Simulation of nuclei cells images using spatial point pattern models

摘要

Markov random fields (MRF) modelling are a popular pattern analysis method with many applications in image restoration, texture analysis, classification and image segmentation. They are used to model spatial interaction on lattice system. The important characteristic of MRF is that they form the global pattern as conditional probabilities of local interaction. Models based on Markov random fields are widely used to model spatial processes, especially in biological spatial patterns. A particular subclass of MRF is the auto-models, introduced in Besag (1974) and further studied in Cross and Jain (1983), Besag (1986), Aykroyd et. al. (1996) and Zimeras (1997). In order to estimate MRF parameter efficiently an MRF parameter estimation method based on MCMC could be applied. The fundamental idea is to use an algorithm, which generates a discrete time Markov chain converging to the desired distribution. The most commonly algorithms include the Gibbs sampler (Geman and Geman, 1984) and the Metropolis-Hasting algorithm (Metropolis et. al., 1953; Hastings, 1970). In this work spatial properties of the auto-Poisson model was studied and a deterministic univariate iterative scheme, which can be used to predict these properties, has been proposed. Realizations from auto-Poisson model have been generated using the Gibbs sampler. As a result, the parameter space can be divided into regions, each with distinct spatial behavior. The iterative procedure classifies each region as either stable or unstable. The auto-Poisson model is fitted to a real data example from he area of medical biology. A variety of image structures of nuclei cells created by the proposed model is presented.