The Use of Markov Random Fields as Models of Texture

Hassner, M.; Sklansky, Jack

doi:10.1016/b978-0-12-597320-5.50015-2

Cited by 39 publications

(45 citation statements)

References 7 publications

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“…[e.g., 58,89,107,263], as well as in spatial statistics more generally [25,26,27,201]. For modeling an image, the simplest use of a Markov random field model is in the pixel domain, where each pixel in the image is associated with a vertex in an underlying graph.…”

Section: Image Processing and Spatial Statisticsmentioning

confidence: 99%

Graphical Models, Exponential Families, and Variational Inference

Wainwright¹,

Jordan²

2007

FNT in Machine Learning

2,179

2,452

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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instancesincluding the key problems of computing marginals and modes of probability distributions -are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide variety of algorithms -among them sum-product, cluster variational methods, expectation-propagation, mean field methods, max-product and linear programming relaxation, as well as conic programming relaxations -can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.

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Section: Image Processing and Spatial Statisticsmentioning

confidence: 99%

Graphical Models, Exponential Families, and Variational Inference

Wainwright¹,

Jordan²

2007

FNT in Machine Learning

2,179

2,452

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“…Because the latter problem has received a considerable amount of attention in the literature over the years 1,8,9,12,14,23,26,29,20], in the sequel the emphasis is on identifying the structural parameters from a given sample of texture.…”

Section: Texture Analysis By Synthesismentioning

confidence: 99%

“…These are chosen to minimise the variance of the spectral density within the corresponding segments of the frequency plane, as illustrated in gure 5: Identi cation of the linear transformation then requires solution of the equations ( 1) i~ (1) j = A 12~ (2) k ; i; j; k = 1; 2 (20) for each of the eight distinct pairings of i; j; k in (20). Note that the term ( 1) …”

Section: Identi Cation Of the Linear Transformationmentioning

confidence: 99%

“…28,24,35,32,4,13]), a trend which looks set to continue under the impetus of developments in wavelet theory. During the same period, Markov Random Field (MRF) models, based on both causal and non-causal neighbourhoods, have found widespread use 20,26,10,18,12,9,14]. In the simplest case, linear models based on a causal or semi-causal neighbourhood, the comparative simplicity of model identi cation is somewhat o set by the limited range of textures which can be produced, while more complex, nonlinear and non-causal models require large amounts of processing, but can model a signi cantly wider range of textures.…”

Section: Introductionmentioning

confidence: 99%

“…The analysis and synthesis of natural textures is one of the most intriguing and dicult problems in image processing, which has received much attention over the years 2,20,26,21,16,10,34,35,5,4,17]. Apart from their signi cance in applications ranging from remote sensing to computer graphics, the analysis and synthesis of texture have remained challenging problems because of the combination of structure and variation which many textures possess: simple structural or statistical models fail to capture the subtlety of this combination in many cases of practical interest.…”

Section: Introductionmentioning

confidence: 99%

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A two-component model of texture for analysis and synthesis

Hsu¹,

Wilson

1998

IEEE Trans. on Image Process.

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Copies of full items can be used for personal research or study, educational, or not-forprofit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions:The version presented in WRAP is the published version or, version of record, and may be cited as it appears here.For more information, please contact the WRAP Abstract A model of natural texture based on a structural component which uses a ne coordinate transformations and a stochastic residual component is presented. It is argued that the selection of an appropriate analysis scale can be formulated in terms of a trade-o between the rate at which parameters are generated and the distortion resulting from the approximation by the structural component. An e cient algorithm for identifying the parameters of the structural model is described and its utility demonstrated on a number of synthetic and natural textures.

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A Tutorial on : R Package for the Linearized Bregman Algorithm in High-Dimensional Statistics

Xiong¹,

Ruan

Yao

2018

Handbook of Big Data Analytics

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The R package, Libra, stands for the LInearized BRegman Algorithm in high dimensional statistics. The Linearized Bregman Algorithm is a simple iterative procedure to generate sparse regularization paths of model estimation, which are firstly discovered in applied mathematics for image restoration and particularly suitable for parallel implementation in large scale problems. The limit of such an algorithm is a sparsity-restricted gradient descent flow, called the Inverse Scale Space, evolving along a parsimonious path of sparse models from the null model to overfitting ones. In sparse linear regression, the dynamics with early stopping regularization can provably meet the unbiased Oracle estimator under nearly the same condition as LASSO, while the latter is biased. Despite their successful applications, statistical consistency theory of such dynamical algorithms remains largely open except for some recent progress on linear regression. In this tutorial, algorithmic implementations in the package are discussed for several widely used sparse models in statistics, including linear regression, logistic regression, and several graphical models (Gaussian, Ising, and Potts). Besides the simulation examples, various application cases are demonstrated, with real world datasets from diabetes, publications of COPSS award winners, as well as social networks of two Chinese classic novels, Journey to the West and Dream of the Red Chamber.

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The Use of Markov Random Fields as Models of Texture

Cited by 39 publications

References 7 publications

Graphical Models, Exponential Families, and Variational Inference

Graphical Models, Exponential Families, and Variational Inference

A two-component model of texture for analysis and synthesis

A Tutorial on : R Package for the Linearized Bregman Algorithm in High-Dimensional Statistics

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