Application of Mellin-Kind Statistics to Polarimetric &lt;inline-formula&gt; &lt;tex-math notation="TeX"&gt;${\cal G}$&lt;/tex-math&gt;&lt;/inline-formula&gt; Distribution for SAR Data

Khan, Salman; Guida, Raffaella

doi:10.1109/tgrs.2013.2273176

Cited by 25 publications

(4 citation statements)

References 43 publications

(105 reference statements)

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“…This estimator is widely used in SAR image processing. Refs [4,10,32] applied this methodology due to its nice properties and good performance. More recently, Nogueira et al [38] used the LC estimator applied in an unsupervised algorithm for SAR image segmentation.…”

Section: Logcumulant Estimatormentioning

confidence: 99%

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An Improved Minimum-Distance Texture Estimator for Speckled Data Under the $$\mathscr {G}^0$$ Model

Cassetti

Frery

2022

J Math Imaging Vis

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The G 0 distribution is an apt model for speckled data, such as SAR imagery, because it possesses the ability to characterize areas with different degrees of texture. In the monopolarized case, this distribution depends on three parameters: the texture, the scale, and the number of looks. The first one is related to the roughness of the image, so its estimation deserves special attention. This paper proposes and compares estimation methods of the texture parameter in intensity format. We treat the multilook case. The proposal is to estimate this parameter by minimizing the triangular distance between the G 0 density and an estimate of the underlying density function using asymmetric kernels. We assess the properties of these estimators with analytic results and simulation. We use actual images to evaluate the performance of our proposal.

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Section: Logcumulant Estimatormentioning

confidence: 99%

“…[18,52] describe attempts to improve the performance of these estimators concerning bias and mean squared error using either resampling or analytic procedures. More recently, using a connection between the Mellin transform, several estimators based on logcumulants and logmoments have been proposed in [4,10,32].…”

Section: Introductionmentioning

confidence: 99%

An Improved Minimum-Distance Texture Estimator for Speckled Data Under the $$\mathscr {G}^0$$ Model

Cassetti

Frery

2022

J Math Imaging Vis

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“…Kp+1(ω) . The above expressions are the PDFs of the scattering vector and the sample covariance matrix following G distributions [8,97].…”

Section: G and G 0 Distributionsmentioning

confidence: 99%

“…PDFs about the G distribution can be found in Section 3.2.1.2. The matrix variate log-cumulants in this case can be calculated using [97] κ…”

Section: Texture Modelmentioning

confidence: 99%

Texture analysis and physical interpretation of polarimetric SAR data

Deng

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This thesis is dedicated to the study of texture analysis and physical interpretation of PolSAR data. As the starting point, a complete survey of the statistical models for PolSAR data is conducted. All the models are classified into three categories: Gaussian distributions, texture models, and finite mixture models. The texture models, which assume that the randomness of the SAR data is due to two unrelated factors, texture and speckle, are the main subject of this study. The PDFs of the scattering vector and the sample covariance matrix in different models are reviewed. Since many models have been proposed, how to choose the most accurate one for a test data is a big challenge. Methods which analyze different polarimetric channels separately or require a filtering of the data are limited in many cases, especially when it comes to high resolution data. In this thesis, the L2-norms of the scattering vectors are studied, and they are found to be advantageous to extract statistical information from PolSAR data. Statistics based on the L2-norms can be utilized to determine what distribution the data actually follow. A number of models are suggested to model the texture of PolSAR data, and some are very complex. But most of them lack a physical explanation. The random walk model, which can be interpreted as a discrete analog of the SAR data focusing process, is studied with the objective to understand the data statistics from the point of view of scattering process. A simulator based on the random walk model is developed, where different variations in the scatterer types and scatterer numbers are considered. It builds a bridge between the mathematical models and underlying physical mechanisms. It is found that both the mixture and the texture could give the same statistics such as log-cumulants of the second order and the third order. The two concepts, texture and mixture, represent two quite different scenarios. A further study was carried on to see if it is possible to distinguish them. And higher order statistics are demonstrated to be favorable in this task. They can be physically interpreted to distinguish the scattering from a single type of target from a mixture of targets. Esta tesis está dedicada al estudio del análisis de texturas y de la interpretación física de datos PolSAR. Como punto de partida, se ha llevado a cabo un estudio completo de los modelos estadísticos para datos PolSAR. Todos los modelos se han clasificado en tres categorías: distribuciónes gaussianas, modelos de textura y modelos de mezcla finita. Los modelos de textura, que asumen que la aleatoriedad de los datos SAR se debe a dos factores no relacionados, la textura y el speckle, son el tema principal de este estudio. Las distribuciones del vector de dispersión y de la matriz de covarianza en diferentes modelos son revisados. Debido a que se han propuesto muchos modelos, cómo elegir el más preciso para unos datos en particular es un gran reto. Los métodos que analizan diferentes canales polarimétricos por separado o requieren de un filtrado de los datos presentan limitacions en muchos casos, especialmente cuando se trata de datos de alta resolución. En esta tesis, la norma L2 de los vectores de dispersión se estudian, demostrando su utilidad para extraer información estadística de los datos PolSAR. Las estadísticas basadas en la norma L2 se pueden utilizar para determinar la distribución de los datos. En la literatura, se sugieren una serie de modelos para modelar la textura de los datos PolSAR, siendo alguno de ellos muy complejos. Sin embargo, la mayoría de ellos carecen de una explicación física. El modelo de random walk, que se puede interpretar como un análogo discreto del proceso de enfocado de los datos SAR, se estudia con el objetivo de comprender las estadísticas de los datos desde el punto de vista de proceso de dispersión. Se desarrolla un simulador basado en el modelo de random walk, donde se consideran diversas variaciones en los tipos de dispersores y número de dispersores. Se construye un puente entre los modelos matemáticos y mecanismos físicos subyacentes. Se encontró que tanto la mezcla como la textura podrían dar las mismas estadísticas, tales como log-cumulantes de segundo orden y tercer orden. Los dos conceptos, la textura y la mezcla, representan dos escenarios muy diferentes. Se realizó un estudio adicional para ver si es posible distinguirlos, demostrando que las estadísticas de orden superior son favorables en esta tarea. Pueden interpretarse físicamente para distinguir la dispersión a partir de un solo tipo de blanco de una mezcla de blancos.

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Goodness‐of‐fit measures based on the Mellin transform for beta generalized lifetime data

Vasconcelos

Cintra

Nascimento

2021

Math Methods in App Sciences

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In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta-G family. However, efficient (GoF) measures for the beta-G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta-G class. We derive PWMs for the Fréchet and Kumaraswamy distributions, and we provide expressions for the MT, and for the log-cumulants (LC) of the beta-Weibull, beta-Fréchet, beta-Kumaraswamy, and beta-log-logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling's T 2 statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability.

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Application of Mellin-Kind Statistics to Polarimetric <inline-formula> <tex-math notation="TeX">${\cal G}$</tex-math></inline-formula> Distribution for SAR Data

Cited by 25 publications

References 43 publications

An Improved Minimum-Distance Texture Estimator for Speckled Data Under the $$\mathscr {G}^0$$ Model

An Improved Minimum-Distance Texture Estimator for Speckled Data Under the $$\mathscr {G}^0$$ Model

Texture analysis and physical interpretation of polarimetric SAR data

Goodness‐of‐fit measures based on the Mellin transform for beta generalized lifetime data

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