Performances of an ATR system via its ROC manifold

A classification system such as an automatic target recognition (ATR) system with N possible output labels (or decisions) will have N(N-1) possible errors. The receiver operating characteristic (ROC) manifold was created to quantify all of these errors. Truthed data will produce an approximation to a ROC manifold. How well does the approximate ROC manifold approximate the true ROC manifold? Several functionals exist that quantify the approximation ability, but researchers really wish to quantify the performance in the approximate ROC manifold. This paper will review different performance definitions for ROC curves and manifolds, and thus, quantify the fusion of ATR systems. Examples of different performances will be given that are defined on manifolds.