Feature fusion of detection systems via their ROC functions

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 combination rule is chosen appropriately. When multiple detection systems are combined, the assumption of independence is usually made in order to mathematically combine the individual ROC functions for each system into one ROC function. This paper investigates feature fusion of multiple detection systems. Given that one knows the ROC function for each individual detection system, we seek a formula with the resultant ROC function of the fused detection systems as a function (specifically, a transformation) of the respective ROC functions. In this paper we derive this transformation for a certain class of feature rules. An example will be given that demonstrates this transformation.