What is an FROC curve?
Free-response data consists of mark-rating pairs. For each mark the investigator decides whether it is "close enough" to a lesion to be credited as a true detection (the definition of a closeness or proximity criterion is presently rather arbitrary). Departing from custom I call a mark that is close to a lesion as lesion localization (LL) rather than true positive. Marks that do not qualify as lesion localizations are non-lesion localizations (NLs) instead of false positives. True positive and false positive terminology risks serious confusion with ROC methods where the same terms apply to the whole image whereas in the free-response context the data units are location specific. While this may take some getting used to, I believe in the long run it is desirable to clearly separate the terminology used to describe two intrinsically different paradigms. Also, I refer to the general paradigm itself as free-response and FROC refers to the operating characteristic. The FROC curve is defined as the plot, as the threshold for reporting a finding is varied, of lesion localization fraction (LLF) along the y-axis vs. non-lesion localization fraction (NLF) along the x-axis, where the denominators for the fractions are the total number of lesions and the total number of images, respectively. A typical FROC curve such as might be observed for a CAD algorithm shown below. It is characterized by a steep high confidence region starting at (0,0), a shoulder corresponding to the middle confidence region, and a plateau in the lowest confidence region, terminating at the end-point where the confidence is at its lowest value. The dotted curve is the complete curve, where the lowest confidence is at negative infinity, and the solid curve is the observable portion of the curve for a radiologist who adopts a finite lowest confidence level for reporting.
