Three Applications
We conclude this text with a small sample of typical applications. They once more illustrate the flexibility of the Bayesian framework. The first example concerns the analysis of motion. It shows how the ideas developed in the context of piecewise smoothi
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This text deals with digital image analysis, probabilistic modelling and statistical inference. It focuses on the extraction of information implicit in recorded image data, and their interpretation. It is not especially concerned with image processing, which encompasses fields like image digitization, enhancement and restoration, encoding, segmentation, representation and description; we refer the reader to standard texts like W.R. PRATT (1991), B.K.P. HORN (1987), R.C. GONZALEZ and P. WINTZ (1999) or R.M. HARALICK and L.G. SHAPIRO (1992). Image analysis is sometimes referred to as 'inverse optics'. Generally, inverse problems are under-determined, and various interpretations may be compatible with data. The art of image analysis is to select those of interest. Bayesian image analysis is a paradigm how to approach this problem from a probabilistic point of view. The 'direct problem' of image synthesis will be interpreted as simulation of patterns from a random field model by means of dynamic or Markov chain Monte Carlo methods. Typical problems in image analysis are such like image restoration, where one tries to recover a 'true' scene from noisy data, boundary detection to locate sudden changes of a surface, of shape, depth or texture, tomographic reconstruction of tissue from showers of atomic particles passing through the body, or motion analysis, estimating the velocity of objects. Concise introductions to the Bayesian and random field based approach are D. G EMAN (1990) and D. GEMAN and B. GIDAS (1991). A collection of such and many other applications can be found in R. CHELLAPA and A. JAIN (1993). A higher level application is shape analysis to recognize biological shapes or to detect anomalies. For introductions and controversial views see F .L. BOOKSTEIN (1991), I.L. DRYDEN and K.V. MARDIA (1998), and D.G. KENDALL et al. (1999). U. GRENANDER et al. (1991) is an attempt to approach the problem from the Bayesian point of view (with a more than recommendable introduction to the matter). Similar problems arise in fields seemingly not related to image analysis: Reconstruction of locations of archeological sites from measurements of the phosphate concentration over a study region (the phosphate content of soil is the result of decomposition of organic matter), or disease mapping from observed incidence rates, d. J. BESAG et al. (1991). Another example - briefly
G. Winkler, Image Analysis, Random Fields and Markov Chain Monte Carlo Methods © Springer-Verlag Berlin Heidelberg 2003
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Introduction
addressed in this text - is brain mapping, where one tries to identify those parts where a given outer stimulus is assimilated. This indicates that it is hard to pin the word 'image' down to something like pictures; frequently it is synonymous for - usually multi-dimensional - correlated data. Part of image processing is concerned with the performance of operations on signals where an operator is fed with an 'input' and returns an 'output'. For some methods there are complete and established theories like Fourier analy
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