The previous post outlined a basic experiment for measuring sensitivity to contrast at detection threshold for a simple target. In this post, I’ll describe how detection thresholds can be affected by other stimuli, which are termed ‘masks’. You can think of a mask as ‘getting in the way’ of a target, and making it harder to detect. I’ll describe two varieties of masking (though several others exist) – when the mask is similar or identical to the target (pedestal masking) and when the mask is very different from the target (cross-channel masking).
In a standard 2AFC detection experiment, the target is shown in one temporal (or spatial) interval, but is absent in the other. This is still the case in a masking experiment, but there is also a mask, which is presented in both intervals. When the mask is spatially identical to the target (i.e. it’s the same image, but probably at a different contrast) it is known as a pedestal. The pedestal affects detection thresholds in interesting ways. For low contrast pedestals, thresholds are reduced (i.e. performance gets better). A good analogy is with height – if detection occurs when someone’s head is visible above a wall, standing them on a box (a pedestal) will make it more likely that their head pops up over the wall. Contrast detection works in a similar way, and the improvement in threshold is often referred to as facilitation. For high contrast pedestals, the task becomes contrast discrimination: the pedestal is visible in both intervals, but the target is added only in one. This is like judging the height of two huge skyscrapers – you’ll only notice the difference if one is substantially taller than the other. So, with high contrast pedestals, thresholds increase, and performance gets worse than at detection threshold (with no pedestal) – this is masking. The interaction of these two effects (masking and facilitation) produces a characteristic ‘dipper’ shaped function, as shown by the red symbols below. In the figure, the dashed horizontal line indicates detection threshold. Note that DHB (left panel) shows a clearer dip, whereas LP (right panel) shows clearer masking.
If the visual system were entirely linear, detection would be unaffected by a pedestal. So, the presence of the dipper reveals a nonlinearity of some kind in the system. Two main candidates for this nonlinearity have been proposed over the years, and there is not yet a consensus amongst researchers over which is truly responsible. It is likely that both are correct to some degree, or perhaps that they are both equally valid descriptions at different levels of analysis. The first is that there is a nonlinear transducer (e.g. Legge & Foley, 1980) or gain control, of the form:
C2.4/(1 + C2)
where C is the input contrast. This equation produces a sigmoidal (s-shaped) contrast response function (see panel B below). The dipper function is determined by the gradient of the contrast response at a given input (pedestal) contrast, because this governs how much contrast the target must add to the pedestal to produce a given increase in output. When the contrast response function is steep, thresholds are low (detection, and the dip region of the dipper). When the function is shallow, target contrast must be higher to produce the same increase in response, so thresholds increase (the handle region of the dipper).
The other explanation for dipper functions was proposed by Pelli (1985). This account has two parts: the first explains facilitation (the dip) and the second explains masking (the handle). Pelli proposed that observers are uncertain about exactly which internal detecting mechanism(s) will respond to the target. Their strategy is to monitor many (linear) mechanisms, and select the most responsive. Because the mechanisms are noisy, when the target contrast is low observers will often select the wrong one. However, the pedestal raises the activity of the correct detecting mechanism above the background noise level (right panel below). This improves thresholds, producing the facilitation effect, as shown by the red curve in the left panel below.
In this scheme, masking occurs because each detecting mechanism is noisy, with the amount of noise being proportional to the activity in the channel (called signal-dependent, or multiplicative noise). So, for a high pedestal contrast, the mechanism will be more noisy, meaning more target contrast is required to overcome the noise. This produces masking, as shown by the blue curve in the left panel below. The dipper function (green) comes from the combination of uncertainty and multiplicative noise.
When the mask is very different from the target, they will activate different detecting mechanisms. This means that the within-channel processes which produce dipper functions do not occur. But masking still happens, for example when the mask is orthogonal (at 90 degrees) to the target (see above stimulus example, and green data points in the top graphs). The most common explanation for this masking is that mechanisms sensitive to different stimuli inhibit each other. This inhibition can be modeled as a divisive process as part of a gain control equation (Heeger, 1992),
C2.4/(1 + C2 + wX)
where X refers to activity in mechanisms other than that which responds to the target, and w is a weight which determines the level of suppression. Note that this form of masking is very different from masking by a pedestal, and does not typically include facilitation.
Masking experiments are important, because they reveal nonlinear properties of the visual system. Pedestal masking tells us about the gradient of the contrast response function, whereas cross-channel masking tells us about interactions between different detecting mechanisms (or channels). Masking also occurs in other sensory domains, such as hearing or touch, and along other visual dimensions, like spatial frequency (size) or speed discrimination.
Heeger, D.J. (1992). Normalization of cell responses in cat striate cortex. Vis Neurosci, 9, 181-197.
Legge, G.E. & Foley, J.M. (1980). Contrast masking in human vision. J Opt Soc Am, 70, 1458-1471.
Pelli, D.G. (1985). Uncertainty explains many aspects of visual contrast detection and discrimination. J Opt Soc Am A, 2, 1508-1532.