Biology Essays - Psychophysical Phenomenon called Masking

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Psychophysical Phenomenon called Masking

Many studies of human pattern vision have concerned a psychophysical phenomenon called masking. In general, masking commonly refers to the “…interference among transient stimuli that are closely coupled in space or time” (Legge & Foley, 1980). In a masking paradigm, this means that when one stimulus (the mask) interferes with the detectability of another stimulus (the test), masking, or suppression, is said to occur (Meese & Hess, 2005). Such masking paradigms have been used by many studies to provide key insights into the characteristics of visual mechanisms which process image information (Meese & Holmes 2002). One commonly known example of this phenomenon in masking literature is where the detection threshold of a test sine-wave grating is elevated in the presence of a superimposed mask (another sine-wave grating), which is sufficiently similar to the test (Meese & Holmes, 2002). In 1980 Legge and Foley obtained detection thresholds of a test grating in the presence of such a mask, known as a pedestal, and are measured as a function of mask contrast using contrast discrimination methods – producing a classic curve called a “dipper function”. They found masking at high levels of mask contrast, corresponding to the “dipper handle”, but found facilitation at low levels of mask contrast, corresponding to the “dipper” region of the curve respectively (Legge & Foley, 1980 quoted by Meese& Holmes, 2002). As the mask is a pedestal, this type of masking is known as within-channel masking (Meese & Hess, 2005). Early models used to describe this type of masking involve the mask stimulating the same detecting mechanism as the test, causing a reduction in the signal-to-noise ratio of the observer either by compressing the detecting mechanism response or by raising the noise level (Legge & Foley, 1980; Wilson, 1980). Legge and Foley’s (1980) model incorporated a non-linear response function on the output of the detecting mechanism (Foley, 1994). This single pathway model, known as model 1, has the following form:

R = Cp / (Cq + Zq)(1)

Where R is the response of the non-linearity, C is the excitation of the detecting mechanism (i.e. the output of spatially tuned filters) and p, q and Z are the constant parameters of the model (Foley, 1994). For low mask contrasts, the response is positively accelerated – for a constant change in C, ΔC, the change in R, ΔR, increases such that detection improves, caused by within-channel drive by the pedestal as it detected by the same mechanism (or pathway). For high mask contrasts, the response is negatively accelerated – for ΔC; ΔR decreases such that detection is more difficult, therefore accounting for within-channel masking (Foley, 1994).

More recently, many studies have shown that substantial masking also occurs when the mask spatial wave-form is very different to the detecting mechanism (Ross & Speed, 1991; Foley, 1994; Chen & Foley, 2004), such that the mask falls outside the range in which masking was generally thought to only occur - approximately ±1 octave of spatial frequency and ±30 deg in orientation (Meese and Hess, 2004). This is commonly referred to as pattern masking. In 1994 Foley found that his first model used to describe within-channel masking was insufficient for this finding, as his model implied that any change in the spatial wave-form of the mask could only result in a specific translation of the dipper function – the experimental data did not support these predictions (Foley, 1994). Importantly, as the mask is remote from the test, the masking data could not be attributed to Legge and Foley’s within-channel (single pathway) model (Meese & Holmes, 2002). Several explanations have been offered, notably that of cross-channel suppression, prompted by observations of cross-channel inhibition in the primary visual cortex (Morrone et al., 1982, 1987; Bonds, 1989). This model explains that this type of masking is due to inhibitory interactions amongst cross channel mechanisms that suppress the detecting mechanism’s response (Foley, 1994). Foley (1994) revised his first model and devised two new models, called model 2 and model 3 respectively, based upon previous gain control models that describe observations of neuronal activity in the visual cortex (Albrecht & Geisler, 1991; Heeger 1992, 1993). He found that model 3 provided a better fit than model 2 to the masking data produced from contrast discrimination experiments (Foley, 1994). Model 3 is such that the excitation produced by the detecting mechanism, in response to the test component is divisively inhibited (suppressed) by a collection of cross-channel interactions. These are produced by mechanisms that respond to the mask components, but also include a contribution from the detecting mechanism (Foley, 1994). This model is an extension of model 1, and can be expressed as:

R = Cp / [Zq + Σ (WiCqi)](2)

Where Wi is a weighted contribution to the inhibitory responses. Foley’s model 3 is described as a non-linear suppression model, as the inhibitory (suppressive) components of the mask were raised to an exponent (q) before summing the responses together (Holmes & Meese 2004). The contrast gain pool (or simply gain pool) is the name given to this collection of cross-channel mechanisms (or pathways, where i = 1: n) that also include a contribution from the detecting mechanism, which controls the response to contrast, leading to suppression (Meese & Holmes, 2002).

Meese and Holmes (2002) investigated the summing rule of mask (and test) components in the contrast gain pool and explored the possibility of developing an alternative model to one which Foley and Chen (1997) used to describe the effect of adaptation on the level of masking (Meese & Holmes, 2002). To do this, they compared the masking effects by measuring the detection thresholds of a vertical test grating in the presence of one (a grating) and two component masks (a plaid, composed of two superimposed gratings) that are spatially remote from the test, over a range of mask contrasts (Meese & Holmes 2002). Their experimental results revealed a key feature in that the masking (dipper) functions for both the grating and plaid masks were superimposed in an almost identical fashion, leading them to suggest that the sum of the mask component contrasts in the plaid mask was linear, contrary to predictions made by Foley’s model 3 - prompting them to interpret that most of the masking, if not all, is performed in the gain pool (Meese & Holmes, 2002). Based upon models that incorporated a linear summing feature (Ross & Speed, 1991; Foley, 1994; Olzak & Thomas, 1999), Meese and Holmes (2002) produced two new models that fitted their masking data whilst also addressing the effects of adaptation on masking – called the early adaptation model and hybrid model respectively (Meese & Holmes, 2002).

In an extension of this work, Holmes and Meese (2004) addressed what rules govern summation of stimulus components in the suppressive gain pool (Holmes & Meese, 2004). Using a pedestal plus masking paradigm, contrast discrimination thresholds of a test grating were measured in the presence of a fixed pattern mask (either a grating or plaid) and pedestal over a range of pedestal contrasts – importantly, the grating and plaid had the same overall mask contrast (Holmes and Meese, 2004). The rules of summation were assessed by directly comparing the fits of Foley’s model 2, model 3 and the hybrid model to the data. As observed in their earlier paper (Meese & Holmes, 2002), the masking functions produced sat almost exactly on top of each other for both pattern masks, indicating the sum of the plaid mask component contrasts is linear. Unsurprisingly, they found that Foley’s model 2 provided a very good fit to the data as the gain pool of this model allows for full linear summation of mask component contrast. Another key finding was the prevalence of a “dipper” region at low to mid levels of pedestal contrast – indicating that the masking is due to cross-channel suppression, as the within-channel excitatory drive that produces facilitation is available from the pedestal (Holmes and Meese, 2004).

From this review, several key points have emerged – that pattern masking is due to cross-channel suppression, not a within-channel process; and the summation of the suppressive components in the gain pool is linear. Of particular interest is the latter observation which has only been measured by previous experiments at detection threshold of a test stimulus (Meese & Holmes, 2002; Meese & Hess, 2004; Holmes & Meese, 2004). Since normal human vision operates well above detection threshold most, if not all of the time, we addressed this by performing contrast matching experiments. Here, the perceived contrast of a supra-threshold test is measured in the presence of one and two component pattern masks (grating and plaid stimuli) by matching the test to a standard stimulus, over a range of standard contrasts. Normal human vision also involves visual experience from both the fovea and periphery – where the foveal region provides high visual acuity and as such, the best vision. Despite the periphery having considerably reduced visual acuity relative to the fovea, it is important in guiding movements and providing human night vision respectively (REF). Again, those experiments that have measured linear summation have done so at the fovea (Meese & Holmes, 2002; Meese & Hess, 2004; Holmes & Meese, 2004). We extended this by performing the matching experiment at three different retinal eccentricities, including measures at the foveal region. In addition, conventional masking experiments (Meese & Holmes, 2002; Meese & Hess, 2004) are performed at these eccentricities to examine whether similar masking effects including linear summation, is observed both at and above detection threshold across the retina. Finally, we performed a control matching condition, where the contrast of the test stimulus without a superimposed pattern mask is matched to a central standard stimulus, allowing us to see how our perception of contrast varies with eccentricity independent of the masking. As Meese and Hess (2004) explained, comparison between the two experiments is possible if the mask and test stimuli are spatially remote (Meese & Hess, 2004).

Methods

Equipment

Both the detection and matching experiments were conducted in two labs, AA and PSB in the Man Ray Lab; BD and SP in the Monet Lab respectively. In the Man Ray lab, the stimuli were generated using Cambridge Research Systems (CRS) VSG 2/4, controlled by a PC. The stimuli were presented on an EIZO 553 monitor with a mean luminance of 58cdm-2. In the Monet lab, the stimuli were generated using ViSaGe, again controlled by a PC. The stimuli were presented on a Sony Trinitron Multiscan 20seII monitor, with a mean luminance of 68cdm-2. Both monitors were gamma corrected to ensure linearity over their entire ranges and both displays had dimensions of 512 × 512 pixels (18.5 × 18.5cm), where each pixel has a visual angle of 0.033 degrees. Frame interleaving of the mask and test stimuli resulted in a picture refresh rate of 60Hz for both monitors. A central fixation point of 0.038 degrees was always present on the screen. A distance of 63cm away from the display screen is comfortably maintained using a head and chin rest.

Observers

Four undergraduate optometry students completing for course credit, including myself served as observers for the two experiments. These were PSB (oneself), SP, AA and BD. All four observers were well versed in the experimental tasks and stimuli before data collection began, with approximately two hours of practice for each experiment. All observers had normal or optically corrected to normal vision.

Stimuli

All of the stimuli used are constructed from circular patches of sinusoidal gratings, spatially modulated by a raised cosine window (function), with a full width at half height of 4.95 degrees. The grating mask consists of one sinusoidal patch (one component) orientated at either -45 degrees or +45 degrees; the plaid mask consists of two sinusoidal patches (two components) superimposed on top of one another orientated at +/-45 degrees, such that they are tilted right and left respectively. Both the grating and plaid mask components have a fixed spatial frequency of 3 c/deg. The test stimulus consists of one sinusoidal patch which is vertically orientated and has a fixed spatial frequency of 1 c/deg. In the matching experiment, the standard stimulus is the same as the test but has a fixed level of contrast. High contrast example stimuli are shown below for clarity:

A) Test Stimulus B) +45° Grating C) -45° Grating D) ±45° Plaid

High contrast example stimuli to be used in both the detection and matching experiments. In the matching experiment, one interval contained both the test (A) and the mask (one of B, C or D with a fixed overall contrast of 48%) and the other interval contains the standard (same as A, but whose contrast is 4%, 8%, 16% or 32%). For the control condition, the mask has an overall contrast of 0%. The observer’s task is to determine in which interval the vertical grating has the highest contrast, where the level of test contrast is controlled by a 1-up 1-down staircase procedure. In the detection experiment, one interval contained both the test (A) and the mask (one of B, C or D with an overall contrast of 0%, 1%, 4%, 8%, 16%, 32% or 48%) and the other interval contains the mask alone. The observer’s task is to identify in which interval they detected the test, whose level of contrast is controlled by a 1-up 3-down staircase procedure.

Matching Experiment

Conditions

Matching contrasts of the test to the standard were obtained for both mask type conditions (the grating and plaid masks), presented at three different spatial locations over a range of standard stimulus contrasts. The three retinal eccentricities are defined as 0 degrees, 4 degrees and 8 degrees relative to the central fixation point in the left visual field. The different levels of standard contrast, Cs, are 4%, 8%, 16% and 32% respectively. The level of contrast is defined by Michelson contrast, expressed as:

C = 100 × [(Lmax – Lmin)/ (Lmax + Lmin)]

Where L is Luminance and C is Contrast. Alternatively, contrast is also expressed in decibels (dB), given by the equation: dB = 20log10(C). The two sinusoidal patches of the plaid mask (±45 deg) each have a fixed contrast of 24%, and the single sinusoidal patch in the grating masks (either +45 deg or -45 deg) have a fixed contrast of 48%. Therefore the overall contrast of both mask types is fixed at 48%. For the control condition, the mask has an overall contrast of 0% (i.e. no mask) and the standard is always presented at an eccentricity of 0 deg.

Procedure

Each observer was seated in a dark room (in their respective lab) and positioned using a head and chin rest 63cm away from the display screen, viewed binocularly. The matching contrast of the test stimulus to the standard stimulus is obtained using a 2IFC method. One interval contains both the test and mask (superimposed on top of one another); in the other interval only the standard is present. For the control condition, one interval contains the standard, always presented centrally, and the other interval contains the test alone. In each trial, the observer’s task is to determine in which interval the vertical grating (either the test or the standard) had the highest contrast whilst maintaining their gaze at the central fixation point. The level of test stimulus contrast is controlled using a 1-up 1-down staircase procedure for each level of standard contrast (Cs), such that each condition is measured by a pair of independent staircases (Wetherill & Levitt, 1965; Meese, 1995). The onset of each interval is signalled by an auditory tone and the duration of each interval is 100ms, separated by a time of 400ms. The observer indicates their response using a two button mouse, where the right hand mouse button corresponds to interval one and the left hand mouse button corresponds to interval two. No auditory feedback is given to the observer.

Detection Experiment

Conditions

Detection thresholds of the test stimulus are obtained for both mask type conditions (the grating and the plaid masks) presented at three different spatial locations over a range of overall mask contrasts. As for the matching experiment, the retinal eccentricities are 0 degrees, 4 degrees and 8 degrees relative to the central fixation point in the left visual field. The different levels of overall mask contrast, Co, are 0%, 1%, 4%, 8%, 16%, 32% and 48%. Again, contrast is defined by Michelson Contrast and is expressed in dB (see conditions for the matching experiment). The two sinusoidal patches of the plaid mask had contrasts that were half that of Co, and the grating mask, consisting of one sinusoidal patch, had contrast of Co. Therefore, both mask conditions had overall mask contrast equivalent to Co.

Procedure

Each observer was seated in a dark room (in their respective lab) and positioned using a head and chin rest 63cm away from the display screen, viewed binocularly. The detection threshold of the test stimulus is obtained using a two-interval forced choice (2IFC) technique - one interval contains both the mask and test, but the other contains the mask alone. In each trial, the observer’s task is to determine in which of the two intervals, presented in random order, they detected the test stimulus whilst maintaining their gaze on the central fixation point. The level of test stimulus contrast is controlled by a three-down one-up staircase procedure for each level of mask contrast (Co), such that each condition is measured by a pair of dependant staircases (Wetherill & Levitt, 1965; Meese, 1995). The onset of each interval is signalled by an auditory tone and the duration of each interval is 100ms, separated by a time of 400ms. The observer indicates their response using a two-button mouse, the right mouse button corresponding to interval one and the left mouse button corresponding to interval two. Auditory feedback is given to the observer depending on how the observer responds, with a different tone for either an incorrect and correct response.

Psychometric Functions and Order of Conditions

For all conditions, psychometric functions were measured using a pair of dependant staircases. For the detection experiment, a 1-up 3-down staircase procedure was employed, with an initial maximum step size of 10dB followed by a reduction in step size by a factor of 2 to a minimum step size of 2.5dB. For the matching experiment a 1-up 1-down staircase procedure was employed, with an initial maximum step size of 8dB followed by a reduction in step size by a factor of 2 to a minimum of 1dB for the matching experiment. The data from the last 12 effective reversals for both staircases for each condition was merged and fitted using probit analysis to find estimates of the threshold for the detection experiment and to find the point of subjective equality (PSE) for the matching experiment. For the detection experiment, detection threshold was taken at the 75% point on the psychometric function of each condition. For the matching experiment, the PSE was taken at the 50% point on the psychometric function of each condition.

For both experiments, the trials of each condition were fully blocked and the order of completion was randomized for each observer for each repetition. Two repetitions were performed by each observer for both the detection experiment (each repetition containing approximately 8400 trials), and the matching experiment (each repetition containing approximately 6000 trials), comprising a total of nearly 15 hours data collection. When the standard error (SE) of the fit to the data (obtained by probit analysis) was greater than 1.4 times the threshold, the data for that condition was discarded and the block was re-run – this criterion was set before data collection began in order to reduce the influence of unreliable threshold estimates (Holmes & Meese, 2004). In a fully counterbalanced design, the thresholds are averaged across mask type and orientation. As a result, the number of plaid conditions is doubled to ensure that the collapsed conditions had an equal number of trials in them. Similarly, the control condition is run four times. After collapsing, there were four estimates of the detection threshold for each data point based upon 2×100 trials, and four estimates of the PSE for each data point based upon 2×100 trials for the matching experiment.

  • EXTEND ALTERNATIVE MODELS WHERE CROSS-CHANNEL MASKING CAUSED BY AN INCREASE IN NOISE OF THE DETECTION MECHANISM INDUCED BY THE MASK: SEE MEESE AND HESS 2004
  • SHOW THAT CROSS-CHANNEL MASKING IS NOT ATTRIBUTED TO THE ABOVE PROCESS USING MEESE AND HESS’S (2004) PAPER
  • EXPLORE EXPLANATIONS AND EXAMPLES OF MECHANISMS IN THE BRAIN THAT INTERACT WITH EACH OTHER E.G) THOSE DESCRIBED BY MEESE AND HESS (2004) WHICH INVOLVE THE PROCESS OF GAIN CONTROL

Results

Matching Experiment

Data Trends

The results of the matching experiment for individual observers are shown in figures 2, 3 and 4, at each different retinal eccentricity respectively. Importantly, only good repetitions of each condition are included such that the standard error is within the limits set in the methods section. Repetitions that did fall outside the criterion were not repeated due to time constraints so the results are based on acceptable data only. Figure 5 shows the results averaged across observers. Consistent with previous matching experiments (Meese & Hess, 2004), the graph is unconventional in that the independent variable is plotted along the y-axis – such that the standard contrast is measured as a function of matching contrast (perceived contrast). The oblique line traversing each figure represents the veridical match i.e. for a particular standard contrast, the matching, or perceived contrast, is the same. Those data points that fall below this line mean that the test contrast must be raised to be perceived the same contrast as the standard, implying suppression of the test by the mask. Those data points that lie above this line imply the contrast of the test must be lower than the standard contrast to be perceived as the same, implying facilitation by the mask. These concepts of suppression and facilitation are consistent with the cross-channel account of masking outlined earlier.

Contrast matching functions shown for all observers measured at an eccentricity of 0 degrees, where observations for AA, BD, PSB and SP are shown in plots 2 A, B, C and D respectively. The contrast of a 1 c/deg test grating in the presence of a superimposed 3 c/deg pattern mask is matched to a 1 c/deg standard grating. The mask is either a grating (red symbols, dashed line) or a plaid (blue symbols, solid line). For the control condition, the test, without a superimposed mask, is matched to a central standard grating (data represented by yellow symbols, dashed line). The data includes only those repetitions that fell within the rejection criterion where the standard errors (SE) of these measures were less than 1.4 times less than the corresponding PSE. The error bars show ±1 SE.

Figure 2 shows the contrast matching functions for all observers at an eccentricity of 0 degrees, such that the stimuli were presented at the central fixation point. For the no mask condition, the data points for all observers generally lie along the veridical; however at low matching contrasts (around 11dB) data points lies above the veridical particularly for AA and PSB, but is less marked for BD and SP. For both pattern masks, suppression is evident at low matching contrasts for all observers but the depth of which is less for BD. Interestingly the matching functions for BD lie almost exactly on top of each other. As matching contrasts increase, facilitation is evident for both pattern masks for all observers; however there are differences between them. For AA PSB and SP, a greater amount of facilitation is shown for the grating than the plaid mask.

Contrast matching functions shown for all observers measured at an eccentricity of 4 degrees, where observations for AA, BD, PSB and SP are shown in plots 3 A, B, C and D respectively. The contrast of a 1 c/deg test grating in the presence of a superimposed 3 c/deg pattern mask is matched to a 1 c/deg standard grating. The mask is either a grating (red symbols, dashed line) or a plaid (blue symbols, solid line). For the control condition, the test, without a superimposed mask, is matched to a central standard grating (data represented by yellow symbols, dashed line). The data includes only those repetitions that fell within the rejection criterion where the standard errors (SE) of these measures were less than 1.4 times less than the corresponding PSE. The error bars show ±1 SE.

Moving away from the fovea to an eccentricity of 4 degrees, differing trends are observed between all four subjects for the no mask condition. For AA, there is a greater amount of suppression for low matching contrasts but the depth reduces as matching contrast increases, tending toward the veridical. Suppression is also observed over the entire range of matching contrasts for BD, but the level of suppression remains consistent. The results for PSB show suppression at low matching contrasts but at around 19dB and above, facilitation is observed. However, SP shows no signs of suppression for the entire range of matching contrasts – but as matching contrasts increase, the data tend toward the veridical. As seen at an eccentricity of 0 degrees, suppression is evident at low matching contrasts for the pattern mask conditions but again there are differences between the observers. Data for BD and PSB are similar in that the all plaid measures lie above the veridical, indicating facilitation. However, small levels of suppression is observed at low matching contrasts for the grating mask condition, but is abolished around 14 dB for BD 15dB for PSB, resulting in facilitation at higher matching contrast, more so for the plaid mask condition, but eventually the matching functions tend to converge. For AA, suppression is observed for both pattern mask conditions but less so for the plaid, however, as for SP, at higher matching contrasts (around 16dB) facilitation is evident but more so for the grating mask. The matching functions for SP superimpose at low matching contrasts, where suppression is evident.

Contrast matching functions shown for all observers measured at an eccentricity of 8 degrees, where observations for AA, BD, PSB and SP are shown in plots 4 A, B, C and D respectively. The contrast of a 1 c/deg test grating in the presence of a superimposed 3 c/deg pattern mask is matched to a 1 c/deg standard grating. The mask is either a grating (red symbols, dashed line) or a plaid (blue symbols, solid line). For the control condition, the test, without a superimposed mask, is matched to a central standard grating (data represented by yellow symbols, dashed line). The data includes only those repetitions that fell within the rejection criterion where the standard errors (SE) of these measures were less than 1.4 times less than the corresponding PSE. The error bars show ±1 SE.

Figure 4 shows contrast matching functions for individual observers at an eccentricity of 8 degrees in the left visual field. Similar trends are seen for the no mask condition for AA, BD and PSB. For these observers, suppression is observed but at higher matching contrasts the data points again tend toward the veridical, however for PSB the veridical is even crossed around 26dB resulting in small amounts of facilitation. For SP, the data points for this condition lie almost on top of the veridical, but at low matching contrasts (17dB and below) small amounts of suppression is observed. For all observers suppression is still present at low matching contrasts for both pattern mask conditions, but again there are differences between them. For AA, greater amounts of suppression is observed for the grating mask condition, and facilitation begins at a lower matching contrasts for the plaid mask, but data points of both pattern masks converge at high matching contrasts. A similar pattern emerges with SP, but the data points lie even closer to each other. For BD, the measures for both pattern mask conditions lie almost on top of each other for low matching contrasts, but at higher matching contrasts they separate, with greater amounts of facilitation for the grating mask condition. The level of suppression for PSB is far greater for the grating mask condition and facilitation occurs around a matching contrast of 23dB, whereas suppression is abolished at a lower matching contrast of 17dB for the plaid mask condition. As for AA, the data points for both pattern masks converge at high matching contrasts.

Contrast matching functions showing data averaged across all observers at eccentricities of 0 (A), 4 (B) and 8 (C) degrees in the left visual field relative to the central fixation point. The contrast of a 1 c/deg test grating in the presence of a superimposed 3 c/deg pattern mask is matched to a 1 c/deg standard grating. The mask is either a grating (red symbols, dashed line) or a plaid (blue symbols, solid line). For the control condition, the test, without a superimposed mask, is matched to a central standard grating (data represented by yellow symbols, dashed line). The data includes only those repetitions that fell within the rejection criterion where the standard errors (SE) of these measures were less than 1.4 times less than the corresponding PSE. The error bars show ±1 SE.

The above descriptions of the trends for all conditions differ between each individual subject at each different retinal eccentricity. To generate a clearer picture of these trends the data is averaged across all four observers. Figure 5 shows the data averaged across all observers at eccentricities of 0, 4 and 8 degrees corresponding to plots A, B and C respectively. Data points for the no mask condition on plot “A” lie almost exactly on top of the veridical, but small levels of facilitation is present at low matching contrasts. Similar levels of suppression is evident for both pattern mask conditions at low matching contrasts and facilitation occurs at around 15dB and above but is greater for the grating mask condition. At an eccentricity of 4 degrees (plot B), suppression is evident at low matching contrasts for the no mask condition, but as the matching contrast increases the data tends toward the veridical and eventually crosses it at around 21dB, resulting in small amounts of facilitation. Small amounts of suppression occur for the grating mask, and very little, if at all for the plaid mask condition. Facilitation is greater for the plaid than the grating mask for low to mid matching contrasts but at higher matching contrasts, the data cross resulting in slightly greater levels of facilitation for the grating mask. The level of suppression at 8 degrees (plot C) for the no mask condition is considerably greater than at 4 degrees. Although the measures tend toward the veridical as the matching contrast increases, no facilitation is observed. Again the level of suppression is greater for both pattern masks at low matching contrasts at 8 degrees than at 0 and 4 degrees. However, greater levels of suppression are exhibited by the grating mask than the plaid mask condition. In both cases, facilitation occurs at matching contrasts around 17dB for the plaid and 18dB for the grating, both higher contrasts than when facilitation occurs at 0 and 4 degrees. Facilitation is greater for the plaid but the data points for both pattern mask conditions converge at high matching contrasts.

In general, with increasing eccentricity the perceived level of contrast is increasingly attenuated, but the level of suppression is greater at low matching contrasts than for high matching contrasts. This is reflected by the matching function for the no mask condition where the measures tend toward the veridical as matching contrast increases. For both pattern mask conditions suppression is evident at low matching contrasts, but at higher matching contrasts the facilitation occurs. As eccentricity increases, the depth of suppression at low matching contrasts increases as does the level of matching contrast where suppression is abolished before facilitation occurs. As eccentricity increases, the matching function for the grating mask moves increasingly toward the right, whereas the matching function for the plaid mask occupies a relatively stable position – at an eccentricity of 0, the level of suppression is slightly greater for the plaid mask but the level of facilitation is greater for the grating. However at an eccentricity of 8 degrees, suppression is greater for the grating mask and facilitation greater for the plaid mask.

Discussion

The results from the matching experiment show for the no mask (control) condition that away from the fovea the level of test contrast must be increased for it to be perceived as the same level of contrast as the standard contrast – even more so as eccentricity increases, indicated by larger amounts of suppression as the matching function lies further away from veridical. This observation can be attributed to the poor vision provided by the periphery and para-foveolar region. Away from the fovea, visual acuity reduces considerably with eccentricity (Anstis, 1974) due to several key retinal factors. This includes observations that with increasing eccentricity, cone photoreceptors, responsible for human colour vision and high acuity, decrease in density significantly (Curcio et al, 1987, 1990). Also, the cone positional mosaic becomes increasingly “jittery” and spacing between each other increases away from the foveal region (Hirsch & Miller, 1987). Banks and Bennett (1988) showed that this very strict cone distribution pattern at the fovea is shown to be important in acuity and colour vision by studying cone migration in neonates (Banks & Bennett, 1988). Similarly, studies of albino vision reveal that their relatively poor vision is directly related to increased cone spacing (Wilson et al, 1988). The combination of low cone density, organisation and increased cone spacing away from the fovea reduces the sampling density of the peripheral retina so although image data is available, there are simply not enough cones to capture this information. Another important factor is that of convergence, where photoreceptor signals converge onto retinal ganglion cells before transmitting to the visual cortex. At the fovea for high acuity to be preserved it is desirable to have low convergence (Curcio & Allen, 1990) – it is shown that a ratio of 1:1 exists at the fovea but this increases significantly with eccentricity (Wässle et al, 1990). This results in reduced acuity as the responses of the cones are pooled over a larger area so image detail can be lost – similarly image detail is lost due to increasing ganglion cell receptive field size with eccentricity (Hubel & Wiesel, 1960). Essentially the spatial grain at which the retina operates increases with eccentricity causing poor peripheral vision, such that images appear blurred. Campbell and Green (1965) showed that blur reduces the perceived contrast of objects – this coupled with the fact vision is increasingly poor away from the fovea can account for the matching functions of the no mask (control) condition reported here. This is because the test must be raised to a higher contrast to be perceived the same as the standard with increasing eccentricity, reflected by the increasing level of suppression.

As Meese and Hess reported in 2004, their matching data showed significant amounts of suppression for monocular, dichoptic and binocular pattern mask conditions over a wide range of matching contrasts (as does Meese & Hess, 2005) – our results also show suppression, but only at low matching contrasts. These differences are most likely due to the different types of mask used for their experiments. Despite these differences, the perceived level of contrast was attenuated, so the alternative account of masking where the level of noise in the detecting mechanism is raised by the mask cannot extend to our matching data - if this account were true, the perception of absolute contrast should not be attenuated, such that contrast of the test need not be raised to produce a perceptual match with the standard; and the pattern mask would only affect the variance of the detecting mechanism response (Meese & Hess, 2004). Again, as Meese and Hess (2004) explained, this implies that above detection threshold cross-channel masking is bought about by cross-channel suppression - not mask induced noise.

*CLARIFY this paragraph with Bikesh.

Clearly, above detection threshold it appears linear summation of the mask components is absent across the retina, even at an eccentricity of 0 degrees. This is because in figures 2 to 5 none of the matching functions for both the grating and plaid superimpose – if this was the case, then this suggests linear summation of the two contrast components in the plaid mask. However, there is an exception where this does occur for BD at an eccentricity of 0 degrees – at high matching contrasts the two matching functions lie parallel to the veridical, suggesting some form of linear facilitation.

*DISCUSS why there are high levels of facilitation at higher matching contrasts.

Similarly, the depth of suppression at low matching contrasts increases with eccentricity, again this can be attributed to poor peripheral vision as described above. SEEK PAPERS DESCRIBING TRENDS – see SHEENA!

Detection Experiment

Data Trends

The results for the detection experiment are shown for all observers in figures 6, 7 and 8 for retinal eccentricity but figure 9 shows the data averaged across all observers. The plots produced show typical masking curves where the detection thresholds of a 1 c/deg test grating in the presence of a 3 c/deg pattern mask (grating or plaid) are measured as a function of overall mask contrast. As explained earlier, only measures from good repetitions are included in the data.

Figure 6: Contrast masking functions shown for all four observers measured at an eccentricity of 0 degrees, where observations for AA, BD, PSB and SP are shown in plots 6 A, B, C and D respectively. The detection threshold of a 1 c/deg test grating in the presence of a superimposed 3 c/deg pattern mask is shown as a function of overall mask contrast. The mask was either a grating (red symbols, dashed line) or a plaid (blue symbols, solid line). The data includes only those repetitions that fell within the rejection criterion where the standard errors (SE) of these measures were less than 1.4 times less than the corresponding threshold. The error bars show ±1 SE.

In figure 6 the masking functions for both mask conditions differ between all four observers. For AA, the detection threshold of the test without a superimposed grating mask is approximately 2dB higher than the detection threshold of the test without a superimposed plaid mask – this is surprising considering they are essentially the same condition (no mask). The two functions do not superimpose, with greater amounts of suppression for the grating mask than the plaid mask, particularly at low mask contrasts. A similar trend is observed for PSB, but there are greater amounts of facilitation for the grating mask at higher mask contrasts. For BD, again the grating produces slightly more suppression than the plaid mask, but the functions lie almost exactly on top of each other for low mask contrasts. The two functions nearly superimpose for SP, but the data points for both mask conditions exhibit erratic trends at low mask contrasts. For all observers, the typical “dipper handle” is present, indicating that the detection threshold is increasingly attenuated as mask contrast increases. However, the “dipper” region, representing facilitation at low mask contrasts, is absent.

Contrast masking functions shown for all four observers measured at an eccentricity of 4 degrees, where observations for AA, BD, PSB and SP are shown in plots 7 A, B, C and D respectively. The detection threshold of a 1 c/deg test grating in the presence of a superimposed 3 c/deg pattern mask is shown as a function of overall mask contrast. The mask was either a grating (red symbols, dashed line) or a plaid (blue symbols, solid line). The data includes only those repetitions that fell within the rejection criterion where the standard errors (SE) of these measures were less than 1.4 times less than the corresponding threshold. The error bars show ±1 SE.

At an eccentricity of 4 degrees both grating and plaid mask functions, shown in figure 7, are elevated for all observers relative to their previous positions at an eccentricity of 0 degrees - indicating the detection thresholds are further attenuated. Also, the dipper handle is still intact indicating greater amounts of suppression as mask contrast increases. As observed earlier, the detection threshold in the absence of the grating mask is slightly higher than that measured without the plaid for AA. This surprising feature is also noted for BD and SP, but in the latter case the detection threshold measured without the plaid mask is slightly higher. Again, for AA, the grating produces greater amounts of suppression for the grating mask, but at around 12dB mask contrast, a small amount of facilitation is observed for the plaid mask (dipper region). For PSB, at around the same mask contrast facilitation is evident for the grating mask. Larger amounts of facilitation over wider range of low mask contrasts is seen for both mask conditions for SP. For BD, no facilitation is observed but suppression is greater for the grating mask for all levels of mask contrast. Similarly, the two masking functions for all observers do not superimpose.

Contrast masking functions shown for all four observers measured at an eccentricity of 8 degrees, where observations for AA, BD, PSB and SP are shown in plots 8 A, B, C and D respectively. The detection threshold of a 1 c/deg test grating in the presence of a superimposed 3 c/deg pattern mask is shown as a function of overall mask contrast. The mask was either a grating (red symbols, dashed line) or a plaid (blue symbols, solid line). The data includes only those repetitions that fell within the rejection criterion where the standard errors (SE) of these measures were less than 1.4 times less than the corresponding threshold. The error bars show ±1 SE.

The masking functions measured at an eccentricity of 8 degrees shown in figure 8 are elevated to an even further extent (relative to their positions at an eccentricity of 0 degrees) than at 4 degrees. This indicates that detection thresholds are raised even higher, even more so as mask contrast increases. Despite this threshold elevation, the region of facilitation is even more noticeable at low mask contrasts for AA, PSB and SP. For AA and PSB, facilitation occurs over wide a range of grating mask contrasts approximately (-9dB to 24dB), but is minimal, or even absent for the plaid mask. For SP, facilitation is observed for both grating and plaid masks over a similar range of mask contrasts. However, for BD, there is little, if at all, any signs of facilitation. Again, at higher mask contrasts facilitation is abolished for all observers and detection thresholds attenuate as mask contrast increases. As seen at 4 degrees of eccentricity, none of the two masking functions for each observer superimpose.

As for the matching experiment the data for the detection experiment are averaged across all observers to produce a clearer description of the trends observed. However, this data does not include observations made by AA, because at an eccentricity of 0 degrees, the difference in detection threshold for both pattern masks with an overall mask contrast of 0% is nearly 2dB. The reason why this occurs is unclear as they are essentially the same condition, but in any case the data for AA is excluded. Figure 10 shows the masking functions averaged across observers BD, PSB and SP for pattern mask conditions.

Discussion

With increasing eccentricity it is clear that the masking functions for both pattern masks are increasingly elevated, indicating threshold elevation across the retina. Studies by Snowden and Hammet (1998) reveal a similar pattern, where they too found increasing threshold elevation of dipper functions at different vertical eccentricities in contrasts discrimination experiments using surround masks (Snowden & Hammet, 1998). The same account used to describe the no mask matching functions can explain why the masking functions for both plaid and grating mask conditions in the detection experiment are both increasingly elevated with eccentricity.

As found for the matching experiment, masking produced by the pattern masks for individual subjects in the detection experiment also indicates cross-channel suppression. This is because the masks were sufficiently remote from the test stimulus; such that they are processed by different mechanisms. Furthermore, similar mask configurations used in previous masking studies where they are spatially remote from the test confirm that pattern masking is due to cross-channel suppression (Meese & Holmes 2002; Holmes & Meese 2001). Studies have also shown that if within-channel masking bought about cross channel masking, then the sigma slope (d’ slope) of the psychometric function would be equal to one – such that it is “linearized” (Georgeson & Meese, 2004). Our results revealed that the sigma slopes of the psychometric functions of the pattern mask conditions were all greater than one, and no less than 1.98 – indicating that within-channel masking is very unlikely, consistent with previous contrast masking studies (Holmes & Meese, 2004; Meese & Holmes 2007). One other possibility exists that could account for the masking is where the mask increases the level of noise in the detecting mechanism, reducing the signal to noise ratio which results in masking (REF) - however, this account cannot extend to our matching data. Another feature of note is at an eccentricity of 0, for observers AA, BD and PSB there is a greater level of masking produced by the grating than the plaid at low mask contrasts. This feature is also present at 4 and 8 degrees, but is less obvious for PSB. Such a finding of non-linear summation at low mask contrasts is consistent with masking experiments performed by Meese & Holmes (2002) where their adaptation model predicts this outcome, confirmed by statistical analysis of the grating and plaid data at each mask contrast (Meese & Holmes, 2002). Interestingly, we found no evidence for linear summation of mask components (hence no linear suppression) across the retina as none of the masking functions superimposed, even at an eccentricity of 0 degrees - although the same stimuli configurations (1 c/deg vertical test, 3 c/deg pattern masks oriented at ±45) were used as in previous studies where linear summation was observed (Meese & Holmes, 2002). One possible explanation for why this was not seen at 0 degrees could be attributed to the fact that the conditions were fully blocked, such that the trials of one condition for all mask contrasts was completed before moving onto another. As the measures were taken over several sessions, an observer may perform better during a particular session – meaning that the measures for each condition could be more accurate than others.

Another interesting feature from our results show that as eccentricity increases, facilitation becomes more apparent at low mask contrasts, even extending to mid levels of contrast at 8 degrees eccentricity. One possibility could be due to the increase in receptive field size of visual neurones and the reduced orientation selectivity of these cells with increasing eccentricity (Hammond, 1974; Wilson & Sherman, 1976; Gur et al, 2005). As these cells are less orientation specific, the detecting mechanism could be excited by both the mask and test, even though the mask is considerably remote from the test. Hence the within-channel drive produced by both the mask and test could enhance the detectability of the detecting mechanism resulting in facilitation – as the receptive fields become less orientation specific further away from the fovea, the within-channel drive from the mask increases, accounting for the increasing levels of facilitation with eccentricity. Another idea that could account for facilitation is reduction of uncertainty by the mask (Pelli, 1985; Petrov et al, 2006). Here, the mask reduces the overall level of noise by reducing the number of mechanisms which provide stimulus information about the mask to the observer – thus facilitating detection. Although this remains a possibility, it is unlikely to extend to our data because the fixation target provided a strong positional cue; and as the order of conditions was fully blocked, the observers were well aware of what they were trying to detect. Similar reasoning has been used by other masking studies to rule out the likelihood of this account (Meese & Holmes, 2007; Meese et al 2007). The mask could also bring about facilitation through sensory interactions (Chen & Tyler, 2002), such that the mask provides a modulatory influence on excitation of the detecting mechanism. In the next section, this possibility is explored in greater depth.

Modelling

It is clear that for the matching experiment, suppression is observed at low matching contrasts and facilitation at mid to high matching contrasts for both pattern mask conditions. However, facilitation occurs at low mask contrasts (at eccentricities greater than 0) and suppression occurs at high matching contrast (for all eccentricities measured), so it is important to address how the data fits together by performing a qualitative analysis of the results. Provision of both the matching and detection data is found in a model developed by Meese and Holmes (2007), which is consistent with interpretations of masking data which are attributed to sensory interactions (Chen & Tyler, 2002). They found that masking is dependent on both spatial and temporal frequency, and related this finding to underlying neurophysiology reflected by their model (Meese & Holmes, 2007). The response, R, of the detecting mechanism is given by the following equation:

R = Cptest (1 + αCmask) / (1 + Cqtest + ωCqmask) (3)

Where Ctest and Cmask are the contrasts (in percent) of the test and mask; and p, q, α and ω are free parameters of the model. The values of p and q are 2.4 and 2.0 respectively, where typically p>q. The denominator contains suppressive influences from both the test and mask, where the latter is controlled by ω, a suppressive weight parameter. The numerator not only contains excitatory influences from the test, but also the mask. This provides a modulatory influence on excitation, controlled by the weight parameter α. The model is designed such that the numerator acts to accommodate facilitation and the denominator acts to divisively suppress excitation to produce masking (this model has many similar parallels to equation 2). Note that the mask component, Cmask is subject to the accelerating exponent q on the denominator, whereas on the numerator it is not. This means that as contrast increases, masking outpaces facilitation. This relationship describes the detection data very well – as low mask contrasts, the suppressive influence of the mask is relatively smaller than the excitatory influences, so facilitation is prevalent. However, as the mask contrast increases, the suppressive influence from the mask accelerates meaning at higher mask contrasts masking wins out. Thus both the excitatory and suppressive influences are in continual competition, but the advantage depends upon mask contrast (Meese & Holmes, 2007). Since the perception of contrast reduces with eccentricity (see earlier discussion), the mask contrast therefore appears reduced, and at low levels of mask contrast the model shows that facilitation outweighs suppression. As increasing levels of facilitation is observed with eccentricity at low mask contrasts, this model therefore describes our detection data very well.

It is also possible to use this model to describe the data in the matching experiment. At low matching contrasts masking is evident because the mask is at a fixed high contrast so suppression outweighs facilitation. However, as the level of matching contrast of the test increases, the influence of facilitation increases as the mask contrast remains fixed - reflected in the matching functions for both pattern masks as they approach the veridical. Eventually when the level of matching contrast is sufficient, facilitation is evident and becomes increasingly apparent at higher matching contrasts. Figures X and Y show the response of the detecting mechanism for both facilitation and suppression as a function of mask contrast for the detection and matching experiment.

Conclusion

The matching experiment results have shown that there is inconclusive evidence for linear suppression above detection threshold as the matching functions for both pattern masks show great inter-observer variability at each different retinal location. There is some evidence of linear suppression at low matching contrasts for observer BD at eccentricities of 0 and 8 degrees and SP at 4 degrees as the matching functions superimpose in this region – this feature is also present in the average data, but again only at low matching contrasts. However it is clear that the perception of contrast is increasingly attenuated with eccentricity, as the matching functions for the no mask (control) condition are shifted towards the right – indicating suppression as they lie further below the veridical. This observation is attributed to increasingly poor vision away from the fovea resulting in reduced contrast perception. The detection experiment is also consistent with this finding as the masking functions are increasingly elevated with eccentricity, meaning detection thresholds are increasingly raised further away from the fovea. Again, at different retinal eccentricities it is apparent that linear suppression is not observed at detection threshold as none of the masking functions superimpose. Despite using the same stimulus configurations as in previous masking experiments where linear suppression is seen (Meese & Holmes, 2002; Meese & Hess, 2004; Holmes & Meese, 2004), the same observation was not observed at an eccentricity of 0 degrees. As discussed earlier, this could be due to the blocking method. However, several other key features have emerged that are consistent with previous studies. Since masking is evident for both pattern masks at high mask contrasts, this indicates that masking is due to cross-channel suppression, not a within-channel process because the masks are spatially remote from the test (Ross & Speed, 1991; Foley, 1994; Chen & Foley, 2004). Similarly, cross-channel suppression also occurs above detection threshold. As the perception of contrast is attenuated (at low matching contrasts), it rules out the possibility that masking is due to mask induced noise in the detecting mechanism – however, this possibility cannot be ignored for the detection data (WHY?). Across the retina, facilitation becomes increasingly apparent at low to mid mask contrasts for the detection experiment – several explanations exist, but the data for both experiments is described very well by Meese and Holmes (2007) model. The model incorporates a modulatory influence on excitation by the mask on the numerator that accommodates facilitation; and an accelerating exponent on the suppressive influences of the mask, that together with self inhibitory influences, divisively suppress the excitatory response. Whether or not facilitation or masking occurs depends upon the level of mask and test contrast and eccentricity.

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