Exploration of Data Scene Characterization and 3D ROC Evaluation for Hyperspectral Anomaly Detection

Abstract

Whether or not a hyperspectral anomaly detector is effective is determined by two crucial issues, anomaly detectability and background suppressibility (BS), both of which are very closely related to two factors, the datasets used for a selected hyperspectral anomaly detector and detection measures used for its performance evaluation. This paper explores how anomaly detectability and BS play key roles in hyperspectral anomaly detection (HAD). To address these two issues, we investigate three key elements attributed to HAD. One is a selected hyperspectral anomaly detector, and another is the datasets used for experiments. The third one is the detection measures used to evaluate the effectiveness of a hyperspectral anomaly detector. As for hyperspectral anomaly detectors, twelve commonly used anomaly detectors were evaluated and compared. To address the appropriate use of datasets for HAD, seven popular and widely used datasets were studied for HAD. As for the third issue, the traditional area under a receiver operating characteristic (ROC) curve of detection probability—PD versus false alarm probability, PF, (AUC(D,F))—was extended to 3D ROC analysis where a 3D ROC curve was developed to generate three 2D ROC curves from which eight detection measures could be derived to evaluate HAD in all round aspects, including anomaly detectability, BS and joint anomaly detectability and BS. Qualitative analysis showed that many works reported in the literature which claimed that their developed hyperspectral anomaly detectors performed better than other anomaly detectors are actually not true because they overlooked these two issues. Specifically, a comprehensive study via extensive experiments demonstrated that these 3D ROC curve-derived detection measures can be further used to address the various characterizations of different data scenes and also to provide explanations as to why certain data scenes are not suitable for HAD.

Keywords

• 3D receiver operating characteristics analysis
• anomaly detectability
• background suppressibility
• constrained energy minimization anomaly detector
• dummy variable trick
• effective anomaly space