The authors propose a new method for unsupervised classification of terrain types and man-made objects using polarimetric synthetic aperture radar (SAR) data. This technique is a combination of the unsupervised classification based on polarimetric target decomposition, S.R. Cloude et al. (1997), and the maximum likelihood classifier based on the complex Wishart distribution for the polarimetric covariance matrix, J.S. Lee et al. (1994). The authors use Cloude and Pottier's method to initially classify the polarimetric SAR image. The initial classification map defines training sets for classification based on the Wishart distribution. The classified results are then used to define training sets for the next iteration. Significant improvement has been observed in iteration. The iteration ends when the number of pixels switching classes becomes smaller than a predetermined number or when other criteria are met. The authors observed that the class centers in the entropy-alpha plane are shifted by each iteration. The final class centers in the entropy-alpha plane are useful for class identification by the scattering mechanism associated with each zone. The advantages of this method are the automated classification, and the interpretation of each class based on scattering mechanism. The effectiveness of this algorithm is demonstrated using a JPL/AIRSAR polarimetric SAR image.

Unsupervised classification using polarimetric decomposition and the complex Wishart classifier

Multi-look polarimetric SAR (synthetic aperture radar) data can be represented either in Mueller matrix form or in complex covariance matrix form. The latter has a complex Wishart distribution. A maximum likelihood classifier to segment polarimetric SAR data according to terrain types has been developed based on the Wishart distribution. This algorithm can also be applied to multifrequency multi-look polarimetric SAR data, as well as 10 SAR data containing only intensity information. A procedure is then developed for unsupervised classification. The classification error is assessed by using Monte Carlo simulation of multilook polarimetric SAR data, owing to the lack of ground truth for each pixel. Comparisons of classification errors using the training sets and single-look data are also made. Applications of this algorithm are demonstrated with NASA/JPL P-, L- and C-band polarimetric SAR data.

Classification of multi-look polarimetric SAR imagery based on complex Wishart distribution

Polarimetric and interferometric SAR data are frequently multilook processed for speckle reduction and data compression. The statistical characteristics of multilook data are quite different from those of single-look data. The authors investigate the statistics of their intensity and phase. Probability density function (PDF's) of the multilook phase difference, magnitude of complex product, and intensity and amplitude ratios between two components of the scattering matrix are derived, and expressed in closed forms. The PDF's depend on the complex correlation coefficient and the number of looks. Comparisons of these theoretically derived PDF's are made to measurements from NASA/JPL AIRSAR data. The results of this paper can be applied to feature classification using polarimetric SAR and to the estimation of decorrelation effects of the interferometric SAR. >

Intensity and phase statistics of multilook polarimetric and interferometric SAR imagery

Following the great success of deep convolutional neural networks (CNNs) in computer vision, this paper proposes a complex-valued CNN (CV-CNN) specifically for synthetic aperture radar (SAR) image interpretation. It utilizes both amplitude and phase information of complex SAR imagery. All elements of CNN including input-output layer, convolution layer, activation function, and pooling layer are extended to the complex domain. Moreover, a complex backpropagation algorithm based on stochastic gradient descent is derived for CV-CNN training. The proposed CV-CNN is then tested on the typical polarimetric SAR image classification task which classifies each pixel into known terrain types via supervised training. Experiments with the benchmark data sets of Flevoland and Oberpfaffenhofen show that the classification error can be further reduced if employing CV-CNN instead of conventional real-valued CNN with the same degrees of freedom. The performance of CV-CNN is comparable to that of existing state-of-the-art methods in terms of overall classification accuracy.

Complex-Valued Convolutional Neural Network and Its Application in Polarimetric SAR Image Classification

In this paper, we proposed an unsupervised terrain and land-use classification algorithm using polarimetric synthetic aperture radar data. Unlike other algorithms that classify pixels statistically and ignore their scattering characteristics, this algorithm not only uses a statistical classifier, but also preserves the purity of dominant polarimetric scattering properties. This algorithm uses a combination of a scattering model-based decomposition developed by Freeman and Durden and the maximum-likelihood classifier based on the complex Wishart distribution. The first step is to apply the Freeman and Durden decomposition to divide pixels into three scattering categories: surface scattering, volume scattering, and double-bounce scattering. To preserve the purity of scattering characteristics, pixels in a scattering category are restricted to be classified with other pixels in the same scattering category. An efficient and effective class initialization scheme is also devised to initially merge clusters from many small clusters in each scattering category by applying a merge criterion developed based on the Wishart distance measure. Then, the iterative Wishart classifier is applied. The stability in convergence is much superior to that of the previous algorithm using the entropy/anisotropy/Wishart classifier. Finally, an automated color rendering scheme is proposed, based on the classes' scattering category to code the pixels to resemble their natural color. This algorithm is also flexible and computationally efficient. The effectiveness of this algorithm is demonstrated using the Jet Propulsion Laboratory's AIRSAR and the German Aerospace Center's (DLR) E-SAR L-band polarimetric synthetic aperture radar images.

Unsupervised terrain classification preserving polarimetric scattering characteristics

A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow-covered fields is developed using the optimum polarimetric classifier. The covariance matrices for various terrain cover are computed from theoretical models of random medium by evaluating the scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Analytical and Monte Carlo simulated classification errors using the fully polarimetric feature vector are compared with classification based on single features which include the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements.

Identification of Terrain Cover Using the Optimum Polarimetric Classifier

There is considerable interest in determining the optimal polarizations that maximize contrast between two scattering classes in polarimetric radar images. A systematic approach is presented for obtaining the optimal polarimetric matched filter, i.e., that filter which produces maximum contrast between two scattering classes. The maximization procedure involves solving an eigenvalue problem where the eigenvector corresponding to the maximum contrast ratio is an optimal polarimetric matched filter. To exhibit the physical significance of this filter, it is transformed into its associated transmitting and receiving polarization states, written in terms of horizontal and vertical vector components. For the special case where the transmitting polarization is fixed, the receiving polarization which maximizes the contrast ratio is also obtained. Polarimetric filtering is then applies to synthetic aperture radar images obtained from the Jet Propulsion Laboratory. It is shown, both numerically and through the use of radar imagery, that maximum image contrast can be realized when data is processed with the optimal polarimeter matched filter.

/pdf/optimal-polarizations-for-achieving-maximum-contrast-in-keieysamkc.pdf

Optimal polarizations for achieving maximum contrast in radar images

The normalized polarimetric classifier (NPC) which uses only the relative magnitudes and phases of the polarimetric data is proposed for discrimination of terrain elements The probability density functions (PDFs) of polarimetric data are assumed to have a complex Gaussian distribution, and the marginal PDF of the normalized polarimetric data is derived by adopting the Euclidean norm as the normalization function The general form of the distance measure for the NPC is also obtained It is demonstrated that for polarimetric data with an arbitrary PDF, the distance measure of NPC will be independent of the normalization function selected even when the classifier is mistrained A complex Gaussian distribution is assumed for the polarimetric data consisting of grass and tree regions The probability of error for the NPC is compared with those of several other single-feature classifiers The classification error of NPCs is shown to be independent of the normalization function

Bayes classification of terrain cover using normalized polarimetric data

Equations for the scattering of electromagnetic waves from a randomly perturbed periodic surface have been formulated using the extended boundary condition method and solved using the small perturbation method. Surface currents and scattered fields are solved for up to the second order. The results indicate that as the correlation length of the random roughness increases, the bistatic scattering patterns of the scattered fields show several beams associated with each Bragg diffraction direction of the periodic surface. The beam shape becomes broader with smaller correlation length. Results obtained using the Kirchhoff approximation are found to agree well with the present results for the hh and vv polarized backscattering coefficients for small angles of incidence.

Scattering of electromagnetic waves from a periodic surface with random roughness

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 significiant depolarized returns when the incident direction is not perpendicular to the row direction of the periodic surface.

H. A. Yueh

Papers

Identification of Terrain Cover Using the Optimum Polarimetric Classifier

Optimal polarizations for achieving maximum contrast in radar images

Bayes classification of terrain cover using normalized polarimetric data

Scattering of electromagnetic waves from a periodic surface with random roughness

Scattering Of Electromagnetic Waves From A Periodic Surface With Random Roughness