Showing papers on "Markov random field published in 1986"

On the statistical analysis of dirty pictures

Abstract: may 7th, 1986, Professor A. F. M. Smith in the Chair] SUMMARY A continuous two-dimensional region is partitioned into a fine rectangular array of sites or "pixels", each pixel having a particular "colour" belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a nondegenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does not depend on these large-scale characteristics. The method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field. Some complications, including parameter estimation, are discussed. Potential applications are mentioned briefly.

Segmentation of textured images using Gibbs random fields

Abstract: A new algorithm for the segmentation of textured images is developed by making use of Gibbs random fields. A hierarchical stochastic model is employed to represent textured images. At the higher level, the region formation process, describing different areas of the image, is modeled as a Gibbs random field, or equivalently as a Markov random field. At the lower level, the textures in different regions of the image are modeled also as Gibbs random fields. Based on this hierarchical model, the segmentation algorithm being proposed seeks to obtain the maximum a posteriori estimate of the region process using the textured image data. The maximization is carried out recursively by making use of a dynamic programming formulation. Computational concerns, however, necessitate the implementation of a suboptimal version of the algorithm that tries to maximize a pseudolikelihood over strips of the image. This is a non-trivial extension of a maximum a posteriori segmentation algorithm for noisy images modeled by Gibbs random fields [1]. The segmentation algorithm is applied on several textured images composed of 2, 3 region (texture) types and 2 or 4 level textures, with remarkable success. Numerous examples on the application of the segmentation algorithm are presented for textured images with region processes and textures generated according to a particular Gibbs distribution.

On parallel stereo

Abstract: We review some of the open issues in computational stereo. In particular, we will discuss the problem of extracting better matching primitives and of dealing with occlusions. Markov Random Field models - an extension of standard regularization - suggest sophisticated stereo matching algorithms. They are, however, ill-suited to efficient, real-time applications. We will conclude reviewing a new simple but fast algorithm implemented by one of us (Drumheller, 1986) on the TMC Connection Machine (TM) computer. Some of its features are: (a) the potential for combining different primitives, including color information; (b) the use of a stronger and new formulation of the uniqueness constraint; and (c) its disparity representation that maps efficiently into the architecture of the Connection Machine computer.

Markov random fields for image modelling and analysis

Abstract: This chapter deals with the problem of image modelling through the use of 2D Markov Random Field (MRF). The MRF’s are parametric models with a noncausal structure where the various dependencies over the plane is described in all directions. We first show how the MRF’s are used as texture image models, region geometry models, as well as edge models.Then we show how they have been successfully used for image classification, surface inspection, image restoration, and image segmentation.

Random Fields And Spatial Renewal Potentials

Abstract: By using an approach similar to that used for Markov random fields, we propose a spatial version of renewal processes, generalizing the usual notion in dimension 1. We characterize the potentials of such renewal random fields and we give a theorem about the presence of phase transition. Finally, we study the problem of the sampling of renewal fields by means of a random automaton, we show simulations and discuss the stopping rules of the process of sampling.

The Use of Gibbs Distributions In Image Processing

Abstract: In this chapter, we discuss the potential of Gibbs distributions (GDs) as models in image processing applications. We briefly review the definitions and basic concepts of Markov random fields (MRFs) and GDs and present some realizations from these distributions. The use of statistical models and methods in image processing has increased considerably over the recent years. Most of these studies involve the use of MRF models and processing techniques based on these models. The pioneering work on MRFs due to Dobrushin [1], Wong [2], and Woods [3] involves extending the Markovian property in one dimension to higher dimensions. However, due to lack of causality in two dimensions the extension is not straightforward. Some properties in one dimension, for example, the equivalence of one-sided and two-sided Markovianity, do not carry over to two dimensions. The early work by Abend et al. [4] presents a causal characterization for a class of MRFs called Markov mesh random fields. This work also includes a formulation pointing out the Gibbsian property of a Markov chain without fully realizing the connection. Other attempts in extending the Markovian property to two dimensions include the autoregressive models: the “simultaneous autoregressive” (SAR) models and the “conditional Markov” models introduced by Chellappa and Kashyap [5].

Statistical Image Restoration and Refinement

Abstract: We consider the problem of reconstructing an image from a noisy record. We describe existing methods due to Geman and Geman (1984) and Besag (1986) which use a Markov random field model for the true scene but assume that each pixel consists of a single colour. In order to improve the quality of the restoration at the boundary of regions of different colours we extend these methods to allow pixels to contain two regions of colour separated by a single straight line. An algorithm for performing the reconstruction is presented and illustrated by an example.

Segmentation And Global Parameter Estimation Of Textured Images Modelled By Markov Random Fields

Abstract: This paper is concerned with identifying and estimating the parameters of the different texture regions that comprise a textured image. A textured region here is modelled by a Markov Random Field (MRF). The MRF is parametrized by a parameter vector α , ana has a noncausal structure. We assume no a prior knowledge about the different texture regions, their associated texture parameters, or the available number of textured regions. The image is partitioned into disjoint square windows and a maximum likelihood estimate (MLE) (or a sufficient statistis) α* for α (for a fixed order model) is obtained in each window. The components of α* are viewed as features, and a as a feature vector. The windows are grouped in different texture regions based on feature selection and clustering analysis of the α* vectors in the different windows. To simplify the clustering process, the dimensionality of the feature vector is reduced via a Karhunen-Loeve decomposition of the between-to-within scatter matrix of the α* vectors. Each α* is projected onto the dominant mode (eigenvector) of the scatter matrix. The projected data is used in the clustering process. The clustering is achieved by minimizing a within group variance criterion which has been weighted by a factor that explicitly depends on the number of groups. To reduce the computational cost associated with this method, it is accompanied by a "valley method". Finally, by exploiting the asymptotic normality of the MLE, we compute the tglobal MLE α* for each textured region by properly combining the locally estimated MLE α* in the various windows that comprise the region. The global MLE α* for a region is notning but an appropriately weighted linear combination of the local MLE set { α k * }.