ROC manifolds of multiple fused independent ATR systems

Abstract

ABSTRACT AnAutomaticTargetRecognition(ATR)systemwith N possibleoutputlabels (ordecisions)will have N (N Š 1) possibleerrors. The Receiver Operating Characteristic (ROC) manifold was created to quantify all of these errors. When multipleATRsystemsarefused,theassumptionofindependenceis usuallymadeinordertomathematicallycombinetheindividualROC manifolds for each system into one ROC manifold. This paper will investigate the label fusion (also called decisionfusion)ofmultipleclassiÞcationsystemsthathavethesamenumberofoutputlabels. Booleanrulesdonotexistformultiplesymbols, thus, we will derive possible Boolean-like rules as well as other rules that will yield label fusion rules. Theformulafor the resultant ROC manifold of the fused classiÞcation systems which incorporatesthe individualclassiÞcationsystems will be derived. SpeciÞcally, given a fusion rule and two classiÞcation systems, the ROC manifold for the fusedsystem is produced. We generate formulas for the Boolean-like OR rule, Boolean-like AND rule, and other rules and givethe resultant ROC manifold for the fused system. Examples will be given that demonstrate how each formulais used.Keywords: Automatic Target Recognition,ClassiÞcation System, ROC manifold,Label Fusion