An ROC analysis for subpixel detection

ROC (Receiver Operating Characteristic) analysis has been widely used to evaluate detection performance. It is based on the Neyman-Pearson detection theory, which solves binary hypothesis testing problems. In mixed pixel classification many algorithms that are developed to estimate abundance fractions (of image endmembers) generally produce gray scale images. As a result, they are not directly applied to hypothesis testing problems. Instead of using the standard ROC curve generated by the detection power versus the false alarm probability, a 3-dimensional (3D) ROC curve is developed in this paper for subpixel detection. It is a 3D plot derived from the mean-detection probability versus the mean-false alarm rate with the third dimension specified by abundance fractions produced by subpixel detection algorithms. In order to illustrate the utility of the proposed 3D ROC analysis in subpixel detection, several linear unmixing-based algorithms are used for performance evaluation.