PMC

ROC curves for the continuous and partially grouped binormal data (a) concave binormal ROC curves for continuous data; b) partially binormal ROC curves, for data with marker values grouped below ξ₀ : fpf(ξ₀)=0.2) a) Continuous binormal data b) Partially grouped binormal data

Improperness of the binormal model corresponding to a bi-chi-squared model. Improperness categories are defined in terms of |r|, where r = a/(1 – b)) is the mean-to-sigma ratio for the corresponding binormal model, as discussed by Hillis and Berbaum []. Notes: a and b define the binormal model corresponding to the bi-chi-squared model defined by (θ, λ), i.e., and ; the λ-axis is scaled logarithmically; values of r for λ = 1 are not included because r is not defined if λ = 1.

The vector drawings at the bottom right show the angle between tangent vectors and the angle between binormal vectors at points i and j, respectively. Averaging over such angles is used in the calculation of the tangent and binormal correlation functions.

Binormal and binormal likelihood-ratio (binormal-LR) ROC curves for the Van Dyke et al [] data. Figures (a) and (b) compare the curves for the two modality-reader combinations having the lowest mean-to-sigma ratios, figures (c) and (d) show two indiscernibly improper combinations where the two methods give similar results, and figure (e) is an indiscernibly improper combination where the two methods give visibly different results. Notes: “AUC(binormal)” and “AUC(binormal-LR)” indicate binormal and binormal-LR AUCs, respectively;“CINE5” indicates the cine modality and reader 5 combination, etc.