It has been known for over 40 years that there are two fundamentally different kinds of detection tasks in the theory of signal detectability. The Type 1 task is to distinguish between events defined independently of the observer; the Type 2 task is to distinguish between one's own correct and incorrect decisions about those Type 1 events. For the Type 1 task, the behavior of the detector can be summarized by the traditional receiver operating characteristic (ROC) curve. This curve can be compared with a theoretical ROC curve, which can be generated from overlapping probability functions conditional on the Type 1 events on an appropriate decision axis. We show how to derive the probability functions underlying Type 2 decisions from those for the Type 1 task. ROC curves and the usual measures of performance are readily obtained from those Type 2 functions, and some relationships among various Type 1 and Type 2 performance measures are presented. We discuss the relationship between Type 1 and Type 2 confidence ratings and caution against the practice of presenting transformed Type 2 ratings as empirical Type 1 ratings.

Although much has been learned about the spatial sampling and filtering properties of peripheral vision, little attention has been paid to the remarkably clear appearance of the peripheral visual field. To study the apparent sharpness of stimuli presented in the periphery, we presented Gaussian blurred horizontal edges at 8.3, 16.6, 24, 32, and 40 deg eccentricity. Observers adjusted the sharpness of a similar edge, viewed foveally, to match the appearance of the peripheral stimulus. All observers matched blurred peripheral stimuli with sharper foveal stimuli. We have called this effect "sharpness overconstancy". For field sizes of 4 deg, there was greater overconstancy at larger eccentricities. Scaling the field size of the peripheral stimuli by a cortical magnification factor produced sharpness overconstancy which was independent of eccentricity. In both cases, there was a slight sharpness underconstancy for peripherally presented edges blurred only slightly. We consider various explanations of peripheral sharpness overconstancy.

Green's relationship, A SI =P(C) 2I , which equates the area, A SI , under the receiver operating characteristic (ROC) curve in the single-interval forcedchoice (SIFC) task with the proportion correct, P(C) 2I , in the two-interval forced-choice (2IFC) task, is rederived using the cross-correlation functions of the SIFC evidence distributions. The relationship is generalized to include discrete random variables, unidimensional decision axes that do not need to be monotonic with likelihood ratio, and arbitrary prior and guessing probabilities. A 2IFC difference decision rule is assumed. Further nonparametric relationships, including an equality between an entropy transform of A SI and the 2IFC channel capacity, nonparametric bounds on the area under the 2IFC ROC curve in terms of A SI , and methods for estimating 2IFC ROC curves based on information from the SIFC task, are developed. These relationships are investigated experimentally. Experiment I is a frequency-discrimination task where the evidence is known to be distributed as a discrete random variable. Experiment II is an amplitude-discrimination task where the theoretical evidence distributions are continuously distributed. The problem of observer inconsistency is addressed by repeating the experiments multiple times, using the same stimuli, then using group operating characteristic (GOC) analysis to remove unique noise. Results from Experiment I show excellent support for all the theoretical relationships, and results from Experiment II show partial support for the theoretical relationships.

In a previous study we found that blurred edges presented in peripheral vision look sharper than when they are looked at directly, a phenomenon we have called peripheral sharpness overconstancy (Galvin et al. (1997). Vision Research, 37, 2035-2039). In the current study we show that when visibility of the stimulus edges is compromised by very brief presentations, we can demonstrate sharpness overconstancy for static, foveal viewing. We also test whether the degree of sharpening is a function of the current visual context, but find no difference between the peripheral sharpness overconstancy (at 24 degrees eccentricity) of edges measured in a blurred context and that measured in a sharp context. We conclude that if the visual system does carry a template for sharp edges which contributes to edge appearance when visibility is poor, then that template is resistant to changes in context.

Motion reversal effects (the apparent reversal of the direction of motion of a high frequency sinusoidal grating) have been attributed to aliasing by the cone mosaic [Coletta et al. (1990). Vision Research, 30, 1631-1648] and postreceptoral layers [Anderson & Hess (1990). Vision Research, 30, 1507-1515] in human observers. We present data and a new model which suggest that at least two sampling arrays of different densities affect direction discrimination out to 30 degrees eccentricity. The first sampling layer matches anatomical estimates of the cone density. The second sampling layer is too dense to be the parasol cells alone; midget ganglion cells certainly contribute to this task. This is further evidence that motion perception is not mediated exclusively by the magnocellular stream.