The effects of correlation on the performance of ATR systems

Abstract

The Receiver Operating Characteristic (ROC) curve is typically used to quantify the performance of Automatic Target Recognition (ATR) systems. When multiple systems are to be fused, assumptions are made in order to mathematically combine the individual ROC curves for each of these ATR systems in order to form the ROC curve of the fused system. Often, one of these assumptions is independence between the systems. However, correlation may exist between the classifiers, processors, sensors and the outcomes used to generate each ROC curve. This paper will demonstrate a method for creating a ROC curve of the fused systems which incorporates the correlation that exists between the individual systems. Specifically, we will use the derived covariance matrix between multiple systems to compute the existing correlation and level of dependence between pairs of systems. The ROC curve for the fused system is then produced, adjusting for this level of dependency, using a given fusion rule. We generate the formula for the Boolean OR and AND rules, giving the exact ROC curve for the fused system, that is, not a bound.