Showing papers on "Markov random field published in 1994"
TL;DR: Results indicate significant improvements in emission image quality using the Bayesian approach, in comparison to filtered backprojection, particularly when reprojections of the MAP transmission image are used in place of the standard attenuation correction factors.
Abstract: The authors describe conjugate gradient algorithms for reconstruction of transmission and emission PET images. The reconstructions are based on a Bayesian formulation, where the data are modeled as a collection of independent Poisson random variables and the image is modeled using a Markov random field. A conjugate gradient algorithm is used to compute a maximum a posteriori (MAP) estimate of the image by maximizing over the posterior density. To ensure nonnegativity of the solution, a penalty function is used to convert the problem to one of unconstrained optimization. Preconditioners are used to enhance convergence rates. These methods generally achieve effective convergence in 15-25 iterations. Reconstructions are presented of an /sup 18/FDG whole body scan from data collected using a Siemens/CTI ECAT931 whole body system. These results indicate significant improvements in emission image quality using the Bayesian approach, in comparison to filtered backprojection, particularly when reprojections of the MAP transmission image are used in place of the standard attenuation correction factors. >
302 citations
07 May 1994
TL;DR: A unified approach for Markov Random Field Models modeling in low and high level computer vision is presented, made possible due to a recent advance in MRF modeling for high level object recognition.
Abstract: A variety of computer vision problems can be optimally posed as Bayesian labeling in which the solution of a problem is defined as the maximum a posteriori (MAP) probability estimate of the true labeling. The posterior probability is usually derived from a prior model and a likelihood model. The latter relates to how data is observed and is problem domain dependent. The former depends on how various prior constraints are expressed. Markov Random Field Models (MRF) theory is a tool to encode contextual constraints into the prior probability. This paper presents a unified approach for MRF modeling in low and high level computer vision. The unification is made possible due to a recent advance in MRF modeling for high level object recognition. Such unification provides a systematic approach for vision modeling based on sound mathematical principles.
284 citations
TL;DR: The authors show an explicit relationship between cooccurrences and a large class of GRF's, and how the aura measure generalizes, to any number of gray levels and neighborhood order, some properties previously known for just the binary, nearest-neighbor GRF.
Abstract: Gibbs random field (GRF) models and features from cooccurrence matrices are typically considered as separate but useful tools for texture discrimination. The authors show an explicit relationship between cooccurrences and a large class of GRF's. This result comes from a new framework based on a set-theoretic concept called the "aura set" and on measures of this set, "aura measures." This framework is also shown to be useful for relating different texture analysis tools. The authors show how the aura set can be constructed with morphological dilation, how its measure yields cooccurrences, and how it can be applied to characterizing the behavior of the Gibbs model for texture. In particular, they show how the aura measure generalizes, to any number of gray levels and neighborhood order, some properties previously known for just the binary, nearest-neighbor GRF. Finally, the authors illustrate how these properties can guide one's intuition about the types of GRF patterns which are most likely to form. >
157 citations
21 Jun 1994
TL;DR: A global contour model based on a stable and regenerative shape matrix, which is invariant and unique under rigid motions is proposed, which yields prior distribution that exerts influence over a global model while allowing for deformations.
Abstract: This paper considers the problem of modeling and extracting arbitrary deformable contours from noisy images. We propose a global contour model based on a stable and regenerative shape matrix, which is invariant and unique under rigid motions. Combined with Markov random field to model local deformations, this yields prior distribution that exerts influence over a global model while allowing for deformations. We then cast the problem of extraction into posterior estimation and show its equivalence to energy minimization of a generalized active contour model. We discuss pertinent issues in shape training, minimax regularization and initialization by generalized Hough transform. Finally, we present experimental results and compare its performance to rigid template matching. >
138 citations
TL;DR: An empirical study of simulated realizations from various models used in the literature is described, however, it is concluded that while large-scale clustering may be represented by such models, strong directional effects are also present for all but very limited parameterizations.
Abstract: Markov random fields are typically used as priors in Bayesian image restoration methods to represent spatial information in the image. Commonly used Markov random fields are not in fact capable of representing the moderate-to-large scale clustering present in naturally occurring images and can also be time consuming to simulate, requiring iterative algorithms which can take hundreds of thousands of sweeps of the image to converge. Markov mesh models, a causal subclass of Markov random fields, are, however, readily simulated. We describe an empirical study of simulated realizations from various models used in the literature, and we introduce some new mesh-type models. We conclude, however, that while large-scale clustering may be represented by such models, strong directional effects are also present for all but very limited parameterizations. It is emphasized that the results do not detract from the use of Markov random fields as representers of local spatial properties, which is their main purpose in the implementation of Bayesian statistical approaches to image analysis. Brief allusion is made to the issue of parameter estimation. >
59 citations
TL;DR: In this article, a new approach to microwave imaging of 2D inhomogeneous dielectric scatterers is presented, where Markov random fields are used to obtain a model of the distributions of dielectrics features in the scattering region.
Abstract: A new approach to microwave imaging of 2D inhomogeneous dielectric scatterers is presented. The method is developed in the space domain, and Markov random fields are used to obtain a model of the distributions of dielectric features in the scattering region. In this way, a-priori knowledge can be easily inserted in the imaging scheme. This stochastic approach gives rise to a functional equation that can be minimized by using a simulated annealing algorithm. An iterative scheme is derived that allows one to bypass the need for storing large matrices in the computer. Numerical simulation results, confirming the capabilities and effectiveness of the proposed method, are reported. Solutions have generally been obtained in few steps, and seem better than those obtained by other imaging techniques in the space domain. The capability of the algorithm to operate in a strongly noisy environment is also proved. >
55 citations
13 Nov 1994
TL;DR: The apparent flow field induced by the camera motion is modeled by a 2D parametric motion model and compensated for using the values of the parameters estimated by a multiresolution robust method.
Abstract: We address the problem of detecting moving objects from a moving camera. The apparent flow field induced by the camera motion is modeled by a 2D parametric motion model and compensated for using the values of the parameters estimated by a multiresolution robust method. Motion detection is achieved through a statistical regularization approach based on multiscale Markov random field (MRF) models. Particular attention has been paid to the definition of the energy function involved and to the considered observations. This method has been validated by experiments carried out on different real image sequences. >
53 citations
TL;DR: The proposed algorithm, called E-GNC, can be considered an extension of the graduated nonconvexity (GNC), first proposed by Blake and Zisserman for noninteracting discontinuities, and is shown to give satisfactory results with a low number of iterations.
48 citations
21 Jun 1994
TL;DR: This paper presents a Markov random field (MRF) model for object recognition in high level vision based on sound mathematical principles from theories of MRF and probability, which is in contrast to heuristic formulations.
Abstract: This paper presents a Markov random field (MRF) model for object recognition in high level vision. The labeling state of a scene in terms of a model object is considered as an MRF or couples MRFs. Within the Bayesian framework the optimal solution is defined as the maximum a posteriori (MAP) estimate of the MRF. The posterior distribution is derived based on sound mathematical principles from theories of MRF and probability, which is in contrast to heuristic formulations. An experimental result is presented. >
47 citations
TL;DR: A novel segmentation algorithm is compared with nonmultiresolution Markov random field-based image segmentation algorithms in the context of synthetic image example problems, and found to be both significantly more efficient and effective.
Abstract: The author formulates a novel segmentation algorithm which combines the use of Markov random field models for image-modeling with the use of the discrete wavepacket transform for image analysis. Image segmentations are derived and refined at a sequence of resolution levels, using as data selected wave-packet transform images or "channels". The segmentation algorithm is compared with nonmultiresolution Markov random field-based image segmentation algorithms in the context of synthetic image example problems, and found to be both significantly more efficient and effective. >
47 citations
30 Oct 1994
TL;DR: An algorithm is described for segmenting 3D MR brain image into K different tissue types, which include gray, white matter and CSF, and maybe other abnormal tissues, which has the potential to routinely process clinical MR images with minimal user involvement.
Abstract: An algorithm is described for segmenting 3D MR brain image into K different tissue types, which include gray, white matter and CSF, and maybe other abnormal tissues. MR images considered can be either scale- or multi-valued. Each scale-valued image is modeled as a collection of regions with slowly varying intensity plus a white Gaussian noise. Each tissue type is modeled by a Markov random field with the second order neighborhood in a 3D lattice. The proposed algorithm is an adaptive K-means clustering algorithm for 3-dimensional and multi-valued images. Each iteration consists of two steps: estimate mean intensity at each location for each type, and estimate tissue types by maximizing the a posteriori probability. The algorithm slowly adapts to the local intensity variation of each region, so it is robust to the "shading" effect. It has the potential to routinely process clinical MR images with minimal user involvement. Its performance is tested using patient data. >
TL;DR: A new method is proposed for image restoration of a gray-level image blurred by an erroneous point spread function and corrupted by either additive or multiplicative noise based on a Markov random field model with an appropriate line field, whereby it has the ability to restore discontinuities.
13 Nov 1994
TL;DR: A new algorithm for segmentation of noisy or textured images using the expectation-maximization (EM) algorithm for estimating parameters of the probability mass function of the pixel class labels and the maximization of the posterior marginals criterion for the segmentation operation is presented.
Abstract: Presents a new algorithm for segmentation of noisy or textured images using the expectation-maximization (EM) algorithm for estimating parameters of the probability mass function of the pixel class labels and the maximization of the posterior marginals (MPM) criterion for the segmentation operation. A Markov random field (MRF) model is used for the pixel class labels. The authors present experimental results demonstrating the use of the new algorithm on synthetic images and medical imagery. >
07 May 1994
TL;DR: A new spatio-temporal model is presented and it is expressed within a Markov random field framework and results are presented with different formulations of the temporal properties.
Abstract: The aim of this work is to track specific anatomical structures in temporal sequences of echocardiographic images. This paper presents a new spatio-temporal model and describes the relevant spatial and temporal properties that must be taken into consideration to obtain the best possible results. It is expressed within a Markov random field framework and results are presented with different formulations of the temporal properties.
TL;DR: A Markov Random Field model-based approach is proposed as a systematic way for integrating constraints for robust image segmentation by defining an MRF model on the corresponding RAG.
19 Apr 1994
TL;DR: An extension of the graduated non convexity principle pioneered by Blake and Zisserman (1987) which allows its use for ill-posed linear inverse problems, and an application of the method to a diffraction tomography imaging problem.
Abstract: We propose a method for the reconstruction of an image, only partially observed through a linear integral operator. As such an inverse problem is ill-posed, prior information must be introduced. We consider the case of a compound Markov random field with a non-interacting line process. In order to maximise the posterior likelihood function, we propose an extension of the graduated non convexity principle pioneered by Blake and Zisserman (1987) which allows its use for ill-posed linear inverse problems. We discuss the role of the observation scale and some aspects of the implemented algorithm. Finally, we present an application of the method to a diffraction tomography imaging problem. >
09 Oct 1994
TL;DR: This paper proposes to use the continuous relaxation labeling (RL) method for the minimization of Markov random field problems, which converts the original NP complete problem into one of polynomial complexity.
Abstract: Using Markov random field (MRF) theory, a variety of computer vision problems can be modeled in terms of optimization based on the maximum a posteriori (MAP) criterion. The MAP configuration minimizes the energy of a posterior (Gibbs) distribution. When the label set is discrete, the minimization is combinatorial. This paper proposes to use the continuous relaxation labeling (RL) method for the minimization. The RL converts the original NP complete problem into one of polynomial complexity. Annealing may be combined into the RL process to improve the quality (globalness) of RL solutions. Performance comparison among four different RL algorithms is given.
08 Aug 1994
TL;DR: The ICM speckle noise filter gave substantially superior visual results on a real SAR image over all the number of considered classes, at the price of an increased computational effort, when more than sixteen classes (grey levels) are considered.
Abstract: The ICM (iterated conditional modes) algorithm is an iterative proposal for the improvement of maximum likelihood segmentation. It is based upon the modelling of the a priori distribution for the classes with a multiclass Potts-Strauss Markov random field (MRF) framework. In this work, a new speckle filtering procedure is proposed, based on the ICM algorithm. This is done by increasing the number of classes on the a priori distribution, considering from 16 up to 256 levels. The model for the SAR image filtering procedure includes a multiplicative noise, described by the Rayleigh distribution, under the conditions of one look and linear detection. The ICM algorithm also uses a parameter estimation technique for the underlying MRF distribution, under the pseudolikelihood framework. These estimators are obtained in a computationally feasible form. The presented results are compared with those obtained by the well-known Nagao-Matsuyama filter, which was proposed as an edge preserving filter. The ICM speckle noise filter gave substantially superior visual results on a real SAR image over all the number of considered classes, at the price of an increased computational effort, when more than sixteen classes (grey levels) are considered. >
30 May 1994
TL;DR: An alternate approach to estimate the parameters of a Markov random field model for images using the concepts of homotopy continuation method and a joint parameter estimation and image restoration scheme is presented.
Abstract: In this paper, we present an alternate approach to estimate the parameters of a Markov random field (MRF) model for images using the concepts of homotopy continuation method. We also develop a joint parameter estimation and image restoration scheme where we have used a fairly general model involving the line fields and tested on a real image. Simulation results using gray level images are presented. >
09 Oct 1994
TL;DR: The multitemperature annealing (MTA), which consists of associating higher temperatures to coarser levels, in order to be less sensitive to local minima at coarser grids, is defined and the convergence to the global optimum is proved.
Abstract: As it is well known, optimization of the energy function of Markov random fields is very expensive. Hierarchical models have usually much more communication per pixel than monogrid ones. This is why classical annealing schemes are too slow, even on a parallel machine, to minimize the energy associated with such a model. However, taking benefit of the pyramidal structure of the model, we can define a new annealing scheme: the multitemperature annealing (MTA), which consists of associating higher temperatures to coarser levels, in order to be less sensitive to local minima at coarser grids. The convergence to the global optimum is proved by a generalisation of the annealing theorem of Geman and Geman (1984). We have applied the algorithm to image classification and tested it on synthetic and real images.
19 Apr 1994
TL;DR: A new roughness penalty for use in estimation problems including image estimation problems is discussed, closely related to a penalty used for density estimation that was introduced by Good and Gaskins (1971).
Abstract: This paper discusses a new roughness penalty for use in estimation problems including image estimation problems. It is one of a new class of penalty functions for use in estimation and image regularization that has recently been proposed. These functions penalize the discrepancy between an image and a shifted version of itself; here the discrepancy measure is the I-divergence. This penalty is closely related to a penalty used for density estimation that was introduced by Good and Gaskins (1971). Roughness penalty methods form an attractive alternative to Markov random field priors, achieving many of the same properties including the introduction of neighborhood structures. An example of the use of this new penalty for radar imaging using real radar data has been examined. >
09 Oct 1994
TL;DR: The benefits of the approach include the embedding of observations into the matching criterion function and the ability of the algorithm to find the global rather than nearest local optimum.
Abstract: This paper presents a new relaxation labelling approach for matching image structures characterized by high order relations. A Markov random field (MRF) is employed to represent the prior contextual information. The consistent labelling is defined as the maximum a posteriori (MAP) labelling. It is achieved using iterative updating according to a rule derived using mean field theory (MFT). The benefits of the approach include the embedding of observations into the matching criterion function and the ability of the algorithm to find the global rather than nearest local optimum. The approach is applied to stereo vision and the experimental results demonstrate its viability.
01 May 1994
TL;DR: An algorithm has been developed which uses stochastic relaxation in three dimensions to segment brain tissues from images acquired using multiple echo sequences from magnetic resonance imaging (MRI) and results correspond well with manual segmentations of the same data.
Abstract: An algorithm has been developed which uses stochastic relaxation in three dimensions to segment brain tissues from images acquired using multiple echo sequences from magnetic resonance imaging (MRI). The initial volume data is assumed to represent a locally dependent Markov random field. Partial volume estimates for each voxel are obtained yielding fractional composition of multiple tissue types for individual voxels. A minimum of user intervention is required to train the algorithm by requiring the manual outlining of regions of interest in a sample image from the volume. Segmentations obtained from multiple echo sequences are determined independently and then combined by forming the product of the probabilities for each tissues type. The implementation has been parallelized using a dataflow programming environment to reduce the computational burden. The algorithm has been used to segment 3D MRI data sets using multiple sclerosis lesions, gray matter, white matter, and cerebrospinal fluid as the partial volumes. Results correspond well with manual segmentations of the same data.
19 Apr 1994
TL;DR: Markov random field based motion field segmentation is used to detect areas of replacement noise in archived motion pictures, and interpolate into the gaps using a motion-compensated interpolation scheme to restore the frame.
Abstract: Many archived motion pictures suffer from what we term replacement noise, that is various degradations such as dirt, scratches, fingerprints, etc., where the original picture is replaced by some unrelated information. We use Markov random field based motion field segmentation to detect these areas, and then interpolate into the gaps using a motion-compensated interpolation scheme to restore the frame. >
01 Jan 1994
TL;DR: Theoretical and experimental results demonstrate superiority of the Monte Carlo estimation approach, and suitability of mathematical morphology in studying important properties of a particular binary random image model, widely known as a Markov random field model.
Abstract: Morphological granulometries are frequently used as descriptors of granularity, or texture, within a binary image. In this paper, we study the problem of estimating the (discrete) size distribution and size density of a random binary image by means of empirical, as well as, Monte Carlo estimators. Theoretical and experimental results demonstrate superiority of the Monte Carlo estimation approach, and suitability of mathematical morphology in studying important properties of a particular binary random image model, widely known as a Markov random field model.
TL;DR: This work proposes a Bayesian model for generating finer resolution images by defining resampling, or aggregation, as a linear operator applied to an original picture to produce derived lower resolution data which represent the available experimental infor-mation.
Abstract: The use of Bayesian models for the reconstruction of images degraded by both some blurring function H and the presence of noise has become popular in recent years. Making an analogy between classical degradation processes and resampling, we propose a Bayesian model for generating finer resolution images. The approach involves defining resampling, or aggregation, as a linear operator applied to an original picture to produce derived lower resolution data which represent our available experimental infor-mation. Within this framework, the operation of making inference on the orginal data can be viewed as an inverse linear transformation problem. This problem, formalized through Bayes' theorem, can be solved by the classical maximum a posteriori estimation procedure. Image local characteristics are assumed to follow a Gaussian Markov random field. Under some mild assumptions, simple, iterative and local operations are involved, making parallel ‘relaxation’ processing feasible. experimental results are shown o...
13 Nov 1994
TL;DR: An image compression algorithm based on a multiresolution Markov random field model used to model the correlations of wavelet coefficients across the scales is presented.
Abstract: Multiresolution image decompositions (e.g., wavelets), in conjunction with a variety of quantization schemes, have been shown to be very effective for image compression. Recently, several promising tree-structured quantization schemes that exploit the correlation across scales have been proposed. In this paper, we present an image compression algorithm based on a multiresolution Markov random field model used to model the correlations of wavelet coefficients across the scales. We also present experimental results obtained using the algorithm. >
13 Nov 1994
TL;DR: A multistage algorithm which makes use of spatial contextual information in a hierarchical clustering procedure has been developed for unsupervised image segmentation.
Abstract: A multistage algorithm which makes use of spatial contextual information in a hierarchical clustering procedure has been developed for unsupervised image segmentation. A Markov random field model is employed to enforce local spatial smoothness, while the maximum entropy principle is utilized to quantify global smoothness in the image processing. A multiwindow approach implemented in a pyramid-like data structure which uses a boundary blocking operation is employed to increase computational efficiency. >
13 Apr 1994
TL;DR: In this paper, a contextual VQ method based on the Markov random field (MRF) theory is proposed to model the speech feature vector space, and its superiority is confirmed by a series of comparative experiments in a speaker independent isolated word recognition task by using different VQ schemes as the front-end of DHMM.
Abstract: By using formulation of the finite mixture distribution identification, several alternatives to the conventional LBG VQ method are investigated. A contextual VQ method based on the Markov random field (MRF) theory is proposed to model the speech feature vector space. Its superiority is confirmed by a series of comparative experiments in a speaker independent isolated word recognition task by using different VQ schemes as the front-end of DHMM. The VQ schemes studied include the LBG VQ, the classification maximum likelihood (CML) approach, the mixture maximum likelihood (MML) procedure, the ergodic large HMM (LHMM) and the contextual VQ (CVQ) method. The motivation to use the MRF to model the contextual dependence information in the underlying speech production process can be readily extended to acoustic modeling of the basic speech units in speech recognition. >