Abstract
In 1996, Ahumada [2] reported the following experiment. On each trial, the observer was presented with two small horizontal bars separated by a small, lateral gap (of 1 pixel width, corresponding to 1.26 min on his display) on a background. The bars could be either aligned or offset vertically (1 pixel) as shown in the top two images of Fig. 6.1, respectively. The observer’s task on each trial was to judge whether an offset was present or not. This is a localization judgment measuring what is called Vernier acuity. Under appropriate conditions, humans are remarkably good at this, detecting offsets that can be an order of magnitude or more finer than the minimum separation that they can resolve between two adjacent bars, hence the term hyperacuity [186]. One innovation for this type of experiment in Ahumada’s design was that stimuli were presented in “noise,” i.e., the luminance of each pixel in the image (128 ×128 pixels) was increased or decreased by a random amount, as illustrated in the bottom two images of Fig. 6.1.
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- 1.
That is, pixels of random luminance added to a vernier target with no offset, or zero misalignment signal.
- 2.
This is a biased criterion. If we calculated d′ directly, we could establish a criterion for unbiased responding. We leave this as an exercise for the reader.
- 3.
The screen refresh rate was set to 100 times/s, so that each sample corresponded to two screen sweeps of the electron beam.
- 4.
A bootstrap procedure for obtaining standard error estimates is outlined in Exercise 6.6.
- 5.
An alternative is to analyze the data with a proportional odds model as in Chap. 3.
- 6.
- 7.
Mineault et al. [128] note that this choice of penalty is equivalent to assuming a Gaussian prior on the coefficients for the basis vectors composing the smooth function to be estimated. They explore an alternative smoothing criterion based on a Laplacian prior that leads to maximizing sparseness in the coefficients.
- 8.
This differs from the definition of higher-order classification images proposed by Nandy and Tjan [133] that is based on correlations of pixel values across regions of an image, thus revealing what they term second-order features.
- 9.
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Knoblauch, K., Maloney, L.T. (2012). Classification Images. In: Modeling Psychophysical Data in R. Use R!, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4475-6_6
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