A new comparison of hyperspectral anomaly detection algorithms for real-time applications

Due to the high spectral resolution that remotely sensed hyperspectral images provide, there has been an increasing interest in anomaly detection. The aim of anomaly detection is to stand over pixels whose spectral signature differs significantly from the background spectra. Basically, anomaly detectors mark pixels with a certain score, considering as anomalies those whose scores are higher than a threshold. Receiver Operating Characteristic (ROC) curves have been widely used as an assessment measure in order to compare the performance of different algorithms. ROC curves are graphical plots which illustrate the trade- off between false positive and true positive rates. However, they are limited in order to make deep comparisons due to the fact that they discard relevant factors required in real-time applications such as run times, costs of misclassification and the competence to mark anomalies with high scores. This last fact is fundamental in anomaly detection in order to distinguish them easily from the background without any posterior processing. An extensive set of simulations have been made using different anomaly detection algorithms, comparing their performances and efficiencies using several extra metrics in order to complement ROC curves analysis. Results support our proposal and demonstrate that ROC curves do not provide a good visualization of detection performances for themselves. Moreover, a figure of merit has been proposed in this paper which encompasses in a single global metric all the measures yielded for the proposed additional metrics. Therefore, this figure, named Detection Efficiency (DE), takes into account several crucial types of performance assessment that ROC curves do not consider. Results demonstrate that algorithms with the best detection performances according to ROC curves do not have the highest DE values. Consequently, the recommendation of using extra measures to properly evaluate performances have been supported and justified by the conclusions drawn from the simulations.