Analysis of Stochastic Distances and Wishart Mixture Models Applied on PolSAR Images

Abstract

This paper address unsupervised classification strategies applied to Polarimetric Synthetic Aperture Radar (PolSAR) images. We analyze the performance of complex Wishart distribution, which is a widely used model for multi-look PolSAR images, and the robustness of five stochastic distances (Bhattacharyya, Kullback-Leibler, Rényi, Hellinger and Chi-square) between Wishart distributions. Two unsupervised classification strategies were chosen: the Stochastic Clustering (SC) algorithm, which is based on the K-means algorithm but uses stochastic distance as the similarity metric, and the Expectation-Maximization (EM) algorithm for Wishart Mixture Model. With the aim of assessing the performance of all algorithms presented here, we performed a Monte Carlo simulation over a set of simulated PolSAR images. A second experiment was conducted using the study area of Tapajós National Forest and the surrounding area, in Brazilian Amazon Forest. The PolSAR images were obtained by the satellite PALSAR. The results, in both experiments, suggest that the EM algorithm and the SC with Hellinger and the SC with Bhattacharyya distance provide a better classification performance. We also analyze the initialization problem for SC and EM algorithms, and we demonstrate how the initial centroid choice influences the final classification result.

Estimation of the Number of Endmembers in Hyperspectral Images Using Agglomerative Clustering

“…The SKL divergence is commonly used to measure the dissimilarity between two distributions [28,29]. Appendix A describes how D SKL (C u , C v ) is estimated from the mixing matrix, the bias vector and the source matrix of C u and C v .…”

Introduction to Radar Scattering Application in Remote Sensing and Diagnostics: Review

“…When an electromagnetic wave passes from one medium to another, changing, therefore, refraction index, or when it strikes an object such as a radar target and it is reflected, it allows a polarization control to acquire knowledge of the characteristic information about the reflectivity, e.g., the orientation and shape of the reflecting object. In classical radars, i.e., amplitude-only radars, the information about a target is mainly obtained from the energy of the returned pulse; interferometric SAR exploits fully the phase and Doppler information, but not the polarization information of the electromagnetic vector wave-scatterer interrogation process [116][117][118][119].…”

Entropy Estimators in SAR Image Classification

“…In particular, entropy measures have been widely used for this purpose. Parameter estimation [9], classification [10], procedures for constructing confidence interval and contrast measures [11,12], edge detection [13], and noise reduction filters [14] are among their applications.…”

“…Ferreira and Nascimento [16] derived a closed-form expression for the Shannon entropy based on the G 0 law for intensity data and proposed a new entropy-based segmentation method. Carvalho et al [10] employed stochastic distances to approach unsupervised classification applied to Polarimetric Synthetic Aperture Radar (PolSAR) images. Shannon entropy has been applied to analyzed SAR imagery in several approaches, from inference [11] to classification [16].…”

“…van Es [18] showed that, under general conditions, (10) converges almost surely to H[Z] when m, n → ∞, m/ log(n) → ∞, and m/n → 0. The author also proved the estimator's asymptotic normality when m, n → ∞ and m = o(n 1/2 ).…”