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Author: Stan Z. Li
Publisher: Springer Science & Business Media
ISBN: 1848002793
Category : Computers
Languages : en
Pages : 372
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Book Description
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.
Author: Stan Z. Li
Publisher: Springer Science & Business Media
ISBN: 1848002793
Category : Computers
Languages : en
Pages : 372
Get Book Here
Book Description
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.
Author: George Christakos
Publisher: Elsevier
ISBN: 1483288307
Category : Science
Languages : en
Pages : 503
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Book Description
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
Author: S.Z. Li
Publisher: Springer Science & Business Media
ISBN: 4431669337
Category : Computers
Languages : en
Pages : 274
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Book Description
Markov random field (MRF) modeling provides a basis for the characterization of contextual constraints on visual interpretation and enables us to develop optimal vision algorithms systematically based on sound principles. This book presents a comprehensive study on using MRFs to solve computer vision problems, covering the following parts essential to the subject: introduction to fundamental theories, formulations of various vision models in the MRF framework, MRF parameter estimation, and optimization algorithms. Various MRF vision models are presented in a unified form, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation. This book is an excellent reference for researchers working in computer vision, image processing, pattern recognition and applications of MRFs. It is also suitable as a text for advanced courses in the subject.
Author: Dionissios T. Hristopulos
Publisher: Springer Nature
ISBN: 9402419187
Category : Science
Languages : en
Pages : 884
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Book Description
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.
Author: Charles Sutton
Publisher: Now Pub
ISBN: 9781601985729
Category : Computers
Languages : en
Pages : 120
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Book Description
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.
Author: Gerhard Winkler
Publisher: Springer Science & Business Media
ISBN: 3642975224
Category : Mathematics
Languages : en
Pages : 321
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Book Description
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.
Author: Zoltan Kato
Publisher: Now Pub
ISBN: 9781601985880
Category : Computers
Languages : en
Pages : 168
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Book Description
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.
Author: Elias T. Krainski
Publisher: CRC Press
ISBN: 0429629850
Category : Mathematics
Languages : en
Pages : 284
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Book Description
Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.
Author: Robert J. Adler
Publisher: SIAM
ISBN: 0898716934
Category : Mathematics
Languages : en
Pages : 295
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Book Description
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.
Author: Murray Rosenblatt
Publisher: Springer Science & Business Media
ISBN: 1461251567
Category : Mathematics
Languages : en
Pages : 253
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Book Description
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.
