Statistical models for polarimetric data: consequences, testing and validity

Abstract

Low resolution polarimetric data gathered by the AirSAR system over the Feltwell U.K. agriculturaltestsite reveals Gaussian behaviour at C band for all vegetation types, but clear evidence of texture at longer wavelengths. The measurements are compared with the predictions of a polarimetric texture model based on a multivariate K distribution (which includes the Gaussian distribution as a special case), from which distributions of the inphase component, amplitude, amplitude ratio, phase difference and real hermitian product between channels are derived. Kolmogorov-Smirnov fits to these marginal distributions verify that C, Land P band observations over a range of vegetation types are consistent with the model, but there is evidence of the model breaking down in cereal fields at P band. The departure from Gaussian behaviour with increasing wavelength is strongest for cereals; less marked trends are observed for root vegetables, while forest appears Gaussian at all wavelengths. These results are unexpected, since texture is normally associated with high resolution, particularly in woodland. Moment based measures are investigated as indicators of distribution and as discriminators of vegetation type. The order parameter of the K distribution appears useful in both respects. These results help to clarify the information content of polarimetric data, but raise questions about how best to use the data (e.g., for classification), and are hard to reconcile with simple physical models.