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Steven Kies, Charles Chubb; Perturbation analysis of perceptual templates. Journal of Vision 2008;8(6):267. doi: https://doi.org/10.1167/8.6.267.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose. Classification images enable estimation of the linear component of the decision statistic (aka the perceptual template (PT)) used by observers in making a given type of judgment. However, this method is inefficient because the expected correlation of the PT with any given noise sample is low. We introduce a more powerful method. Method. Suppose (1) the task is to detect a target T and (2) the PT for this task seems likely to project strongly into the space P spanned by orthonormal images P1, P2,…, Pπ (all orthogonal to T). In addition, Let X1, X2,…, Xm be a fixed set of orthonormal noise images spanning space X, orthogonalized with respect to T and all of the Pk's. Let a be the threshold for detecting aT in a random linear combination of the Xk's. Then for b small enough that perturbations are not noticeable, we measure performance at detecting each of aT+bPk and aT−bPk (in the same kind of noise). Performance in these 2n conditions is used to (1) estimate the projection of the PT into P (which should be large), (2) estimate the projection of the PT into X (which should be small), (3) test whether the PT accounts for performance, and if not (4) estimate a quadratic component of the decision statistic. We used this method to derive the projection into a 6-dimensional space of the PT for a task requiring the observer to detect a Gaussian blob in noise. Results. The PT deviated significantly from T; more interestingly, the linear model embodied by the PT was rejected; the decision statistic involved a significant quadratic component. Conclusions. Because the space of stimuli explored using perturbation analysis is only n+m+1 dimensional, this method enables stronger inferences than classification images given the same amount of data.
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