Hyperspectral Data Processing: Algorithm Design and Analysis

3

Three-Dimensional Receiver Operating Characteristics (3D ROC) Analysis

Receiver operating characteristics (ROC) analysis is a widely used performance evaluation tool in signal processing, communications, and medical diagnosis. It utilizes two-dimensional (2D) curves plotted between detection rate (P_D) and false alarm rate (P_F) to assess effectiveness of a detector or sensor/device for detection. However, P_D and P_F are actually dependent parameters resulting from a more crucial but implicit parameter hidden in the ROC curves, that is, threshold τ, which is determined by the cost of implementing a detector or sensor/device except the case when the Bayes theory is used for detection, where τ is completely determined by the Bayes cost. This chapter extends the traditional ROC analysis for single-signal detection to multiple-signal detection and classification. It also explores the relationship among the three parameters, P_D, P_F, and τ, and further develops a new concept of three-dimensional ROC (3D ROC) analysis that uses 3D ROC curves plotted with P_D, P_F, and τ to evaluate detection effectiveness rather than only P_D and P_F used by 2D ROC analysis. As a result of using the 3D ROC curves, three 2D ROC curves can also be derived, the conventional 2D ROC curve plotted by P_D versus P_F and two new 2D ROC curves plotted by P_D versus τ and P_F versus τ. To demonstrate the utility of 3D ROC analysis, four applications are considered: hyperspectral target detection, medical diagnosis, chemical/biological ...