title: Restrictions on the three-class ideal observer's decision boundary lines.
abstract: We are attempting to develop expressions for the coordinates of points on the three-class ideal observer's receiver operating characteristic (ROC) hypersurface as functions of the set of decision criteria used by the ideal observer. This is considerably more difficult than in the two-class classification task, because the conditional probabilities in question are not simply related to the cumulative distribution functions of the decision variables, and because the slopes and intercepts of the decision boundary lines are not independent; given the locations of two of the lines, the location of the third will be constrained depending on the other two. In this paper, we attempt to characterize those constraining relationships among the three-class ideal observer's decision boundary lines. As a result, we show that the relationship between the decision criteria and the misclassification probabilities is not one-to-one, as it is for the two-class ideal observer.
authors.affiliation: Department of Radiology, the University of Chicago, 5841 S. Maryland Ave., Chicago, IL 60637, USA. d-edwards@uchicago.edu
authors.forename: Darrin C
authors.initials: DC
authors.lastname: Edwards
authors.forename: Charles E
authors.initials: CE
authors.lastname: Metz
mesh_terms: D000465:Algorithms; D003627:Data Interpretation, Statistical; D020000:Decision Support Systems, Clinical; D003661:Decision Support Techniques; D003936:Diagnosis, Computer-Assisted / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D012372:ROC Curve; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity