Showing papers on "Markov random field published in 1993"
TL;DR: Attempts have been made to cover both fuzzy and non-fuzzy techniques including color image segmentation and neural network based approaches, which addresses the issue of quantitative evaluation of segmentation results.
3,527 citations
TL;DR: In this article, a generalized Gaussian Markov random field (GGMRF) is proposed for image reconstruction in low-dosage transmission tomography, which satisfies several desirable analytical and computational properties for map estimation, including continuous dependence of the estimate on the data and invariance of the character of solutions to scaling of data.
Abstract: The authors present a Markov random field model which allows realistic edge modeling while providing stable maximum a posterior (MAP) solutions. The model, referred to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisfies several desirable analytical and computational properties for map estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the a posteriori log-likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low-dosage transmission tomography. >
978 citations
TL;DR: In this paper, the authors make an analogy between images and statistical mechanics systems, where pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system.
Abstract: We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, non-linear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low-energy states (‘annealing’), or what is the same thing, the most probable states under the Gib...
764 citations
TL;DR: The early development of MCMC in Bayesian inference is traced, some recent computational progress in statistical physics is reviewed, based on the introduction of auxiliary variables, and its current and future relevance in Bayesesian applications are discussed.
Abstract: on Wednesday, May 6th, 1992, Professor B. W. Silverman in the Chair] SUMMARY Markov chain Monte Carlo (MCMC) algorithms, such as the Gibbs sampler, have provided a Bayesian inference machine in image analysis and in other areas of spatial statistics for several years, founded on the pioneering ideas of Ulf Grenander. More recently, the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a Markov random field has opened the way to the use of MCMC in general Bayesian computation. In this paper, we trace the early development of MCMC in Bayesian inference, review some recent computational progress in statistical physics, based on the introduction of auxiliary variables, and discuss its current and future relevance in Bayesian applications. We briefly describe a simple MCMC implementation for the Bayesian analysis of agricultural field experiments, with which we have some practical experience.
500 citations
TL;DR: This method serves three purposes: it accurately locates boundaries between changed and unchanged areas, it brings to bear a regularizing effect on these boundaries in order to smooth them, and it eliminates small regions if the original data permits this.
342 citations
TL;DR: It is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances and is presented a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints.
Abstract: The estimation of dense velocity fields from image sequences is basically an ill-posed problem, primarily because the data only partially constrain the solution. It is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches. In this paper, the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints. It is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances. The theoretical framework relies on Bayesian estimation associated with global statistical models, namely, Markov random fields. The constraints introduced here aim to address the following issues: optical flow estimation while preserving motion boundaries, processing of occlusion regions, fusion between gradient and feature-based motion constraint equations. Deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field. The algorithm is well suited to a multiresolution implementation which brings an appreciable speed-up as well as a significant improvement of estimation when large displacements are present in the scene. Experiments on synthetic and real world image sequences are reported. >
322 citations
Book•
01 Jan 1993
TL;DR: Image modeling during the 1980s - a brief overview, A Rosenfeld compound Gauss-Markov random fields for parallel image processing, J.W. Woods, et al stochastic algorithms for restricted image spaces and experiments in deblurring, and a continuation method for image estimation using the A-diabatic approximation.
Abstract: Image modeling during the 1980s - a brief overview, A Rosenfeld compound Gauss-Markov random fields for parallel image processing, JW Woods, et al stochastic algorithms for restricted image spaces and experiments in deblurring, D Geman, et al a continuation method for image estimation using the A-diabatic approximation, A Rangarahan and R Chellappa isotropic priors for single photon emission computed tomography, S Geman Gaussian Markov random fields at multiple resolution, S Lakshmanan and H Derin texture synthesis and classification, S Chatterjee spectral estimation for random fields with applications to Markov Modelling and texture classification, J Yuan and TS Rao probabilistic network inference for cooperative high and low level vision, PB Chow, et al stereo matching, S Barnard 3-D analysis of A shaded and textural surface image, RL Kashyap shape from texture using Gaussian Markov random fields, FS Cohen and M Patel the use of Markov random fields in estimating and reorganizing objects in 3D spaces, DB Cooper, et al A Markov random field model-based approach to image interpretation, JW Modestino and J Zhang A Markov random field restoration of image sequences, TJ Hainsworth and KV Mardia the MIT vision machine - progress in the integration of vision modules, T Poggio and D Weinshall parameter estimation for Gibbs distributions from fully observed data, B Gidas on sampling methods and annealing algorithms, SB Gelfand and S Mitter adaptive Gibbsian automata, JL Marroquin and A Ramirez
289 citations
TL;DR: A Markov random field model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described, and results show that this approach provides good blur estimates and restored images.
Abstract: A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing. >
144 citations
TL;DR: In this paper, it is assumed that the local characteristics of the true scene can be represented by a non-degenerate Markov random field, and the reconstruction can be estimated according to standard criteria.
Abstract: 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 non-degenerate 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 large-scale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does ...
88 citations
TL;DR: In this paper, the authors consider a class of local updating dynamics that are reversible with respect to Markov random fields II and investigate the speed of weak convergence of these Markov chains in terms of their second largest eigenvalues in absolute value.
Abstract: Sampling from a Markov random field II can be performed efficiently via Monta Carlo methods by simulating a Markov chain that converges weakly to II. We consider a class of local updating dynamics that are reversible with respect to II. It includes the Metropolis algorithm (MII) and the Gibbs sampler (GS). We investigate the speed of weak convergence of these Markov chains in terms of their second-largest eigenvalues in absolute value. We study the general algebraic structure and then the stochastic Ising model in detail
87 citations
TL;DR: An unsupervised segmentation strategy for textured images, based on a hierarchical model in terms of discrete Markov Random Fields, where the textures are modeled as Gaussian Gibbs Fields, while the image partition is modeled as a Markov Mesh Random Field.
11 May 1993
TL;DR: A hierarchical model is proposed, which consists of a label pyramid and a whole observation field, which allows propagation of local interactions more efficiently, giving estimates closer to the global optimum for deterministic as well as for stochastic relaxation schemes.
Abstract: The authors consider multiscale Markov random field (MRF) models. It is well known that multigrid methods can improve significantly the convergence rate and the quality of the final results of iterative relaxation techniques. A hierarchical model is proposed, which consists of a label pyramid and a whole observation field. The parameters of the coarse grid can be derived by simple computation from the finest grid. In the label pyramid, a new local interaction is introduced between two neighbor grids. This model gives a relaxation algorithm which can be run in parallel on the entire pyramid. The model allows propagation of local interactions more efficiently, giving estimates closer to the global optimum for deterministic as well as for stochastic relaxation schemes. It can also be seen as a way to incorporate cliques with far apart sites for a reasonable price. >
TL;DR: A Markov Random Field model-based approach is proposed as a systematic way for modeling, encoding and applying scene knowledge to the image understanding problem and is exploited to interpret the color scenes.
TL;DR: In this paper, discontinuities of the motion field are taken into account by using a Markov random field (MRF) model, which leads to solutions less sensitive to noise than an all-or-nothing Boolean line process.
Abstract: A motion field estimation method for image sequence coding is presented. Motion vector field is estimated to remove the temporal redundancy between two successive images of a sequence. Motion estimation is an ill-posed inverse problem. Usually, the solution has been stabilized by regularization, as proposed by Tikhonov in 1963, i.e., by assuming a priori the smoothness of the solution. Here, discontinuities of the motion field are taken into account by using a Markov random field (MRF) model. Discontinuities, which unavoidably appear at the edges of a moving object, can be modeled by a continuous line process, as introduced by Geman and Reynolds in 1992, via a regularization function that belongs to the Φ function family. This line process leads to solutions less sensitive to noise than an all-or-nothing Boolean line process. Taking discontinuities into account leads to the minimization of a nonconvex functional to get the maximum a posteriori (MAP) optimal solution. We derive a new deterministic relaxation algorithm associated with the Φ function, to minimize the nonconvex criterion. We apply this algorithm in a coarse-to-fine multiresolution scheme, leading to more accurate results. We show results on synthetic and real-life sequences.
15 Jun 1993
TL;DR: An unsupervised segmentation algorithm which uses Markov random fields for modeling color texture is presented and is successfully applied to a range of textured color images of natural scenes.
Abstract: An unsupervised segmentation algorithm which uses Markov random fields for modeling color texture is presented. These models characterize a texture in terms of spatial interaction within each color plane and interaction among different color planes. These models are used for segmentation in conjunction with an agglomerative clustering procedure that at each step minimizes a global performance functional based on the conditional pseudo-likelihood of the image. This algorithm is successfully applied to a range of textured color images of natural scenes. >
27 Apr 1993
TL;DR: It is shown how the MFT (mean field theory) can be applied to MRF (Markov random field) model-based motion estimation and the efficacy of this approach is demonstrated on synthetic and real-world images.
Abstract: It is shown how the MFT (mean field theory) can be applied to MRF (Markov random field) model-based motion estimation. Specifically, the motion is characterized by a coupled MRF including a displacement field (motion continuity), a line field (motion discontinuity), and a segmentation field (identifying uncovered areas). These fields are estimated by using the MFT. The efficacy of this approach is demonstrated on synthetic and real-world images. >
27 Apr 1993
TL;DR: A novel deterministic reconstruction method preserving discontinuities is presented, based on a Markov random field image model, coupled with a line-process, for single photon emission computed tomography reconstruction.
Abstract: A novel deterministic reconstruction method preserving discontinuities is presented. This method is based on a Markov random field image model, coupled with a line-process. The reconstruction method uses a deterministic and adaptive relaxation algorithm. This algorithm is presented for single photon emission computed tomography (SPECT) reconstruction, but can also be applied to a large class of inverse problems in image processing. The experimental results are very promising. The proposed method is robust to noise and yields good results. The reconstructed images are composed of smooth areas, bordered by sharp edges. >
08 Sep 1993
TL;DR: In this paper, a maximum a posteriori (MAP) estimation based on a Markov random field model for the prior image distribution is proposed to reconstruct both the smooth regions of the image and the discontinuities along the edges.
Abstract: There has been a tremendous amount of research in the area of image halftoning. Where the goal has been to find the most visually accurate representation given a limited palette of gray- levels (often just two, black and white). This paper focuses on the inverse problem, that of finding efficient techniques for reconstructing high-quality continuous-tone images from their halftoned versions. The proposed algorithms are based on a maximum a posteriori (MAP) estimation criteria using a Markov random field model for the prior image distribution. Image estimates obtained with the proposed model accurately reconstruct both the smooth regions of the image and the discontinuities along the edges. Algorithms are developed and example gray-level reconstructions are presented generated from both dithered and error diffused halftone originals.
15 Jun 1993
TL;DR: Given an initial segmentation of the sequence, this approach can segment and track a cardiac cavity during the cardiac cycle and its performance is demonstrated on a real echocardiographic sequence.
Abstract: Spatiotemporal segmentation in echocardiographic image sequences is discussed. Spatial properties and temporal properties are combined to compute segmentation and tracking in a single process. The Markov random field (MRF) framework is used for modeling the energy function. Starting from a reference image, where a manual segmentation is made, a method is developed to estimate the model parameters. An estimation is a crucial point in MRF models. Thus, given an initial segmentation of the sequence, this approach can segment and track a cardiac cavity during the cardiac cycle. Its performance is demonstrated on a real echocardiographic sequence. >
01 Jan 1993
TL;DR: Semi-Markov Random Fields as discussed by the authors are a sub-class of Markov Random Field models and have a clear physical interpretation as size distributions of homogeneous volumes and border relations, which can be regarded as a three-dimensional generalization of the well known semi-markov chain in one dimension.
Abstract: The spatial distribution of sedimentary fades in petroleum reservoirs is of major concern due to its influence on the flow regime in the reservoir, and thereby the production of oil and gas. A class of stochastic models, called semi-Markov Random Fields, for the facies distribution in petroleum reservoirs is presented. Semi-Markov Random Fields are a sub-class of Markov Random Field models. The model parameters in semi-Markov Random Fields have, in contrast to the usual Markov Random Fields with local neighborhood, a clear physical interpretation as size distributions of homogeneous volumes and border relations. Semi-Markov Random Fields can be regarded as a three dimensional generalization of the well known semi-Markov chain in one dimension. Simulation results both from semi-Markov Random Fields and Markov Random Fields with local neighborhood are presented.
TL;DR: Novel generating probabilistic models representing a raster region map, i.e. an image with nominal scale of signal values (region labels), as sample realization of a Markov random field of labels with Gibbs joint probability distribution are introduced.
29 Oct 1993
TL;DR: In this paper, a coupled Gibbs/Markov random field (GMRF) is used to estimate the displacement field in image sequences, and an objective function yielding the MAP estimate with respect to some model assumptions is derived.
Abstract: This paper addresses the problem of displacement field estimation and segmentation in image sequences. Emerging from the Bayesian paradigm, we derive an objective function yielding the MAP estimate with respect to some model assumptions. It can be interpreted as a measure for the estimates' explanation of the image data regularized by our prior assumptions on the estimates. The observation model we impose, considers experimental studies of the displaced frame difference and decovered regions. It involves some unknown parameters. The a priori is modelled by a coupled Gibbs/Markov random field. Optimization is performed via deterministic relaxation in a multiscale pyramid maintaining the structure of the algorithm in all pyramid levels. Iteratively, the unknown parameters of the observation model are estimated. The relaxation procedure tests only a small number of likely displacement-label candidates at each site. The relationship of regularization weights in the pyramid is thoroughly investigated. Simulation results with complex natural scenes demonstrate the good performance of the algorithm.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: Bayesian methods for recovering a 2-D surface are discussed and parametric and nonparametric methods are used to enforce smoothness of these surfaces.
Abstract: Bayesian methods for recovering a 2-D surface are discussed. It is assumed that there is a textural image that can be modeled by a Markov random field and that the original surface is composed of different surfaces, each of which is associated with one textural state. Both parametric and nonparametric methods are used to enforce smoothness of these surfaces. Iterative procedures are examined for simultaneous restoration of the textural image and estimation of underlying parameters. From the estimated textural image and the estimated parameters, an estimate for the original surface is obtained. Two illustrative examples are presented. >
01 Feb 1993
TL;DR: It is shown that this approach, thanks to the common probabilistic basis of the two techniques, is able to combine in a natural way causal inference properties at different abstraction levels as provided by Bayesian networks with optimisation criteria usually applied to find the best configuration for an MRF.
Abstract: In this paper, Bayesian networks of Markov random fields (BN-MRFs) are proposed as a technique for representing and applying apriori knowledge at different abstraction levels inside a distributed image processing framework. It is shown that this approach, thanks to the common probabilistic basis of the two techniques, is able to combine in a natural way causal inference properties at different abstraction levels as provided by Bayesian networks with optimisation criteria usually applied to find the best configuration for an MRF. Examples of two-level BN-MRFs are given, where each node uses a coupled Markov random field which has to solve a coupled restoration and segmentation problem. Experiments are concerned with expert-driven registered segmentation and tracking of regions from image sequences.
TL;DR: The architecture of a distributed vision system is presented, with particular attention directed to the bottom-up indexing mechanism performed by a hierarchically organized network of information processing modules.
Abstract: The architecture of a distributed vision system is presented, with particular attention directed to the bottom-up indexing mechanism performed by a hierarchically organized network of information processing (IP) modules. Each IP module adaptively transforms input data passed by lower-level modules into more complete observations and performs a transformation that is modeled as a regularization process. This scheme is applied to the problem of recognizing objects whose 3-D shape can be described as a set of planar surfaces. Edge detection, straight-line extraction, grouping, and matching are the P modules considered. In particular, the regularization process consists of either a voting scheme or a Markov random field labeling process, depending on the level. At the higher level, a degree of belief is given about the presence of objects contained in the scene and considered in the model database. Results demonstrate both the validity of the processes applied separately at each level and the global consistency of the method.
TL;DR: This paper tests a suggestion of Hancock and Kittler (1990) for supplying the probabilities of improbable labelings which are otherwise not estimated correctly by sampling, and determines the parameters that optimize the reconstruction of binary images.
31 Oct 1993
TL;DR: In this paper, the performance of several PET image reconstruction procedures through the use of ensemble averages was evaluated on a pixel-by-pixel basis and also for larger regions of interest (ROIs).
Abstract: Presents preliminary results of a Monte-Carlo study in which the authors quantify the relative performance of several PET image reconstruction procedures Through the use of ensemble averages they estimate bias and variance on a pixel-by-pixel basis and also for larger regions of interest (ROIs) They compare the performance of filtered back-projection (FBP), maximum likelihood (ML) and several maximum a posteriori (MAP) estimators The MAP estimators are based on Markov random field image models with the following Gibbs energy functions: (i) quadratic, (ii) Geman and McClure (1985), (iii) weak membrane model, (iv) weak membrane with additional line process interactions In all cases the MAP estimators use an automated procedure to chose the prior parameter which is based on the "L-curve" as described below The weak membrane prior includes a line process which models the locations of discontinuities in image intensity In cases where prior information, in the form of an anatomical MR image, is available concerning the potential locations of discontinuities in the PET image, this can be incorporated into the prior and used to influence the formation of boundaries The impact of this additional information on the reconstructed image is quantified through the authors' Monte-Carlo study Results indicate that MAP estimation procedures are able to reduce variance considerably, in comparison to ML, with a corresponding small increase in bias The addition of boundary information results in further reductions in variance and reduced bias >
13 Sep 1993
TL;DR: A probabilistic model representing piecewise-homogeneous digital (raster) gray- scale textured images as samples of certain Markov random field with short- and long-range pairwise interactions between the signals in the pixels is described.
Abstract: We describe a probabilistic model representing piecewise-homogeneous digital (raster) gray- scale textured images as samples of certain Markov random field with short- and long-range pairwise interactions between the signals (gray-scale levels and labels of homogeneous regions) in the pixels The model is given by a Gibbs probability distribution specified by a sum of terms which gives a total strength of the interaction Each term defines the probability of the signal values in a pixel or a pair of the pixels in superim-posed image and region map Unknown parameters of the model can be estimated by using a stochastic approximation technique Several results in generating and segmenting the textured images are presented
25 Oct 1993
TL;DR: A deterministic iterative algorithm is proposed which searches for the maximum a posteriori (MAP) estimate of the textured regions of a textured image.
Abstract: The problem of textured image segmentation is considered. A textured image is modeled by a hierarchical Markov random field (HMRF). The image segmentation is realized as the maximum a posteriori (MAP) estimate of the textured regions. Following an argument based on the mean field approximation, a deterministic iterative algorithm is proposed which searches for the MAP segmentation of the textured image.
TL;DR: A stereo-windows concept is introduced to obtain a unique and consistent parent texture from the image data that, under appropriate transformations, yields the observed texture in the image.
Abstract: The problem of extracting the local shape information of a 3-D texture surface from a single 2-D image by tracking the perceived systematic deformations the texture undergoes by virtue of being present on a 3-D surface and by virtue of being imaged is examined. The surfaces of interest are planar and developable surfaces. The textured objects are viewed as originating by laying a rubber planar sheet with a homogeneous parent texture on it onto the objects. The homogeneous planar parent texture is modeled by a stationary Gaussian Markov random field (GMRF). A probability distribution function for the texture data obtained by projecting the planar parent texture under a linear camera model is derived, which is an explicit function of the parent GMRF parameters, the surface shape parameters. and the camera geometry. The surface shape parameter estimation is posed as a maximum likelihood estimation problem. A stereo-windows concept is introduced to obtain a unique and consistent parent texture from the image data that, under appropriate transformations, yields the observed texture in the image. The theory is substantiated by experiments on synthesized as well as real images of textured surfaces. >