Statistical Modelling and Inference in Image Analysis

Statistics

Qian, Wei

University:University of Glasgow

关键词: Statistics;   

Others  :  http://theses.gla.ac.uk/76500/1/13834282.pdf

来源: University of Glasgow

【 摘 要 】

The aim of the thesis is to investigate classes of model-based approaches to statistical image analysis. We explored the properties of models and examined the problem of parameter estimation from the original image data and, in particular, from noisy versions of the the scene. We concentrated on Markov random field (MRF) models, Markov mesh random field (MMRF) models and Multi-dimensional Markov chain (MDMC) models. In Chapter 2, for the one-dimensional version of Markov random fields, we developed a recursive technique which enables us to achieve maximum likelihood estimation for the underlying parameter and to carry out the EM algorithm for parameter estimation when only noisy data are available. This technique also enables us, in just a single pass, to generate a sample from a one-dimensional Markov random field. Although, unfortunately, this technique cannot be extended to two- or multi-dimensional models, it was applied to many cases in this thesis. Since, for two-dimensional Markov random fields, the density of each row (column), conditionally on all other rows (columns) is of the form of a one-dimensional Markov random field, and since the distribution of the original image, conditionally on the noisy version of data, is still a Markov random field, the technique can be used on different forms of conditional density of one row (column). In Chapter 3, therefore, we developed the line-relaxation method for simulating MRFs and maximum line pseudo-likelihood estimation of parameter(s), and in Chapter 5, we developed a simultaneous procedure of parameter estimation and restoration, in which line pseudo-likelihood and a modified EM algorithm were used. The first part of Chapter 3 and Chapter 4 concentrate on inference for two-dimensional MRFs. We obtained a matrix expression for partition functins for general models, and a more explicit form for a multi-colour Ising model, and thus located the positions of critical points of this multi-colour model. We examined the asymptotic properties of an asymmetric, two-colour Ising model. For general models, in Chapter 4, we explored asymptotic properties under an "independence" or a "near independence" condition, and then developed the approach of maximum approximate-likelihood estimation. For three-dimensional MMRF models, in chapter 6, a generalization of Devijver's F-G-H algorithm is developed for restoration. In Chapter 7, the recursive technique was again used to introduce MDMC models, which form a natural extension of a Markov chain. By suitable choice of model parameters, textures can be generated that are similar to those simulated from MRFs, but the simulation procedure is computationally much more economical. The recursive technique also enables us to maximize the likelihood function of the model. For all three sorts of prior random field models considered in this thesis, we developed a simultaneous procedure for parameter estimation and image restoration, when only noisy data are available. The currently restored image was used, together with noisy data, in modified versions of the EM algorithm. In simulation studies, quite good results were obtained, in terms of estimation of parameters in both the original model and, particularly, in the noise model, and in terms of restoration.