Download or read book Random Fields Estimation written by Alexander G. Ramm and published by World Scientific. This book was released on 2005 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory.This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory.
Download or read book Markov Random Field Modeling in Image Analysis written by Stan Z. Li and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov random field (MRF) theory provides a basis for modeling contextual constraints in visual processing and interpretation. It enables us to develop optimal vision algorithms systematically when used with optimization principles. This book presents a comprehensive study on the use of MRFs for solving computer vision problems. Various vision models are presented in a unified framework, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation. This third edition includes the most recent advances and has new and expanded sections on topics such as: Bayesian Network; Discriminative Random Fields; Strong Random Fields; Spatial-Temporal Models; Learning MRF for Classification. This book is an excellent reference for researchers working in computer vision, image processing, statistical pattern recognition and applications of MRFs. It is also suitable as a text for advanced courses in these areas.
Download or read book Image Analysis Random Fields and Dynamic Monte Carlo Methods written by Gerhard Winkler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is concerned with a probabilistic approach to image analysis as initiated by U. GRENANDER, D. and S. GEMAN, B.R. HUNT and many others, and developed and popularized by D. and S. GEMAN in a paper from 1984. It formally adopts the Bayesian paradigm and therefore is referred to as 'Bayesian Image Analysis'. There has been considerable and still growing interest in prior models and, in particular, in discrete Markov random field methods. Whereas image analysis is replete with ad hoc techniques, Bayesian image analysis provides a general framework encompassing various problems from imaging. Among those are such 'classical' applications like restoration, edge detection, texture discrimination, motion analysis and tomographic reconstruction. The subject is rapidly developing and in the near future is likely to deal with high-level applications like object recognition. Fascinating experiments by Y. CHOW, U. GRENANDER and D.M. KEENAN (1987), (1990) strongly support this belief.
Download or read book Random Field Models in Earth Sciences written by George Christakos and published by Elsevier. This book was released on 2013-10-22 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about modeling as a prinicipal component of scientific investigations. In general terms, modeling is the funamental process of combining intellectual creativity with physical knowledge and mathematical techniques in order to learn the properties of the mechanisms underlying a physical phenomenon and make predictions. The book focuses on a specific class of models, namely, random field models and certain of their physical applications in the context of a stochastic data analysis and processing research program. The term application is considered here in the sense wherein the mathematical random field model is shaping, but is also being shaped by, its objects.This book explores the application of random field models and stochastic data processing to problems in hydrogeology, geostatistics, climate modeling, and oil reservoir engineering, among others Researchers in the geosciences who work with models of natural processes will find discussion of; - Spatiotemporal random fields - Space transformation - Multidimensional estimation - Simulation - Sampling design - Stochastic partial differential equations
Download or read book Markov Random Fields in Image Segmentation written by Zoltan Kato and published by Now Pub. This book was released on 2012-09 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Random Fields in Image Segmentation provides an introduction to the fundamentals of Markovian modeling in image segmentation as well as a brief overview of recent advances in the field. Segmentation is formulated within an image labeling framework, where the problem is reduced to assigning labels to pixels. In a probabilistic approach, label dependencies are modeled by Markov random fields (MRF) and an optimal labeling is determined by Bayesian estimation, in particular maximum a posteriori (MAP) estimation. The main advantage of MRF models is that prior information can be imposed locally through clique potentials. MRF models usually yield a non-convex energy function. The minimization of this function is crucial in order to find the most likely segmentation according to the MRF model. Classical optimization algorithms including simulated annealing and deterministic relaxation are treated along with more recent graph cut-based algorithms. The primary goal of this monograph is to demonstrate the basic steps to construct an easily applicable MRF segmentation model and further develop its multi-scale and hierarchical implementations as well as their combination in a multilayer model. Representative examples from remote sensing and biological imaging are analyzed in full detail to illustrate the applicability of these MRF models. Furthermore, a sample implementation of the most important segmentation algorithms is available as supplementary software. Markov Random Fields in Image Segmentation is an invaluable resource for every student, engineer, or researcher dealing with Markovian modeling for image segmentation.
Download or read book Stationary Sequences and Random Fields written by Murray Rosenblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has a dual purpose. One of these is to present material which selec tively will be appropriate for a quarter or semester course in time series analysis and which will cover both the finite parameter and spectral approach. The second object is the presentation of topics of current research interest and some open questions. I mention these now. In particular, there is a discussion in Chapter III of the types of limit theorems that will imply asymptotic nor mality for covariance estimates and smoothings of the periodogram. This dis cussion allows one to get results on the asymptotic distribution of finite para meter estimates that are broader than those usually given in the literature in Chapter IV. A derivation of the asymptotic distribution for spectral (second order) estimates is given under an assumption of strong mixing in Chapter V. A discussion of higher order cumulant spectra and their large sample properties under appropriate moment conditions follows in Chapter VI. Probability density, conditional probability density and regression estimates are considered in Chapter VII under conditions of short range dependence. Chapter VIII deals with a number of topics. At first estimates for the structure function of a large class of non-Gaussian linear processes are constructed. One can determine much more about this structure or transfer function in the non-Gaussian case than one can for Gaussian processes. In particular, one can determine almost all the phase information.
Download or read book Random Fields for Spatial Data Modeling written by Dionissios T. Hristopulos and published by Springer Nature. This book was released on 2020-02-17 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.
Download or read book The Geometry of Random Fields written by Robert J. Adler and published by SIAM. This book was released on 2010-01-28 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important treatment of the geometric properties of sets generated by random fields, including a comprehensive treatment of the mathematical basics of random fields in general. It is a standard reference for all researchers with an interest in random fields, whether they be theoreticians or come from applied areas.
Download or read book Spatiotemporal Random Fields written by George Christakos and published by Elsevier. This book was released on 2017-07-26 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of spatiotemporal random field models to problems in ocean, earth, and atmospheric sciences, spatiotemporal statistics, and geostatistics, among others. The new edition features considerable detail of spatiotemporal random field theory, including ordinary and generalized models, as well as space-time homostationary, isostationary and hetrogeneous approaches. Presenting new theoretical and applied results, with particular emphasis on space-time determination and interpretation, spatiotemporal analysis and modeling, random field geometry, random functionals, probability law, and covariance construction techniques, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time variability functions, the validity of major theoretical assumptions in real-world practice (covariance positive-definiteness, metric-adequacy etc.), and the emergence of interdisciplinary phenomena in conditions of multi-sourced real-world uncertainty. - Contains applications in the form of examples and case studies, providing readers with first-hand experiences - Presents an easy to follow narrative which progresses from simple concepts to more challenging ideas - Includes significant updates from the previous edition, including a focus on new theoretical and applied results
Download or read book Collecting Spatial Data written by Werner G. Müller and published by Springer Science & Business Media. This book was released on 2007-08-17 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is concerned with the statistical theory for locating spatial sensors. It bridges the gap between spatial statistics and optimum design theory. After introductions to those two fields the topics of exploratory designs and designs for spatial trend and variogram estimation are treated. Special attention is devoted to describing new methodologies to cope with the problem of correlated observations.
Download or read book Markov Random Fields written by Y.A. Rozanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we study Markov random functions of several variables. What is traditionally meant by the Markov property for a random process (a random function of one time variable) is connected to the concept of the phase state of the process and refers to the independence of the behavior of the process in the future from its behavior in the past, given knowledge of its state at the present moment. Extension to a generalized random process immediately raises nontrivial questions about the definition of a suitable" phase state," so that given the state, future behavior does not depend on past behavior. Attempts to translate the Markov property to random functions of multi-dimensional "time," where the role of "past" and "future" are taken by arbitrary complementary regions in an appro priate multi-dimensional time domain have, until comparatively recently, been carried out only in the framework of isolated examples. How the Markov property should be formulated for generalized random functions of several variables is the principal question in this book. We think that it has been substantially answered by recent results establishing the Markov property for a whole collection of different classes of random functions. These results are interesting for their applications as well as for the theory. In establishing them, we found it useful to introduce a general probability model which we have called a random field. In this book we investigate random fields on continuous time domains. Contents CHAPTER 1 General Facts About Probability Distributions §1.
Download or read book Multiparameter Processes written by Davar Khoshnevisan and published by Springer Science & Business Media. This book was released on 2006-04-10 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-contained presentation: from elementary material to state-of-the-art research; Much of the theory in book-form for the first time; Connections are made between probability and other areas of mathematics, engineering and mathematical physics
Download or read book Markov Random Fields for Vision and Image Processing written by Andrew Blake and published by MIT Press. This book was released on 2011-07-22 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art research on MRFs, successful MRF applications, and advanced topics for future study. This volume demonstrates the power of the Markov random field (MRF) in vision, treating the MRF both as a tool for modeling image data and, utilizing recently developed algorithms, as a means of making inferences about images. These inferences concern underlying image and scene structure as well as solutions to such problems as image reconstruction, image segmentation, 3D vision, and object labeling. It offers key findings and state-of-the-art research on both algorithms and applications. After an introduction to the fundamental concepts used in MRFs, the book reviews some of the main algorithms for performing inference with MRFs; presents successful applications of MRFs, including segmentation, super-resolution, and image restoration, along with a comparison of various optimization methods; discusses advanced algorithmic topics; addresses limitations of the strong locality assumptions in the MRFs discussed in earlier chapters; and showcases applications that use MRFs in more complex ways, as components in bigger systems or with multiterm energy functions. The book will be an essential guide to current research on these powerful mathematical tools.
Download or read book Random Fields and Geometry written by R. J. Adler and published by Springer Science & Business Media. This book was released on 2009-01-29 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.
Download or read book Hybrid Random Fields written by Antonino Freno and published by Springer Science & Business Media. This book was released on 2011-04-11 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an exciting new synthesis of directed and undirected, discrete and continuous graphical models. Combining elements of Bayesian networks and Markov random fields, the newly introduced hybrid random fields are an interesting approach to get the best of both these worlds, with an added promise of modularity and scalability. The authors have written an enjoyable book---rigorous in the treatment of the mathematical background, but also enlivened by interesting and original historical and philosophical perspectives. -- Manfred Jaeger, Aalborg Universitet The book not only marks an effective direction of investigation with significant experimental advances, but it is also---and perhaps primarily---a guide for the reader through an original trip in the space of probabilistic modeling. While digesting the book, one is enriched with a very open view of the field, with full of stimulating connections. [...] Everyone specifically interested in Bayesian networks and Markov random fields should not miss it. -- Marco Gori, Università degli Studi di Siena Graphical models are sometimes regarded---incorrectly---as an impractical approach to machine learning, assuming that they only work well for low-dimensional applications and discrete-valued domains. While guiding the reader through the major achievements of this research area in a technically detailed yet accessible way, the book is concerned with the presentation and thorough (mathematical and experimental) investigation of a novel paradigm for probabilistic graphical modeling, the hybrid random field. This model subsumes and extends both Bayesian networks and Markov random fields. Moreover, it comes with well-defined learning algorithms, both for discrete and continuous-valued domains, which fit the needs of real-world applications involving large-scale, high-dimensional data.
Download or read book Gaussian and Non Gaussian Linear Time Series and Random Fields written by Murray Rosenblatt and published by Springer Science & Business Media. This book was released on 2000 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal focus here is on autoregressive moving average models and analogous random fields, with probabilistic and statistical questions also being discussed. The book contrasts Gaussian models with noncausal or noninvertible (nonminimum phase) non-Gaussian models and deals with problems of prediction and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. Intended as a text for gradutes in statistics, mathematics, engineering, the natural sciences and economics, the only recommendation is an initial background in probability theory and statistics. Notes on background, history and open problems are given at the end of the book.
Download or read book An Introduction to Conditional Random Fields written by Charles Sutton and published by Now Pub. This book was released on 2012 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Conditional Random Fields provides a comprehensive tutorial aimed at application-oriented practitioners seeking to apply CRFs. The monograph does not assume previous knowledge of graphical modeling, and so is intended to be useful to practitioners in a wide variety of fields.
