There is considerable interest in deterxiiixiirig the opt iiiial polarizations that maxiniize contrast hetweeri two scatteriiig classes i n polariiiietric radar images. In this payer a systematic approach is presented for obtaining the optimal polariiiiet ric xiiatclied filter, i.e.. that filter which produces niaxiiiiuiii contrast bet ween t w o scattering classes. The xiiax- iiiiizatioxi procedure involves solving a n eigenvalue problem where the eigenvector correspoiidiiig to t lie iiiaxixiium contrast ratio is optimal polarixnet ric xiiatclied filter. To exhibit the physical sigiiificaiice of this filter, it is traiisforiiied into its associated transmitting a n d For the special case where t lie t ransiiiit tiiig polarization is fixed, the receiving polariza--i a 4:t ion which xiiasixiiizes t h e coxit rast rat,io is also obtained. Polarimetric filtering is then applied to synt liet ic aperture radar illiages ohtained from the J e t Propulsion Laboratory.It is shown. hot 11 tiunierically and through the use of radar iniagery, that iiiaxin1um image coiit rast can he realized w h e n d a t a is processed with the optiiiial polariiiietric xilatched filter.

Supervised and unsupervised classification procedures are developed and applied to synthetic aperture radar (SAR) polarimetric images in order to identify their various Earth terrain components. For supervised classification processing, the Bayes technique is used to classify fully polarimetric and normalized polarimetric SAR data. Simpler polarimetric discriminates, such as the absolute and normalized magnitude response of the individual receiver channel returns, in addition to the phase difference between the receiver channels, are also considered. Another processing algorithm, based on comparing general properties of the Stokes parameters of the scattered wave to that of simple scattering models, is also discussed. This algorithm, which is an unsupervised technique, classifies terrain elements based on the relationship between the orientation angle and handedness of the transmitting and receiving polarization states. These classification procedures have been applied to San Francisco Bay and Traverse City SAR images, supplied by the Jet Propulsion Laboratory. It is shown that supervised classification yields the best overall performance when accurate classifier training data are used, whereas unsupervised classification is applicable when training data are not available. INTRODUCTIONClassification of Earth terrain within an image is one of the many important applications of polarimetric data. A systematic classification procedure will place the classification process on a more quantitative level and reduce the amount of photointerpretation necessary [Thompson, 1986;Evans et al., 1986]. Single feature and multifrequency classification has been used in the past, but classification can now be applied to fully polarimetric data which have become available due to recent developments in radar technology [Stovall, 1978;Novak and Sechtin, 1986]. It has been shown that Bayes classification using fully polarimetric data yields optimal results as compared to classification performance using any subset of the complete polarimetry [Kong et al., 1988].In some cases, the absolute magnitude and phase of the radar return are not reliable features for data classification purposes. This is due to the fact that radar system calibration procedures vary in accuracy as well as the fact that they cannot account for attenuation and phase shifts caused by atmospheric distortions. Normalization schemes [Yueh et al., 1988], which preserve only the relative components of the returns, were applied to radar polarimetry in order to circumvent this problem. Previously, normalized polarimettic classification schemes were implemented by assuming a multivariate Gaussian distribution for normalized data [Kriegler et al., 1971; Smedes et al., 1971]. However, this technique yields inconsistent results since the probability of error, as well as classification performance, becomes a function of the particular normalization scheme selected. Therefore the optimal normalized classification algorithm will be employed in which the probability density funct...

No abstract

The normalized polarimetric classifier which uses only the relative magnitudes and phases of the polarimetric data is proposed for discrimination of terrain elements. For polarimetric data with arbitrary probability density function, the distance measures of the normalized polarimetric classifier based on a general class of normalization functions are shown to be equivalent to one another. When the system absolute calibration factors are common to all polarimetric channels, the normalized polarimetric classifier derived is shown to be optimal. Further assuming a complex Gaussian distribution of the unnormalized data, the distance measure of the normalized polarimetric classifier is given explicitly and is shown to be independent of the number of scatterers illuminated. The usefulness of the normalized polarimetric classifier is demonstrated by the classification of grass and tree regions in experimental data obtained from the Massachusetts Institute of Technology Lincoln Laboratory. The classification errors generated using the optimal normalized polarimetric classifier are shown to be smaller than those generated using other types of classifiers which employ only magnitude ratios or phase differences to classify radar images.

The scattering of electromagnetic waves from a randomly perturbed periodic surface is formulated by the extended boundary condition (EBC) method and solved by the small perturbation method (SPM). The scattering from periodic surface is solved exactly and this solution is used in the SPM to solve for the surface currents and scattered fields up to the second order. The random perturbation is modeled as a Gaussian random process. The theoretical results are illustrated by calculating the bistatic and backscattering coefficients. It is shown that as the correlation length of the random roughness increases, the bistatic scattering pattern of the scattered fields show several beams associated with each Bragg diffraction direction of the periodic surface. When the correlation length becomes smaller, then the shape of the beams become broader. The results obtained using the EBC/SPM method is also compared with the results obtained using the Kirchhoff approximation. It is shown that the Kirchhoff approximation results show quite a good agreement with EBC/SPM method results for the hh and vv polarized backscattering coefficients for small angles of incidence. However, the Kirchhoff approximation does not give depolarized returns in the backscattering direction, whereas the results obtained using the EBC/SPM method give significant depolarized returns when the incident direction is not perpendicular to the row direction of the periodic surface.