Mareschal et al. 10.1073/pnas.0507259103. |
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Supporting Figure 4
Fig. 4. Illustration of templates for target dissection and discrimination. (a) Typical target. (b) Hypothetical detection template for a detection task or component template for a discrimination task. (c) Ideal decision-template. (d) Average best-fitting difference-of-Gabor to classification images derived from the experiment; it has a ratio of »3:1 between the two template components and, intuitively, lies on a continuum between b and c. (e) Classification image derived using a Monte Carlo simulation of a simulated observer using the stimulus show in a, the template shown in b, and incorporating a free parameter: a "hard threshold" as proposed by Solomon (1). (f) The best-fitting difference-of-Gabor to e, which clearly captures the appearance of the template estimated from human observers shown in d.
1. Solomon, J. A. (2002) J. Vision 2, 105–120.
Supporting Text
The standard ideal observer for a classification image experiment multiplies a noisy stimulus by a template that weights the contribution of each part of that stimulus according to how informative it is for the task. The pooled response then is computed by summing over all pixels in this product, and a decision is made accordingly. For a two-alternative (present vs. absent) "detection" task, the optimal template is the (noise-free) stimulus. However, for a target like Fig. 4a, the operation of real visual processes will lead to estimated detection templates that are suboptimal (e.g., Fig. 4b). For a two-alternative "discrimination" task the optimal template is composed of the difference between two "component templates" essentially similar to the detection template in Fig. 4b (because these regions will do most to disambiguate the two possible stimuli) with one component template a sign-inverted version of the other. (Note we refer to these as component and not detection templates to distinguish between detection and discrimination tasks in general.) For the task described in this work, using component-templates like in Fig. 4b, the ideal "decision template" therefore should converge on the difference-of-Gabor pattern depicted in Fig. 4c. In practice, classification images (CIs) are more like Fig. 4d (which shows the average CI template across observes I.M., P.J.B., and S.C.D.) and clearly fall somewhere between a component and a decision template. Why should this be? Consider how the ideal observer makes its decision. It multiplies a given stimulus by the two possible component templates and then makes a classification according to which pooled response is the greater one. Pixels in the product image contribute to the pooled response in linear proportion to their magnitude even though, in practice, some very low contrast regions of the stimulus would fall below the detection threshold for a real visual system. To account for this possibility, Solomon (1) added an additional "hard-threshold" stage so that the two pooled responses to a given stimuli are thresholded (i.e., set to zero if they fail to exceed some value) before comparison. A decision is still made based on which response is the larger one, but an additional constraint is added: that a random response is given if both pooled responses are equal (typically arising if both are equal to zero). Fig. 4f shows the best-fitting predictions of an ideal observer with the hard-threshold component added to the classification image in Fig. 4e. In other words, a variable hard threshold effectively accounts for how much observers are limited by their ability to discriminate vs. detect. If the threshold is low, then the simulated observer is equivalent to a standard ideal observer, which is unconstrained by any ability to detect, and on every trial is comparing between two pooled responses, so generating a pure discrimination template (like Fig. 4c). If the threshold is high, low-contrast stimulus components are sometimes ignored with the consequence that some trials involve a comparison between two pooled responses, whereas others (where one component fails to reach threshold) effectively approximates detection. Thus, the resulting classification image reflects a mixture of limits arising from detection and discrimination.
1. Solomon, J. A. (2002) J. Vision 2, 105–120.