Nonparametric signal detectability evaluation using an exponential transformation of the FROC curve
Example of EFROC graph. The ratio of detected signals relative to the total number of signals μ is plotted as function of the projected ratio of false images, as given by 1 − e−ν , where ν is the average number of false-signals per image, shown on the top axis.
Example of a truncated EFROC curve due the partial reporting of the signal scores.
Plots of the variation of the number of false-signals per image with z, ν(z) (left scale), and of the signal distribution f(z) and the distribution of the maximum false-signal score in an image g(z) (right scale), for the two cases studied.
Comparison of the ROC, LROC, AFROC, EFROC, and FROC curves for the two cases considered. The error bars correspond to one standard deviation from the mean, and were determined for a series of fixed points on the abscissa using multiple sets of 200 simulated data samples, out of which 60% correspond to signal-present images.
The distributions of the performance index estimates (AUC for ROC, LROC, AFROC and EFROC methods, and in addition for LROC the Q l estimate) are shown on the left-hand column. The distributions of the corresponding standard deviation estimates are shown on the right-hand column. The theoretical values are marked on the plots.
The variation with the number of image samples and the fraction of signal-present images of the performance separation power of the ROC, LROC, AFROC, and EFROC methods. The contour plots for δ = 1, 2, and 3 of the two-dimensional dependency function of each method are displayed.
The maximum separation power, max δ, realized for a given number of total image samples T = N + M for each method ROC, LROC, AFROC, and EFROC at their the most efficient prevalence point.
Comparison between the standard deviations of G(z) nonparametric estimates in AFROC and EFROC .
The variation of the performance separation power of the EFROC method (EFROC) with the reference area size Ωref expressed in multiples of the original image area Ω used in simulations.
Summary of nonparametric signal detectability estimators for ROC, LROC, AFROC, and EFROC methods.
Numerical values obtained for the two cases considered. For each estimator we have: the theoretical value A, the sample mean of the estimations ⟨Â⟩, the sample standard deviation s Â , the theoretical standard deviation σ Â , and the sample mean of standard deviation estimations .
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