scholarly journals Modeling of the Markiv random field for the purpose of its further optimization and application

Connectivity ◽  
2020 ◽  
Vol 146 (5) ◽  
Author(s):  
V. V. Zhebka ◽  
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Random Fields ◽  
Markov Random Fields ◽  
Markov Models ◽  
Scale Model ◽  
Small Scale ◽  
Advantages And Disadvantages ◽  
Markov Random ◽  
Different Types

Models of the Markov random field are investigated. The main improvements of the Markov random field model are investigated. If we consider Markov models of random fields with binary conditional distributions, which include stochastic evolution in time, which is based on the autoregression structure for a large-scale model, these models retain the flexibility of static Markov random field models to reproduce the representation of spatial dependence in a small-scale model. Bayesian estimation in this case is achieved through the use of a so-called algorithm that requires the generation of auxiliary random fields, but does not require the use of ideal samples. Markov random fields are a powerful tool in machine learning. It is often necessary to model such fields between dissimilar objects, which leads to the fact that the nodes in the graph belong to different types of data. To model inhomogeneous areas using graphical models, it is necessary to assign different types of distributions (binary, Gaussian, Poisson, exponent, exponential, etc.) to the model nodes. The concept of conditional random fields is considered in the article, their features, advantages and disadvantages are established. The application of binary data in Markov models of random fields is considered, which generates a class of models of binary Markov random fields. It is established that the discrete nature of Markov random fields allows a wider range of possible values of dependence, ie negative dependence. The model, loss function and distribution of the Markov random field function are investigated. Strengthening of Markov random fields is proposed. The pairwise exponential Markov random field is considered.

New models for Markov random fields

1992 ◽  
Vol 29 (04) ◽  
pp. 877-884 ◽  
Author(s):  
Noel Cressie ◽  
Subhash Lele
Keyword(s):  
Random Field ◽  
Conditional Probability ◽  
Markov Random Field ◽  
Random Fields ◽  
Markov Random Fields ◽  
Sufficient Conditions ◽  
Joint Probability ◽  
Probability Models ◽  
Markov Random ◽  
New Models

The Hammersley–Clifford theorem gives the form that the joint probability density (or mass) function of a Markov random field must take. Its exponent must be a sum of functions of variables, where each function in the summand involves only those variables whose sites form a clique. From a statistical modeling point of view, it is important to establish the converse result, namely, to give the conditional probability specifications that yield a Markov random field. Besag (1974) addressed this question by developing a one-parameter exponential family of conditional probability models. In this article, we develop new models for Markov random fields by establishing sufficient conditions for the conditional probability specifications to yield a Markov random field.

Conditional cyclic Markov random fields

1996 ◽  
Vol 28 (1) ◽  
pp. 1-12 ◽  
Author(s):  
John T. Kent ◽  
Kanti V. Mardia ◽  
Alistair N. Walder
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Random Fields ◽  
Markov Random Fields ◽  
Field Model ◽  
Random Field Model ◽  
Markov Random Field Model ◽  
Gaussian Markov Random Field ◽  
Markov Random ◽  
Limiting Behaviour

Grenander et al. (1991) proposed a conditional cyclic Gaussian Markov random field model for the edges of a closed outline in the plane. In this paper the model is recast as an improper cyclic Gaussian Markov random field for the vertices. The limiting behaviour of this model when the vertices become closely spaced is also described and in particular its relationship with the theory of ‘snakes' (Kass et al. 1987) is established. Applications are given in Grenander et al. (1991), Mardia et al. (1991) and Kent et al. (1992).

New models for Markov random fields

1992 ◽  
Vol 29 (4) ◽  
pp. 877-884 ◽  
Author(s):  
Noel Cressie ◽  
Subhash Lele
Keyword(s):  
Random Field ◽  
Conditional Probability ◽  
Markov Random Field ◽  
Random Fields ◽  
Markov Random Fields ◽  
Sufficient Conditions ◽  
Joint Probability ◽  
Probability Models ◽  
Markov Random ◽  
New Models

The Hammersley–Clifford theorem gives the form that the joint probability density (or mass) function of a Markov random field must take. Its exponent must be a sum of functions of variables, where each function in the summand involves only those variables whose sites form a clique. From a statistical modeling point of view, it is important to establish the converse result, namely, to give the conditional probability specifications that yield a Markov random field. Besag (1974) addressed this question by developing a one-parameter exponential family of conditional probability models. In this article, we develop new models for Markov random fields by establishing sufficient conditions for the conditional probability specifications to yield a Markov random field.

Conditional cyclic Markov random fields

1996 ◽  
Vol 28 (01) ◽  
pp. 1-12 ◽  
Author(s):  
John T. Kent ◽  
Kanti V. Mardia ◽  
Alistair N. Walder
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Random Fields ◽  
Markov Random Fields ◽  
Field Model ◽  
Random Field Model ◽  
Markov Random Field Model ◽  
Gaussian Markov Random Field ◽  
Markov Random ◽  
Limiting Behaviour

Grenander et al. (1991) proposed a conditional cyclic Gaussian Markov random field model for the edges of a closed outline in the plane. In this paper the model is recast as an improper cyclic Gaussian Markov random field for the vertices. The limiting behaviour of this model when the vertices become closely spaced is also described and in particular its relationship with the theory of ‘snakes' (Kass et al. 1987) is established. Applications are given in Grenander et al. (1991), Mardia et al. (1991) and Kent et al. (1992).

Poisson and extreme value limit theorems for Markov random fields

1987 ◽  
Vol 19 (01) ◽  
pp. 106-122 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Random Fields ◽  
Conditional Distribution ◽  
Markov Random Fields ◽  
Limit Theorems ◽  
Nearest Neighbor ◽  
Extreme Value ◽  
Markov Random ◽  
Corner Points

Let Xt , be a Markov random field assuming values in RM. Let In be a rectangular box in Zm with its center at 0 and corner points with coordinates ±n. Let (An ) be a sequence of measurable subsets of RM such that neighborhood of t) → 0, for n → ∞; and let fn (x) be the indicator of An. Under appropriate conditions on the nearest-neighbor distributions of (Xt ), the conditional distribution of given the values of Xs , for s on the boundary of In , converges to the Poisson distribution. An immediate application is an extreme value limit theorem for a real-valued Markov random field.

Poisson and extreme value limit theorems for Markov random fields

1987 ◽  
Vol 19 (1) ◽  
pp. 106-122 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Random Fields ◽  
Conditional Distribution ◽  
Markov Random Fields ◽  
Limit Theorems ◽  
Nearest Neighbor ◽  
Extreme Value ◽  
Markov Random ◽  
Corner Points

Let Xt, be a Markov random field assuming values in RM. Let In be a rectangular box in Zm with its center at 0 and corner points with coordinates ±n. Let (An) be a sequence of measurable subsets of RM such that neighborhood of t) → 0, for n → ∞; and let fn(x) be the indicator of An. Under appropriate conditions on the nearest-neighbor distributions of (Xt), the conditional distribution of given the values of Xs, for s on the boundary of In, converges to the Poisson distribution. An immediate application is an extreme value limit theorem for a real-valued Markov random field.

Optimizing image segmentation of pavement defects using graph-based method

2021 ◽  
pp. 1-7
Author(s):  
T.H. Nguyen ◽  
T.L. Nguyen ◽  
A.D. Afanasiev ◽  
T.L. Pham
Keyword(s):  
Machine Learning ◽  
Image Segmentation ◽  
Defect Detection ◽  
Random Fields ◽  
Markov Random Fields ◽  
Classification Systems ◽  
Machine Learning Algorithms ◽  
Advantages And Disadvantages ◽  
Markov Random ◽  
Segmentation Algorithms

Pavement defect detection and classification systems based on machine learning algorithms are already very advanced and are increasingly demonstrating their outstanding advantages. One of the most important steps in the processing is image segmentation. In this paper, some image segmentation algorithms used in practice are presented, compared and evaluated. The advantages and disadvantages of each algorithm are evaluated and compared based on the criteria PA, MPA, F1. We propose a method to optimize the process of image segmentation of pavement defects using a combination of Markov Random Fields and graph theory. Experiments were conducted on 3 datasets from Portugal, Russia and Vietnam. Empirical results show that the segmentation of pavement defects is more accurate and effective when the two methods are combined.

scholarly journals Random Fields in Physics, Biology and Data Science

2021 ◽  
Vol 9 ◽  
Author(s):  
Enrique Hernández-Lemus
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Markov Random Fields ◽  
Statistical Physics ◽  
Data Science ◽  
Joint Probability ◽  
Theoretical Aspect ◽  
Joint Probability Distribution ◽  
Computational Molecular Biology ◽  
Markov Random

A random field is the representation of the joint probability distribution for a set of random variables. Markov fields, in particular, have a long standing tradition as the theoretical foundation of many applications in statistical physics and probability. For strictly positive probability densities, a Markov random field is also a Gibbs field, i.e., a random field supplemented with a measure that implies the existence of a regular conditional distribution. Markov random fields have been used in statistical physics, dating back as far as the Ehrenfests. However, their measure theoretical foundations were developed much later by Dobruschin, Lanford and Ruelle, as well as by Hammersley and Clifford. Aside from its enormous theoretical relevance, due to its generality and simplicity, Markov random fields have been used in a broad range of applications in equilibrium and non-equilibrium statistical physics, in non-linear dynamics and ergodic theory. Also in computational molecular biology, ecology, structural biology, computer vision, control theory, complex networks and data science, to name but a few. Often these applications have been inspired by the original statistical physics approaches. Here, we will briefly present a modern introduction to the theory of random fields, later we will explore and discuss some of the recent applications of random fields in physics, biology and data science. Our aim is to highlight the relevance of this powerful theoretical aspect of statistical physics and its relation to the broad success of its many interdisciplinary applications.

scholarly journals DESIGN ASPECTS OF BLOCK REVETMENTS

1988 ◽  
Vol 1 (21) ◽  
pp. 151
Author(s):  
K.W. Pilarczyk
Keyword(s):  
Large Scale ◽  
Rapid Development ◽  
Concrete Block ◽  
Scale Model ◽  
Small Scale ◽  
Design Criteria ◽  
Advantages And Disadvantages ◽  
Different Types ◽  
The Stability ◽  
The Moment

The increasing shortage and costs of natural materials in certain geographical areas has resulted in recent years, inter alia, in the rapid development of artificial (concrete) block revetments. In general, two main types of revetments can be distinguished: permeable (stone pitching, placed relatively open block-mats) and (relatively-) impermeable (closed blocks, concrete slabs). Regarding the shape and/or placing technique a distinction can be made between: a) free (mostly rectangular-) blocks and b) interlocking blocks of different design (tongue-and-groove connection, ship- lap, cabling, blocks connected to geotextile by pins etc.). In all these cases the type of sublayer (permeable/impermeable) and the grade of permeability of the toplayer are very important factors in the stability of these revetments. The design also needs to be made (executed) and maintained. Both aspects must therefore already be taken along within the stadium of designing. At the moment there is a large variety of types of revetment-blocks and other defence systems (i.e. block-mats), see Fig. 1. Until recently no objective design-criteria were available for most types/systems of blocks. The choice (type and size) of the revetments built sofar is only based on experience and on personal points of view, sometimes supported by small-scale model investigations. In the light of new (stricter) rules regarding the safety of the Dutch dikes, as they have been drawn up by the Delta-Commission, the need for proper design-criteria for the revetments of dikes has evidently grown. Because of the complexity of the problem no simply, generally valid mathematical model for the stability of the revetment are available yet. For restricted areas of application however, fairly reliable criteria (often supported by large-scale tests) have been developed in the Netherlands not only for the kind of revetment, but also for conditions of loads. This new approach is discussed in (Klein Breteler, 1988). This paper presents a short state-of-the-art review of existing knowledge on the designing of different types of revetments and, where ever possible, the available stability criteria are mentioned. There is also given some comparison of the different types of revetments with their advantages and disadvantages and suggestions regarding their practical application.

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