Estimating Gaussian Markov random field parameters in a nonstationary framework: application to remote sensing imaging

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Abstract
In this paper, we tackle the problem of estimating textural parameters. We do not consider the problem of texture synthesis, but the problem of extracting textural features for tasks such as image segmentation. We take into account nonstationarities occurring in the local mean. We focus on Gaussian Markov random fields for which two estimation methods are proposed, and applied in a nonstationary framework. The first one consists of extracting conditional probabilities and performing a least square approximation. This method is applied to a nonstationary framework, dealing with the piecewise constant local mean. This framework is adapted to practical tasks when discriminating several textures on a single image. The blurring effect affecting edges between two different textures is thus reduced. The second proposed method is based on renormalization theory. Statistics involved only concern variances of Gaussian laws, leading to Cramer-Rao estimators. This method is thus especially robust with respect to the size of sampling. Moreover, nonstationarities of the local mean do not affect results. We then demonstrate that the estimated parameters allow texture discrimination for remote sensing data. The first proposed estimation method is applied to extract urban areas from SPOT images. Since discontinuities of the local mean are taken into account, we obtain an accurate urban areas delineation. Finally, we apply the renormalization based on method to segment ice in polar regions from AVHRR data.

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