| In the current dissertation, we propose three statistical approaches to the analysis of SAR images.; SAR image is composed of several classes of pixels. In the first part of this thesis, we assume that each of these classes can be modeled by a Gamma distribution. The multi-modal SAR image histogram is thus a mixture of Gamma distributions. The maximum likelihood technique (ML) is used to estimate the parameters of each mode in the multimodal SAR image histogram. The number of looks of the SAR image is estimated by using either Gamma maximum likelihood or the maximum of the Gamma function.; Second, we use a method taken from statistical inference theory, called the minimum message length approach (MML) to model SAR images. The MML permits to minimize the length of a message transmitted from sender to receiver. The parameters of the message are random. The message length is the logarithm of the posterior probability of the model, so the MML approach can also be regarded as finding the model with the highest posterior probability. The multimodal SAR image histogram is assumed to be a mixture of Gamma distributions. The MML algorithm finds the best model and estimates the number of modes and the statistics of the multimodal histogram.; Third, the distribution of a given class in the SAR image depends on the form of the scene surfaces and on the radar parameters. Due to SAR image preprocessing and other factors, the use of one distribution is insufficient and we need a method for modeling each class (mode) in the SAR image (histogram) by an appropriate distribution. Using a set of distributions with flexible shapes that are likely to fit the SAR image histogram, we form a system called GGBL which includes four parametric distributions: Gaussian, Gamma, Beta and Log-Normal. The selection of a parametric distribution from the GGBL system for each mode of the heterogeneous multimodal SAR histogram is performed according to the location of the skewness and flatness coefficients in this space. We propose a distribution stability method for distribution selection, using the asymmetry and flatness coefficients. The statistics of heterogeneous multimodal SAR histogram are estimated using the characteristic points of the histogram.; Algorithms are validated in the context of segmentation of SAR images using threshold information. Thresholds are computed by minimizing the discrimination error between classes of pixels in the SAR image. Finally, the major results and key features of the ML, MML and GGBL proposals are analyzed, and extensions for future research are discussed. |
