On ideal AFROC and FROC observers

Abstract

Detection of multiple lesions (signals) in images is a medically important task and Free-response Receiver Operating Characteristic (FROC) analyses and its variants, such as Alternative FROC (AFROC) analyses, are commonly used to quantify performance in such tasks. However, ideal observers that optimize FROC or AFROC performance metrics have not yet been formulated in the general case. If available, such ideal observers may turn out to be valuable for imaging system optimization and in the design of computer aided diagnosis (CAD) techniques for lesion detection in medical images. In this paper we derive ideal AFROC and FROC observers. They are ideal in that they maximize, amongst all decision strategies, the area under the associated AFROC or FROC curve. In addition these ideal observers minimize Bayes risk for particular choices of cost constraints. Calculation of observer performance for these ideal observers is computationally quite complex. We can reduce this complexity by considering forms of these observers that use false positive reports derived from signal-absent images only. We present a performance comparison of our ideal AFROC observer versus that of a more conventional scan-statistic observer.