Fusion within a Detection System Family

A detection system outputs two distinct labels, thus, there are two errors it can make. The Receiver Operating Characteristic (ROC) function quantifies both of these errors as parameters vary within the system. Combining two detection systems typically yields better performance when a combining rule is chosen appropriately. When two or more detection systems are combined the assumption of independence is usually made in order to simplify the mathematics, so that we need only combine the individual ROC curves from each system into one ROC curve. This paper investigates label fusion of two and more detection systems drawn from a single Detection System Family (DSF). Given that one knows the ROC function for the DSF, we seek a formula with the resultant ROC function of the fused detection systems as a function (specifically, a transformation) of the ROC function. In previous work, we derived this transformation for the disjunction and conjunction label rules. This paper extends those results to several detection systems within the same family. Examples are given that demonstrates these new transformations acting on the ROC function.