Statistical Tests for a Ship Detector Based on the Polarimetric Notch Filter

Ship detection is an important topic in remote sensing, and synthetic aperture radar (SAR) has a valuable contribution, allowing detection at nighttime and with almost any weather conditions. In addition, polarimetry can play a significant role considering its capability to discriminate between different targets. Recently, a new ship detector exploiting polarimetric information has been developed, namely, the Geometrical Perturbation-Polarimetric Notch Filter (GP-PNF). This work is focused on devising two statistical tests for the GP-PNF. The latter allow an automatic and adaptive selection of the detector threshold. Initially, the probability density function (pdf) of the detector is analytically derived. Finally, the Neyman-Pearson lemma is exploited to set the threshold calculating probabilities using the clutter pdf (i.e., a constant false-alarm rate) and a likelihood ratio. The goodness of fit of the clutter pdf is tested with four real SAR data sets acquired by the RADARSAT-2 and the TanDEM-X satellites. The former images are quad-polarimetric, whereas the latter are dual-polarimetric HH/VV. The data are accompanied by the Automatic Identification System (AIS) location of vessels, which facilitates the validation of the detection masks. It can be observed that the pdfs fit the data histograms, and they pass the two sample Kolmogorov-Smirnov and χ² tests.