An End-to-End Error Model for Classification Methods Based on Temporal Change or Polarization Ratio of SAR Intensities

Abstract

This paper aims at defining the expression of the probability of error of classification methods using a synthetic aperture radar (SAR) intensity ratio as a classification feature. The two SAR intensities involved in this ratio can be measurements from different dates, polarizations, or, also possibly, frequency bands. Previous works provided a baseline expression of the probability of error addressing the two-class problem with equal a priori class probabilities and no calibration error. This study brings up a novel expression of the error, providing the possibility to assess the effect of class probabilities and calibration errors. An extended expression is described for the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex> </formula> -class problem. The effect of calibration errors such as channel gain imbalance, radiometric stability, and crosstalk is assessed in the general case. The results indicate that, for the applications under study, channel gain imbalance is usually not a decisive parameter, but radiometric stability is more critical in methods based on the temporal change. Crosstalk has a negligible effect in the case of copolarizations. The impacts of other system parameters, such as ambiguity ratio, time-lapse between repeat-pass orbits, spatial resolution, and number of looks, are illustrated through a set of assumptions on the backscattering values of the considered classes. The model is validated by comparing some of its outputs to experimental results calculated from the application of rice fields mapping methods on real data. This error model constitutes a tool for the design of future SAR missions and for the development of robust classification methods using existing SAR instruments.