178 research outputs found
On the use of the l(2)-norm for texture analysis of polarimetric SAR data
In this paper, the use of the l2-norm, or Span, of the scattering vectors is suggested for texture analysis of polarimetric synthetic aperture radar (SAR) data, with the benefits that we need neither an analysis of the polarimetric channels separately nor a filtering of the data to analyze the statistics. Based on the product model, the distribution of the l2-norm is studied. Closed expressions of the probability density functions under the assumptions of several texture distributions are provided. To utilize the statistical properties of the l2-norm, quantities including normalized moments and log-cumulants are derived, along with corresponding estimators and estimation variances. Results on both simulated and real SAR data show that the use of statistics based on the l2-norm brings advantages in several aspects with respect to the normalized intensity moments and matrix variate log-cumulants.Peer ReviewedPostprint (published version
Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions
The scaled complex Wishart distribution is a widely used model for multilook
full polarimetric SAR data whose adequacy has been attested in the literature.
Classification, segmentation, and image analysis techniques which depend on
this model have been devised, and many of them employ some type of
dissimilarity measure. In this paper we derive analytic expressions for four
stochastic distances between relaxed scaled complex Wishart distributions in
their most general form and in important particular cases. Using these
distances, inequalities are obtained which lead to new ways of deriving the
Bartlett and revised Wishart distances. The expressiveness of the four analytic
distances is assessed with respect to the variation of parameters. Such
distances are then used for deriving new tests statistics, which are proved to
have asymptotic chi-square distribution. Adopting the test size as a comparison
criterion, a sensitivity study is performed by means of Monte Carlo experiments
suggesting that the Bhattacharyya statistic outperforms all the others. The
power of the tests is also assessed. Applications to actual data illustrate the
discrimination and homogeneity identification capabilities of these distances.Comment: Accepted for publication in the IEEE Transactions on Geoscience and
Remote Sensing journa
Statistical modeling of polarimetric SAR data: a survey and challenges
Knowledge of the exact statistical properties of the signal plays an important role in the applications of Polarimetric Synthetic Aperture Radar (PolSAR) data. In the last three decades, a considerable research effort has been devoted to finding accurate statistical models for PolSAR data, and a number of distributions have been proposed. In order to see the differences of various models and to make a comparison among them, a survey is provided in this paper. Texture models, which could capture the non-Gaussian behavior observed in high resolution data, and yet keep a compact mathematical form, are mainly explained. Probability density functions for the single look data and the multilook data are reviewed, as well as the advantages and applicable context of those models. As a summary, challenges in the area of statistical analysis of PolSAR data are also discussed.Peer ReviewedPostprint (published version
Region-Based Classification of PolSAR Data Using Radial Basis Kernel Functions With Stochastic Distances
Region-based classification of PolSAR data can be effectively performed by
seeking for the assignment that minimizes a distance between prototypes and
segments. Silva et al (2013) used stochastic distances between complex
multivariate Wishart models which, differently from other measures, are
computationally tractable. In this work we assess the robustness of such
approach with respect to errors in the training stage, and propose an extension
that alleviates such problems. We introduce robustness in the process by
incorporating a combination of radial basis kernel functions and stochastic
distances with Support Vector Machines (SVM). We consider several stochastic
distances between Wishart: Bhatacharyya, Kullback-Leibler, Chi-Square,
R\'{e}nyi, and Hellinger. We perform two case studies with PolSAR images, both
simulated and from actual sensors, and different classification scenarios to
compare the performance of Minimum Distance and SVM classification frameworks.
With this, we model the situation of imperfect training samples. We show that
SVM with the proposed kernel functions achieves better performance with respect
to Minimum Distance, at the expense of more computational resources and the
need of parameter tuning. Code and data are provided for reproducibility.Comment: Accepted for publication in the International Journal of Digital
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