馬爾可夫點進程及其應用MARKOV POINT PROCESSES AND THEIR APPLICATIONS

內(nèi)容概要

These days, an increasing amount of information can be obtained in graphical forms, such as weather maps, soil samples, locations of nests in a breeding colony, microscopical slices, satellite images, radar or medical scans and X-ray techniques. "High level" image analysis is concerned with the global interpretation of images, attempting to reduce it to a compact description of the salient features of the scene. This book takes a stochastic approach. It studies Markov object processes, showing that they form a flexible class of models for a range of problems involving the interpretation of spatial data. Applications can be found in statistical physics (under the name of "Gibbs processes"), environmental mapping of diseases, forestry, identification of ore structure in materials science, signal analysis, object recognition, robot vision, and interpretation of images from medical scans or confocal microscopy.

書籍目錄

Chapter 1  Point Processes　1.1  Introduction　1.2  Definitions and notation　1.3  Simple point processes　1.4  Finite point processes　1.5  Poisson point processes　1.6  Finite point processes specified by a density　1.7  Campbell and moment measures　1.8  Interior and exterior conditioning　　1.8.1  A review of Palm theory  :　　1.8.2  A review of conditional intensitiesChapter 2  Markov Point Processes　2.1  Ripley-Kelly Markov point processes　2.2  The Hammersley-Clifford theorem　2.3  Markov marked point processes　2.4  Nearest-neighbour Maxkov point processes　2.5  Connected component Markov point processesChapter 3  Statistical Inference　3.1  Introduction　3.2  The Metropolis-Hastings algorithm　3.3  Conditional simulation　3.4  Spatial birth-and-death processes　3.5  Exact simulation  　3.6  Auxiliary variables and the Gibbs sampler　3.7  Maximum likelihood estimation　3.8  Estimation based on the conditional intensity　　3.8.1  Takacs-Fiksel estimation　　3.8.2  Maximum pseudo-likelihood estimation　3.9  Goodness of fit testing　3.10 DiscussionChapter 4  Applications　4.1  Modelling spatial patterns　4.2  Pairwise interaction processes　4.3  Area-interaction processes　4.4  Shot noise and quermass-interaction processes　4.5  Morphologically smoothed area-interaction processes　4.6  Hierarchical and transformed processes　4.7  Cluster processes　4.8  Case study　　4.8.1  Exploratory analysis 　　4.8.2  Model fitting　4.9  Interpolation and extrapolation　　4.9.1  Model　　4.9.2  Posterior sampling　　4.9.3  Monotonicity properties and coupling from the pastBibliographyIndex

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