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Image Processing and Jump Regression Analysis (Wiley Series in Probability and Statistics)

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Statistical approaches to image analysis often take the route of Markov random field which presents a reasonable model for many spatial processes including images. This is the case with Besag or Geman and Geman, or recent developments in penalized likelihood or Markov chain Monte Carlo, for example Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Stochastic Modelling and Applied Probability). However, image analysis is a much broader field, not the least of which are the many important issues in preprocessing such as background correction, normalization, and segmentation. Many filtering and smoothing algorithms have much in common with time series analysis, and the statistical smoothing or nonparametric regression techniques. The book has given in depth some recent developments of local polynomial regression, including piecewise polynomials for discontinuous surfaces. The jump regression approach is among several recent developments of nonparametric regression for image analysis, and better comparison can be made to alternative approaches such as adaptive weights smoothing, nonlinear adaptive filtering, or PDE-based anisotropic diffusion. All these methods are for image restoration and image denoising. Image segmentation and boundary estimation are apparrently different problems, for example, both Canny edge detection (based on some ad hoc thresholding of partial derivative estimation) and Mumford and Shah (variational approach leading to complicated PDE numerics) have been used. The important issue of computation in the jump regression approach remains to be developed in order to make the new techniques in the book accessible and useful to the wider image analysis community.