Discriminant Analysis with Spatial Weights for Urban Land Cover Classification

Classifying urban area images is challenging because of the heterogeneous nature of the urban landscape resulting in mixed pixels and classes with highly variable spectral ranges. Approaches using ancillary data, such as knowledge based or expert systems, have shown to improve the classification accuracy in urban areas. Appropriate ancillary data, however, may not always be available. The goal of this study is to compare the results of the discriminant analysis statistical technique with discriminant analysis with spatial weights to classify urban land cover. Discriminant analysis is a statistical technique used to predict group membership for a target based on the linear combination of independent variables. Strict per pixel statistical analysis however does not consider the spatial dependencies among neighbouring pixels. Our study shows that approaches using ancillary data continue to outperform strict spectral classifiers but that using a spatial weight improved the results. Furthermore, results show that when the discriminant analysis technique works well then the spatially weighted approach performs better. However, when the discriminant analysis performs poorly, those poor results are magnified in the spatially weighted approach in the same study area. The study shows that for dominant classes, adding spatial weights improves the classification accuracy.

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

SAR Amplitude Probability Density Function Estimation Based on a Generalized Gaussian Model

International audienceIn the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed “method-of-log-cumulants” (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena

Mixture of Latent Variable Models for Remotely Sensed Image Processing

The processing of remotely sensed data is innately an inverse problem where properties of spatial processes are inferred from the observations based on a generative model. Meaningful data inversion relies on well-defined generative models that capture key factors in the relationship between the underlying physical process and the measurements. Unfortunately, as two mainstream data processing techniques, both mixture models and latent variables models (LVM) are inadequate in describing the complex relationship between the spatial process and the remote sensing data. Consequently, mixture models, such as K-Means, Gaussian Mixture Model (GMM), Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA), characterize a class by statistics in the original space, ignoring the fact that a class can be better represented by discriminative signals in the hidden/latent feature space, while LVMs, such as Principal Component Analysis (PCA), Independent Component Analysis (ICA) and Sparse Representation (SR), seek representational signals in the whole image scene that involves multiple spatial processes, neglecting the fact that signal discovery for individual processes is more efficient. Although the combined use of mixture model and LVMs is required for remote sensing data analysis, there is still a lack of systematic exploration on this important topic in remote sensing literature. Driven by the above considerations, this thesis therefore introduces a mixture of LVM (MLVM) framework for combining the mixture models and LVMs, under which three models are developed in order to address different aspects of remote sensing data processing: (1) a mixture of probabilistic SR (MPSR) is proposed for supervised classification of hyperspectral remote sensing imagery, considering that SR is an emerging and powerful technique for feature extraction and data representation; (2) a mixture model of K “Purified” means (K-P-Means) is proposed for addressing the spectral endmember estimation, which is a fundamental issue in remote sensing data analysis; (3) and a clustering-based PCA model is introduced for SAR image denoising. Under a unified optimization scheme, all models are solved via Expectation and Maximization (EM) algorithm, by iteratively estimating the two groups of parameters, i.e., the labels of pixels and the latent variables. Experiments on simulated data and real remote sensing data demonstrate the advantages of the proposed models in the respective applications

Modeling the statistics of high resolution SAR images

In the context of remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of pixel intensities. In this work, we develop a parametric finite mixture model for modelling the statistics of intensities in high resolution Synthetic Aperture Radar (SAR) images. Along with the models we design an efficient parameter estimation scheme by integrating the Stochastic Expectation Maximization scheme and the Method of log-cumulants with an automatic technique to select, for each mixture component, an optimal parametric model taken from a predefined dictionary of parametric probability density functions (pdf). In particular, the proposed dictionary consists of eight most efficient state-of-the-art SAR-specific pdfs: Nakagami, log-normal, generalized Gaussian Rayleigh, Heavy-tailed Rayleigh, Weibull, K-root, Fisher and generalized Gamma. The experiment results with a set of several real SAR (COSMO-SkyMed) images demonstrate the high accuracy of the designed algorithm, both from the viewpoint of a visual comparison of the histograms, and from the viewpoint of quantitive measures such as correlation coefficient (always above 99,5%) . We stress, in particular, that the method proves to be effective on all the considered images, remaining accurate for multimodal and highly heterogeneous images

Higher order statistics for texture analysis and physical interpretation of polarimetric SAR data

The logarithmic cumulants (log-cumulants for short) of the second and third orders are widely used in the statistical analysis of polarimetric synthetic aperture radar (PolSAR) data. However, both the product model and the finite mixture model may produce the same values of these statistics, which means that the use of these log-cumulants is not enough to determine the statistical model of the data. In this letter, it is demonstrated that the log-cumulants of higher orders can help to distinguish the concept of texture from that of mixture, providing a physical insight into the data statistics. A tool called log-cumulant cube, which helps to visualize this difference, is proposed by considering texture distributions from the Pearson's family. Results on both simulated and real SAR data show that the use of higher order statistics is useful when it comes to the texture analysis of PolSAR data.Peer ReviewedPostprint (author's final draft

Spatial Modeling of Compact Polarimetric Synthetic Aperture Radar Imagery

The RADARSAT Constellation Mission (RCM) utilizes compact polarimetric (CP) mode to provide data with varying resolutions, supporting a wide range of applications including oil spill detection, sea ice mapping, and land cover analysis. However, the complexity and variability of CP data, influenced by factors such as weather conditions and satellite infrastructure, introduce signature ambiguity. This ambiguity poses challenges in accurate object classification, reducing discriminability and increasing uncertainty. To address these challenges, this thesis introduces tailored spatial models in CP SAR imagery through the utilization of machine learning techniques. Firstly, to enhance oil spill monitoring, a novel conditional random field (CRF) is introduced. The CRF model leverages the statistical properties of CP SAR data and exploits similarities in labels and features among neighboring pixels to effectively model spatial interactions. By mitigating the impact of speckle noise and accurately distinguishing oil spill candidates from oil-free water, the CRF model achieves successful results even in scenarios where the availability of labeled samples is limited. This highlights the capability of CRF in handling situations with a scarcity of training data. Secondly, to improve the accuracy of sea ice mapping, a region-based automated classification methodology is developed. This methodology incorporates learned features, spatial context, and statistical properties from various SAR modes, resulting in enhanced classification accuracy and improved algorithmic efficiency. Thirdly, the presence of a high degree of heterogeneity in target distribution presents an additional challenge in land cover mapping tasks, further compounded by signature ambiguity. To address this, a novel transformer model is proposed. The transformer model incorporates both fine- and coarse-grained spatial dependencies between pixels and leverages different levels of features to enhance the accuracy of land cover type detection. The proposed approaches have undergone extensive experimentation in various remote sensing tasks, validating their effectiveness. By introducing tailored spatial models and innovative algorithms, this thesis successfully addresses the inherent complexity and variability of CP data, thereby ensuring the accuracy and reliability of diverse applications in the field of remote sensing