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This paper deals with spatial analysis of texture in synthetic aperture radar (SAR) images. A new parametric model for local two-point statistics of the image is introduced, in order to characterize the spatially nonstationary and anisotropic behavior of the image. The texture is first modeled by a nonstationary Gaussian process resulting from the convolution of a Gaussian white noise with a field of anisotropic Gaussian kernel with spatially varying parameters. Hence, under the hypothesis of locally stationary signal, the analytic expression of the local autocovariance is derived. It is then explained how to simulate nonstationary K-distributed random fields by combining the new model with an already existing simulation method. A method for parameter estimation is then introduced. This method, based on the statistical product model, first corrects the speckle contribution to the local autocovariance and estimates the parameters of the model by analyzing the shape of the autocovariance. The algorithm is then evaluated over simulated and experimental data. Stationary simulations permit to show that, for a sufficient sample size, the estimator is unbiased. A test over a nonstationary simulation proves the ability of the algorithm to capture the spatial fluctuations of the texture. Finally, the method is applied to the experimental SAR data, and it is shown that a large amount of spatial information may be retrieved from the data.