2497–2513.