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 detection systems are combined the assumption of independence is usually made in order to simplify the math- ematics, so that we need only combine the individual ROC curve from each system into one ROC curve. This paper investigates label fusion of two 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 this paper, we derive this transformation for the disjunction and conjunction label rules. Examples are given that demonstrates this transformation. Furthermore, another transformation is given to account for the dependencies between the two systems within the family. Examples will be given that demonstrates these ideas and the corresponding transformation acting on the ROC curve.
Mark E. Oxley and Christine M. Schubert Kabban, "Fusion within a classification system family," Proc. SPIE 10200, Signal Processing, Sensor/Information Fusion, and Target Recognition XXVI, 102000H (Presented at SPIE Defense + Security: April 11, 2017; Published: 2 May 2017); https://doi.org/10.1117/12.2265966.
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