Quantitative determination of the optimal threshold of Permanent Scatterer based on ROC Curve

Permanent Scatterer (PS) identification is a key step in the PS-InSAR technology, which is mainly used for obtaining ground subsidence data. The density and accuracy of the PS points are determined by setting the optimal threshold of PS identification. Receiver Operating Characteristic (ROC) curve is used to quantitatively analyze and determine the optimal threshold for PS identification.The ROC curve is drawn with some thresholds of every PS identification algorithm. According to the ROC curve, the larger area under the ROC curve indicates that the PS recognition method is more reliable. When the area under the ROC curve is sufficiently large, the optimal threshold of PS identification, which is the closest to the upper left of the ROC curve, is determined quantitatively according to the maximum sum of the sensitivity and specificity of the ROC curve. The positive ratio of PS points is sufficiently high, the false positive ratio of PS points is sufficiently low, and the density of the PS point is sufficient, using the optimal threshold.The PS points are identified with 60 X-band TerraSAR-X images (2010-2017) by three algorithms as amplitude dispersion (TD), correlation coefficient (Tγ), and dual-threshold (TD, Tγ) with amplitude dispersion index (ADI) and correlation coefficient index (CCI). The experimental area is approximately Beijing Longtan Park. First, three ROC curves are drawn separately with the algorithms ADI, CCI, and dual-threshold. Second, the optimal thresholds of every algorithm have been calculated according to the maximum sum of the sensitivity and specificity of ROC curve. Research found that: (1) the optimal threshold of ADI is TD=0.45; the optimal threshold of CCI is Tγ=0.45; the optimal threshold of dual-threshold of ADI and CCI is (TD, Tγ) = (0.50, 0.50). (2) The area under the ROC curve of dual threshold is AUC=0.762, which is higher than the AUC of the single threshold algorithm, such as ADI and CCI. Evidently the dual-threshold algorithm is much better than the single threshold of ADI or CCI to identify the PS points.Result of this research shows that the ROC curve can not only quantitatively determine the optimal threshold of PS identification, but can also be further applied for the quantitative selection of the thresholds during GIS spatial analysis and remote sensing image interpretation. © 2021, Science Press. All right reserved.