Bounds on the ROC curves from fused correlated ATR systems

Receiver operating characteristic (ROC) curves provide a means to evaluate the performance of ATR systems. Of specific interest, is the ability to evaluate the performance of fused ATR systems in order to gain information on how well the combined system performs with respect to, for instance, single systems, other fusion methods, or pre-specified performance criteria. Although various ROC curves for fused systems have been demonstrated by many researchers, information regarding the bounds for these curves has not been examined thoroughly. This paper seeks to describe several bounds that exist on ROC curves from fused, correlated ATR systems. These bounds include the lower bound for systems fused using Boolean rules and bounds based on a measure of the variance of the ATR system. Examples using simulated ROC curves generated from correlated and uncorrelated ATR systems will be given as well as a discussion of how correlation affects these bounds. Examining such bounds for a set of candidate fusion rules a priori can focus efforts towards those fused systems that better meet specified ATR system performance criteria.