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25 March 1996 Maximum-likelihood estimation for the two-dimensional discrete Boolean model using cross-windowed observations
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The Boolean model is a random set process in which random shapes are positioned according to the outcomes of an independent point process. In the discrete case, the point process is Bernoulli. To do estimation on the two-dimensional discrete Boolean model, we sample the germ-grain model at widely spaced points. An observation using this procedure consists of jointly distributed horizontal and vertical runlengths. An approximate likelihood of each cross observation is computed. Since the observations are taken at widely spaced points, they are considered independent and are multiplied to form a likelihood function for the entire sampled process. Estimation for the two-dimensional process is done by maximizing the grand likelihood over the parameter space. Simulations on random-rectangle Boolean models show significant decrease in variance over the method using horizontal and vertical linear samples. Maximum-likelihood estimation can also be used to fit models to real textures.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
John C. Handley and Edward R. Dougherty "Maximum-likelihood estimation for the two-dimensional discrete Boolean model using cross-windowed observations", Proc. SPIE 2662, Nonlinear Image Processing VII, (25 March 1996);

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