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Image Modelling and Estimation, A Statistical Approach Author: Finn Lindgren, Lund Univer. Content: 1. Introduction 1.1 Why a statistical approach? 2. Statistical modelling and estimation 2.1 Statistical modelling 2.1.1 Conditional probabilities 2.1.2 Hierarchical models 2.1.3 Covariance matrices 2.1.4 Bayesian methods 2.2 Object classification 2.2.1 Maximum likelihood classification 2.2.2 Maximum A Posteriori classification 2.2.3 Classification with loss functions 2.2.4 Data reduction PCA PCA for multi-spectral images 2.3 Estimation 2.3.1 Training set 2.3.2 Covariance estimation 2.3.3 The EM-algorithm for mixture distributions Exercises 3. Distribution, correlation, and filters Random and fixed image elements 3.1 Grey level distributions and histograms 3.1.1 Histogram transformations 3.2 Covariance and correlation 3.2.1 The covariance matrix Covariances and linear operations 3.2.2 Model covariance and correlation function 3.2.3 Homogeneity and isotropy 3.2.4 Data covariance and correlation 3.3 Fourier transforms and spectrum 3.3.1 Fourier transforms in R and Z Fourier transform of covariance functions; power spectral density 3.3.2 Sum of random harmonics 3.3.3 Fourier transforms in R^2 and Z^2 The Fourier transform of a double indexed sequence Power spectral densities in R^2 and Z^2 Power spectrum for an isotropic field 3.3.4 Discrete Fourier transforms of 1D and 2D data Discrete Fourier transform of a data sequence The Fourier transform of an observed random sequence Relation between DFT of a data vector and a spectral density Discrete Fourier transform of 2D data 3.4 Linear Filters 3.4.1 Random elements in linear filters Smoothing filter Sharpening filter Correlation matching Wiener filter 4 Random fields with Markov structures 4.1 Markov random fields 4.2 Gaussian Markov random fields 4.3 Gibbs distributions 4.4 Estimation 5 Markov chain Monte Carlo (MCMC) simulation 5.1 Introduction Why simulation? How to simulate? 5.2 MCMC 5.2.1 The Metropolis algorithm 5.2.2 The Metropolis-Hastings algorithm 5.2.3 Gibbs-sampling Block-update Gibbs-sampling Parallel Gibbs-sampling 5.2.4 MCMC convergence conditions 6 Shape analysis 6.1 Empirical and Bayesian templates 6.1.1 Prior distributions 6.1.2 Data likelihood and model estimation 6.1.3 Templates and global transformations 6.2 Landmark templates 6.2.1 Vertex perturbations 6.2.2 Edge perturbations 6.2.3 Global perturbations and simulations 6.3 Free-form templates 6.3.1 Curves Snakes Splines 6.3.2 Surfaces 6.4 Shapes from images 6.4.1 GMRF-snakes 6.5 Estimation algorithm example 6.5.1 The data model 6.5.2 Construction of the loss function 6.5.3 Loss function derivatives 6.5.4 Practical optimisation 6.5.5 Uncertainty estimation 7 Warping 7.1 Embedded deformation 7.1.1 Warping 7.1.2 Morphing Physical deformation models 附件(1.4MB) Image_analysis_and_estimation.pdf

[ebook]Image Modelling and Estimation