Showing papers on "Markov random field published in 1989"

Random field models in image analysis

Abstract: Image models are useful in quantitatively specifying natural constraints and general assumptions about the physical world and the imaging process. This review paper explains how Gibbs and Markov random field models provide a unifying theme for many contemporary problems in image analysis. Random field models permit the introduction of spatial context into pixel labeling problems, such as segmentation and restoration. Random field models also describe textured images and lead to algorithms for generating textured images, classifying textures and segmenting textured images. In spite of some impressive model-based image restoration and texture segmentation results reported in the literature, a number of fundamental issues remain unexplored, such as the specification of MRF models, modeling noise processes, performance evaluation, parameter estimation, the phase transition phenomenon and the comparative analysis of alternative procedures. The literature of random field models is filled with great promise, but...

Automatic ventricular cavity boundary detection from sequential ultrasound images using simulated annealing

Abstract: An automatic algorithm has been developed for high-speed detection of cavity boundaries in sequential 2-D echocardiograms using an optimization algorithm called simulated annealing (SA). The algorithm has three stages. (1) A predetermined window of size n*m is decimated to size n'*m' after low-pass filtering. (2) An iterative radial gradient algorithm is employed to determine the center of gravity (CG) of the cavity. (3) 64 radii which originate from the CG defined in stage 2 are bounded by the high-probability region. Each bounded radius is defined as a link in a 1-D, 64-member cyclic Markov random field. This algorithm is unique in that it compounds spatial and temporal information along with a physical model in its decision rule, whereas most other algorithms base their decisions on spatial data alone. This is the first implementation of a relaxation algorithm for edge detection in echocardiograms. Results attained using this algorithm on real data have been highly encouraging. >

A Markov random field model-based approach to image interpretation

Abstract: A Markov random field (MRF) model-based approach to automated image interpretation is described and demonstrated as a region-based scheme. In this approach, an image is first segmented into a collection of disjoint regions which form the nodes of an adjacency graph. Image interpretation is then achieved through assigning object labels, or interpretations, to the segmented regions, or nodes, using domain knowledge, extracted feature measurements, and spatial relationships between the various regions. The interpretation labels are modeled as a MRF on the corresponding adjacency graph, and the image interpretation problem are formulated as a maximum a posteriori estimation rule. Simulated annealing is used to find the best realization, or optimal interpretation. Through the MRF model, this approach also provides a systematic method for organizing and representing domain knowledge through the clique functions of the probability density function underlying MRF. Results of image interpretation experiments performed on synthetic and real-world images using this approach are described. >

Integration of vision modules and labeling of surface discontinuities

Abstract: It is assumed that a major goal of the early vision modules and their integration is to deliver a cartoon of the discontinuities in the scene and to label them in terms of their physical origin. The output of each of the vision modules is noisy, possibly sparse, and sometimes not unique. The authors suggest the use of a coupled Markov random field (MRF) at the output of each module (image cues)-stereo, motion, color, and texture-to achieve two goals: first, to counteract the noise and fill in sparse data, and secondly, to integrate the image within each MRF to find the module discontinuities and align them with the intensity edges. The authors outline a theory of how to label the discontinuities in terms of depth, orientation, albedo, illumination, and specular discontinuities. They present labeling results using a simple linear classifier operating on the output of the MRF associated with each vision module and coupled to the image data. The classifier has been trained on a small set of a mixture of synthetic and real data. >

Mutually compatible Gibbs random fields

Abstract: A unified theory for the mathematical description of Gibbs random fields that answers some important theoretical and practical questions about their statistical behavior is presented. The local transfer function is introduced, and the joint probability measure of the general Gibbs random field is derived in terms of this function. The resulting probability structure is required to satisfy the property of mutual compatibility. A necessary and sufficient condition for a Gibbs random field to be mutually compatible is developed and used to prove that a mutually compatible Gibbs random field is a unilateral Markov random field. The existence of some special nontrivial cases of Gibbs random fields that are mutually compatible is demonstrated. Conditions on the translation invariance and isotropy of the general Gibbs random field with a free boundary are studied. The class of Gibbs random fields with a homogeneous local transfer function and the class of horizontally and vertically translation-invariant Gibbs random fields are introduced and treated. The concept of a translation-invariant Gibbs random field is also explored. The problem of the statistical inference of mutually compatible Gibbs random fields is discussed. >

A Markov Random Field Model-Based Approach To Image Interpretation

Abstract: In this paper, a Markov random field (MRF) model-based approach to automated image interpretation is described and demonstrated as a region-based scheme. In this approach, an image is first segmented into a collection of disjoint regions which form the nodes of an adjacency graph. Image interpretation is then achieved through assigning object labels, or interpretations, to the segmented regions, or nodes, using domain knowledge, extracted feature measurements and spatial relationships between the various regions. The interpretation labels are modeled as a MRF on the corresponding adjacency graph and the image interpretation problem is formulated as a maximum a posteriori (MAP) estimation rule. Simulated annealing is used to find the best realization, or optimal MAP interpretation. Through the MRF model, this approach also provides a systematic method for organizing and representing domain knowledge through the clique functions of the pdf of the underlying MRF. Results of image interpretation experiments performed on synthetic and real-world images using this approach are described and appear promising.

Multivariate Tissue Classification of MRI Images for 3-D Volume Reconstruction - A Statistical Approach

Abstract: One of the major problems in 3-D volume reconstruction from magnetic resonance imaging (MRI) is the difficulty in automating the classification of soft tissues. Because of the complicated soft tissue structures revealed by MRI, it is not easy to segment the images with simple algorithms. MRI can obtain multiple images from the same anatomical section with different pulse sequences, with each image having different response characteristics for each soft tissue. Using the gray level distributions of soft tissues, we have developed two statistical classifiers that utilize the image context information based on the Markov Random Field (MRF) image model. One of the classifiers classifies each voxel to a specific tissue type and the other estimates the partial volume of each tissue within each voxel. Since the voxel sizes of tomographic images are finite and the measurements from tissue boundaries represent the mixture of multiple tissue types, it is preferable that the classifier should not classify each voxel in all-or-none fashion; rather, it should be able to tell the percentage volume of each class in each voxel for the better visualization of the prepared 3-D dataset. The paper presents the theoretical basis of the algorithms and experimental evaluation results of the classifiers in terms of classification accuracy, as compared to the conventional maximum likelihood classifier.

Reconstruction of polygonal images

Abstract: Let T be a two-dimensional region, and let X be a surface dejined on T. The values of X on T, constitute an image, or pattern. The true value of X at any point on T cannot be directly observed, but data can be recorded which provide information about X. The aim is to reconstruct X using the prior knowledge that X will vary smoothly over most of T, but may exhibit jump discontinuities over line segments. This information can be incorporated via Bayes' theorem, using a polygonal Markov random field on T as prior distribution. Under this continuum model, X may in principle be estimated according to standard criteria. In practice, the techniques rely on simulation of the posterior distribution. A natural family of conjugate priors is identified, and a class of spatial-temporal Markov processes is constructed on the uncountable state space; simulation then proceeds by a method of analogous to the Gibbs sampler.

The Use of Bayesian and Entropic Methods in Neural Network Theory

Abstract: There has been much interest recently in the use of neural networks to solve complicated information processing problems such as those which arise in signal and image processing. In this paper we review Markov random field (MRF) neural network techniques for representing joint probability density functions (PDF). The “Boltzmann machine” serves as the paradigm, and we present a generalised version of its learning algorithm. We also present a technique for designing MRF potentials with low information redundancy for modelling image texture. To improve further the computational efficiency of such neural networks we introduce a novel method of cluster decomposing a PDF by using topographic mappings. The outcome of this programme is a means of designing sampling functions for extracting information from datasets (typically images).

Parallel object recognition from structure (the tinkertoy project)

Abstract: This thesis examines the problem of recognizing structurally composed objects. The task is the recognition of Tinkertoys--objects whose identity is defined solely by the spatial relationships between simple parts. Ultimately, a massively parallel framework incorporating a principled treatment of uncertainty and domain dependence is developed to address the problem. The basic architecture of the solution is formed by posing structure matching as a part-wise correspondence problem in a labelling framework, then applying the unit/value principle. The solution is developed incrementally. Complexity and correctness analyses and implementation experiments are provided at each phase. In the first phase, a special purpose network implementing discrete connectionist relaxation is used to topologically discriminate between objects. In the second step, the algorithm is generalized to a massively parallel formulation of constraint satisfaction, yielding an arc consistency algorithm with the fastest known time complexity. At this stage the formulation of the application problem is also generalized, so geometric discrimination can be achieved. Developing an implementation required defining a method for the domain specific optimization of the parallel arc consistency algorithm. The optimization method is applicable to arbitrary domains. In the final phase, the solution is generalized to handle uncertain input information and statistical domain dependence. Segmentation and recognition are computed simultaneously by a coupled Markov Random Field. Both problems are posed as labelling problems within a unified high-level MRF architecture. In the segmentation subnet, evidence from the image is combined with clique potentials expressing both qualitative a priori constraints and learnable domain dependent knowledge. Matching constraints and coupling constraints complete the definition of the field. The effectiveness of the framework is demonstrated in experiments involving the traditionally difficult problems of occulsion and accidental alignment.

Markov models and Bayesian methods in image analysis

Abstract: Markov random field models and Bayesian methods have provided answers to various contemporary problems in image analysis. We give a very brief introduction to the topic. In particular, we highlight the use of Bayesian methods in classifying the image into different classes. Some other current developments are also described and their relationship with other chapters in this volume is indicated. Some future directions are also outlined.

Bayesian restoration of image sequences using 3-D Markov random fields

Abstract: The authors describe a method for restoring sequences of noisy images obtained by acquiring different views of the same scene. The method uses a 3-D Markov random field and a least-square-error matching to establish the temporal-spatial neighborhood of a pixel in an image under restoration. The problem of image sequence restoration is posed as the problem of maximizing the conditional probabilities. This task is accomplished by a modified version of the iterated conditional modes method where Gibbs distribution is used to model the prior probability. >

A Bayesian Reconstruction Algorithm for Emission Tomography using a Markov Random Field Prior

Abstract: A Bayesian generalized expectation - maximization (GEM) algorithm using a locally correlated Markov random field prior in the form of a Gibbs function is developed for emission tomography. A close-form coordinate gradient ascent M-step which updates the image pixels sequentially is derived. The resulting GEM Bayesian algorithm is applied to estimating the 3-D image parameters in the Poisson model of emission sources based upon simulation of a parallel collimated gamma camera.

Parameter estimation and restoration of noisy images using Gibbs distributions in hidden Markov models

Abstract: A noisy image model is formulated by integrating the image and noise models into the hidden and observation layers of a hidden Markov model (HMM). The true image is modeled by a Markov random field (MRF), and the noise is a flip error that changes the gray level of image pixels according to a stochastic matrix. An algorithm for parameter estimation is developed on the basis of the reestimation formulation in HMM. At each iteration of the reestimation, the Gibbs distribution (GD) parameters are estimated using gradient ascent, and the noise parameter is estimated as the percentage of pixels in the unobserved image having the same gray levels as the observed image, where the percentage is the posterior expectation over all possible configurations of the unobserved image. Gibbs samplers are used to generate the samples of MRFs, and sample averages are taken to approximate the expectation terms. Images are restored using the minimum misclassification technique. Experiments on binary images contaminated by 20-30% noise showed good restoration results. >

Event detection in multisource imaging using contextual estimation

Abstract: The authors propose a novel approach to the problem of detecting events, i.e. significant differences between pictures of a given scene taken at different wavelengths or with different sensors. It is shown that event detection can be expressed, within a Bayesian decision framework, as a contextual estimation problem. The unknown process to be estimated corresponds to the significant interimage changes. A grey-level map assigned to the unknown event maximizes the a posteriori distribution of the event image, given the observed images. A Markov random field model is used to describe the spatial statistics of the unknown process. The authors present an application to the fine arts, that of finding an underpainting from a visible/X-ray pair of images of the same painting. >

Echocardiographic myocardial edge detection using an optimization protocol

Abstract: The definition of the ventricular myocardial shape in echocardiographic ultrasound cross-sectional images is a difficult task due to the low quality of these images and the high noise levels present. An automatic protocol has been developed for high-speed detection of cavity boundaries in sequential 2-D echocardiograms. A 1-D cyclic Markov random field is defined, where the field's random variables are radii emanating from the cavity's center of gravity. An optimization using simulated annealing is performed upon an energy function defined by these random variables. This energy function is composed of a linear combination of elements which represent optimal edge detection, cavity wall smoothness, temporal continuity, and cavity volume maximization. The improved decision rule, which results from this optimization, produced highly encouraging results. >

Integration of intensity-based and edge-based stereo algorithms using Markov random fields

Abstract: Summary form only given, as follows. A method is introduced where image intensity and edge information from a pair of stereo images are integrated into a single stereo vision technique. A Bayesian model is used to derive the maximum a posteriori (MAP) stereo matched solution for the proposed integrated matching algorithm. The disparity is modeled as a Markov random field (MRF) and the input image data as a coupled MRF (intensity and edge orientation process together). The left and right stereo images are considered as degraded observations and external inputs to the system. The well-known MRF-Gibbs distribution equivalence is used to reduce the MAP problem to that of finding an appropriate energy function (cost function) that describes the constraints on the solution. A stochastic relaxation algorithm (simulated annealing) is used to find the best disparity solution by minimizing the energy equation. Results are presented for the proposed integrated stereo technique. >

Estimation of cloud microstructural parameters from satellite imagery: A Markov random field approach

Abstract: Estimation of microstructural parameters controlling clustering in different directions or a cloud scene is investigated. The cloud scene is represent.ed as a Markov ran~om field and the parameters are estimated by a maximum likelihood technique. A surrogate Image, corresp°!ldmg to each scene, is generated by a Monte-Carlo procedure. Results of analysing NOAA and INSA T cloud Images are presented

Partial volume tissue classification of multivariate MR images

Abstract: A statistical classifier is described that classifies each tissue for the partial volume within each voxel, using the gray-level distribution of soft tissues. The classifier utilizes the image context information and is based on the Markov random field (MRF) image model. The classification algorithm proposed takes advantage of the fact that in magnetic resonance imaging multiple images can be obtained from the same anatomical section with different pulse sequences, with each image having different response characteristics for each soft tissue. The classification accuracy of the classifier was evaluated in terms of root-mean-squares estimation error. Results for a simulated and a real image are shown and discussed. >

Labeling of Surface Discontinuities through the Integration of Vision Modules

Abstract: We assume that a major goal of the early vision modules and their integration is to deliver a cartoon of the discontinuities in the scene and to label them in terms of their physical origin. The output of each of the vision modules is noisy, possibly sparse and sometimes not unique. We have used a coupled Markov Random Field (MRF) at the output of each module - stereo, motion, color, texture - to achieve two goals: first, to counteract the noise and fill sparse data and second, to integrate the image within each MRF to find the mod ale discontinuities and align them with the intensity edges. In this work we discuss the extension of this scheme for the integration of all the low-level modules and the labeling of discontinuities in terms of depth, orientation, albedo, illumination and specular discontinuities. We present labeling results using a simple linear classifier operating on the output of the MRF associated with each vision module and coupled to the usage data. The classifier has been trained on a small set of a mixture of synthetic and real data.

3D Bayesian image reconstruction using the generalized EM algorithm

Abstract: Summary form only given. The use of the generalized expectation maximization (GEM) algorithm for image reconstruction from projections and restoration from broad point spread functions is proposed. A GEM algorithm has been developed for maximum a posteriori (MAP) estimation using Markov random field prior distributions for a set of Poisson data whose mean is related to the unknown image by a linear transformation. This method is applicable in emission tomography (PET and SPECT) and to the restoration of radioastronomical images. The EM algorithm is applicable to problems in which there is a more natural formulation of the estimation problem in terms of a set of complete unobserved data which is related to the incomplete observed data by a known many-to-one transformation. Applying this approach to the MAP image reconstruction problem results in a two-step iterative algorithm. The resulting computational costs are significantly lower than those for the coordinate descent algorithms. The algorithm does not guarantee convergence to a global maximum, but will converge to a stationary point of the posterior density for the image conditional on the observed data. >