Showing papers on "Markov random field published in 2000"

A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients

Abstract: We present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. We develop an efficient algorithm for synthesizing random images subject to these constraints, by iteratively projecting onto the set of images satisfying each constraint, and we use this to test the perceptual validity of the model. In particular, we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set. We also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures.

Automatic analysis of the difference image for unsupervised change detection

Abstract: One of the main problems related to unsupervised change detection methods based on the "difference image" lies in the lack of efficient automatic techniques for discriminating between changed and unchanged pixels in the difference image. Such discrimination is usually performed by using empirical strategies or manual trial-and-error procedures, which affect both the accuracy and the reliability of the change-detection process. To overcome such drawbacks, in this paper, the authors propose two automatic techniques (based on the Bayes theory) for the analysis of the difference image. One allows an automatic selection of the decision threshold that minimizes the overall change detection error probability under the assumption that pixels in the difference image are independent of one another. The other analyzes the difference image by considering the spatial-contextual information included in the neighborhood of each pixel. In particular, an approach based on Markov Random Fields (MRFs) that exploits interpixel class dependency contexts is presented. Both proposed techniques require the knowledge of the statistical distributions of the changed and unchanged pixels in the difference image. To perform an unsupervised estimation of the statistical terms that characterize these distributions, they propose an iterative method based on the Expectation-Maximization (EM) algorithm. Experimental results confirm the effectiveness of both proposed techniques.

Traffic monitoring and accident detection at intersections

Abstract: We have developed an algorithm, referred to as spatio-temporal Markov random field, for traffic images at intersections. This algorithm models a tracking problem by determining the state of each pixel in an image and its transit, and how such states transit along both the x-y image axes as well as the time axes. Our algorithm is sufficiently robust to segment and track occluded vehicles at a high success rate of 93%-96%. This success has led to the development of an extendable robust event recognition system based on the hidden Markov model (HMM). The system learns various event behavior patterns of each vehicle in the HMM chains and then, using the output from the tracking system, identifies current event chains. The current system can recognize bumping, passing, and jamming. However, by including other event patterns in the training set, the system can be extended to recognize those other events, e.g., illegal U-turns or reckless driving. We have implemented this system, evaluated it using the tracking results, and demonstrated its effectiveness.

Sonar image segmentation using an unsupervised hierarchical MRF model

Abstract: This paper is concerned with hierarchical Markov random field (MRP) models and their application to sonar image segmentation. We present an original hierarchical segmentation procedure devoted to images given by a high-resolution sonar. The sonar image is segmented into two kinds of regions: shadow (corresponding to a lack of acoustic reverberation behind each object lying on the sea-bed) and sea-bottom reverberation. The proposed unsupervised scheme takes into account the variety of the laws in the distribution mixture of a sonar image, and it estimates both the parameters of noise distributions and the parameters of the Markovian prior. For the estimation step, we use an iterative technique which combines a maximum likelihood approach (for noise model parameters) with a least-squares method (for MRF-based prior). In order to model more precisely the local and global characteristics of image content at different scales, we introduce a hierarchical model involving a pyramidal label field. It combines coarse-to-fine causal interactions with a spatial neighborhood structure. This new method of segmentation, called the scale causal multigrid (SCM) algorithm, has been successfully applied to real sonar images and seems to be well suited to the segmentation of very noisy images. The experiments reported in this paper demonstrate that the discussed method performs better than other hierarchical schemes for sonar image segmentation.

A probabilistic background model for tracking

Abstract: A new probabilistic background model based on a Hidden Markov Model is presented. The hidden states of the model enable discrimination between foreground, background and shadow. This model functions as a low level process for a car tracker. A particle filter is employed as a stochastic filter for the car tracker. The use of a particle filter allows the incorporation of the information from the low level process via importance sampling. A novel observation density for the particle filter which models the statistical dependence of neighboring pixels based on a Markov random field is presented. The effectiveness of both the low level process and the observation likelihood are demonstrated.

A Probabilistic Background Model for Tracking

Abstract: A new probabilistic background model based on a Hidden Markov Model is presented. The hidden states of the model enable discrimination between foreground, background and shadow. This model functions as a low level process for a car tracker. A particle filter is employed as a stochastic filter for the car tracker. The use of a particle filter allows the incorporation of the information from the low level process via importance sampling. A novel observation density for the particle filter which models the statistical dependence of neighboring pixels based on a Markov random field is presented. The effectiveness of both the low level process and the observation likelihood are demonstrated.

Brain tissue classification of magnetic resonance images using partial volume modeling

Abstract: Presents a fully automatic three-dimensional classification of brain tissues for Magnetic Resonance (MR) images. An MR image volume may be composed of a mixture of several tissue types due to partial volume effects. Therefore, the authors consider that in a brain dataset there are not only the three main types of brain tissue: gray matter, white matter, and cerebro spinal fluid, called pure classes, but also mixtures, called mixclasses. A statistical model of the mixtures is proposed and studied by means of simulations. It is shown that it can be approximated by a Gaussian function under some conditions. The D'Agostino-Pearson normality test is used to assess the risk or of the approximation. In order to classify a brain into three types of brain tissue and deal with the problem of partial volume effects, the proposed algorithm uses two steps: (1) segmentation of the brain into pure and mixclasses using the mixture model; (2) reclassification of the mixclasses into the pure classes using knowledge about the obtained pure classes. Both steps use Markov random field (MRF) models. The multifractal dimension, describing the topology of the brain, is added to the MRFs to improve discrimination of the mixclasses. The algorithm is evaluated using both simulated images and real MR images with different T1-weighted acquisition sequences.

The EM/MPM algorithm for segmentation of textured images: analysis and further experimental results

Abstract: In this paper we present new results relative to the "expectation-maximization/maximization of the posterior marginals" (EM/MPM) algorithm for simultaneous parameter estimation and segmentation of textured images. The EM/MPM algorithm uses a Markov random field model for the pixel class labels and alternately approximates the MPM estimate of the pixel class labels and estimates parameters of the observed image model. The goal of the EM/MPM algorithm is to minimize the expected value of the number of misclassified pixels. We present new theoretical results in this paper which show that the algorithm can be expected to achieve this goal, to the extent that the EM estimates of the model parameters are close to the true values of the model parameters. We also present new experimental results demonstrating the performance of the EM/MPM algorithm.

On-line retrainable neural networks: improving the performance of neural networks in image analysis problems

Abstract: A novel approach is presented in this paper for improving the performance of neural-network classifiers in image recognition, segmentation, or coding applications, based on a retraining procedure at the user level. The procedure includes: 1) a training algorithm for adapting the network weights to the current condition; 2) a maximum a posteriori (MAP) estimation procedure for optimally selecting the most representative data of the current environment as retraining data; and 3) a decision mechanism for determining when network retraining should be activated. The training algorithm takes into consideration both the former and the current network knowledge in order to achieve good generalization. The MAP estimation procedure models the network output as a Markov random field (MRF) and optimally selects the set of training inputs and corresponding desired outputs. Results are presented which illustrate the theoretical developments as well as the performance of the proposed approach in real-life experiments.

A concealment method for video communications in an error-prone environment

Abstract: In this paper, we propose a two-stage error-concealment method for block-based compressed video which was transmitted in an error-prone environment. In the first stage, we obtain initial estimates of the missing blocks. If the motion vectors associated with the missing blocks are available, motion compensation is used to provide good estimates. Otherwise, a novel algorithm which preserves image continuity is used to estimate the blocks. In the second stage, a maximum a posteriori (MAP) estimator, which employs an adaptive Markov random field (MRF) as the image a priori model is used to improve the video reconstruction quality. The adaptive model enables the estimation to incorporate information embedded not only in the immediate neighborhood pixels but also in a wider neighborhood into the reconstruction procedure without increasing the order of the MRF model. The proposed concealment method achieves very good computation-performance tradeoffs, as demonstrated via experimental results.

Equivalence of Julesz Ensembles and FRAME Models

Abstract: In the past thirty years, research on textures has been pursued along two different lines. The first line of research, pioneered by Julesz (1962, IRE Transactions of Information Theory, IT-8:84–92), seeks essential ingredients in terms of features and statistics in human texture perception. This leads us to a mathematical definition of textures in terms of Julesz ensembles (Zhu et al., IEEE Trans. on PAMI, Vol. 22, No. 6, 2000). A Julesz ensemble is a set of images that share the same value of some basic feature statistics. Images in the Julesz ensemble are defined on a large image lattice (a mathematical idealization being Z2) so that exact constraint on feature statistics makes sense. The second line of research studies Markov random field (MRF) models that characterize texture patterns on finite (or small) image lattice in a statistical way. This leads us to a general class of MRF models called FRAME (Filter, Random field, And Maximum Entropy) (Zhu et al., Neural Computation, 9:1627–1660). In this article, we bridge the two lines of research by the fundamental principle of equivalence of ensembles in statistical mechanics (Gibbs, 1902, Elementary Principles of Statistical Mechanics. Yale University Press). We show that 1). As the size of the image lattice goes to infinity, a FRAME model concentrates its probability mass uniformly on a corresponding Julesz ensemble. Therefore, the Julesz ensemble characterizes the global statistical property of the FRAME models 2). For a large image randomly sampled from a Julesz ensemble, any local patch of the image given its environment follows the conditional distribution specified by a corresponding FRAME model. Therefore, the FRAME model describes the local statistical property of the Julesz ensemble, and is an inevitable texture model on finite (or small) lattice if texture perception is decided by feature statistics. The key to derive these results is the large deviation estimate of the volume of (or the number of images in) the Julesz ensemble, which we call the entropy function. Studying the equivalence of ensembles provides deep insights into questions such as the origin of MRF models, typical images of statistical models, and error rates in various texture related vision tasks (Yuille and Coughlan, IEEE Trans. on PAMI, Vol. 2, No. 2, 2000). The second thrust of this paper is to study texture distance based on the texture models of both small and large lattice systems. We attempt to explain the asymmetry phenomenon observed in texture “pop-out” experiments by the asymmetry of Kullback-Leibler divergence. Our results generalize the traditional signal detection theory (Green and Swets, 1988, Signal Detection Theory and Psychophysics, Peninsula Publishing) for distance measures from iid cases to random fields. Our theories are verified by two groups of computer simulation experiments.

Occlusion robust tracking utilizing spatio-temporal Markov random field model

Abstract: It is very important to achieve reliable vehicle tracking in ITS application such as accident detection. The most difficult problem associated with vehicle tracking is the occlusion effect among vehicles. In order to resolve this problem, we applied the dedicated algorithm which we defined as spatio-temporal Markov random field model to traffic images at an intersection. The spatio-temporal MRF considers texture correlations between consecutive images as well as the correlation among neighbors within a image. As a result, we were able to track vehicles at the intersection robustly against occlusions. Vehicles appear in various kinds of shapes and they move in random manners at the intersection. Although occlusions occur in such complicated manners, the algorithm given was able to segment and track such occluded vehicles at a high success rate of 93-96%. The algorithm requires only gray scale images and does not assume any physical models of vehicles.

A simple unsupervised MRF model based image segmentation approach

Abstract: A simple technique has been suggested to obtain optimal segmentation based on tonal and textural characteristics of an image using the Markov random field (MRF) model. The technique takes an initially over segmented image as well as the original image as its inputs and defines an MRF over the region adjacency graph (RAG) of the initially segmented regions. A tonal-region based segmentation technique due to Kartikeyan and Sarkar (1989) has been used for initial segmentation. The energy function has been defined over the first order cliques of the MRF. The essence of this approach is primarily based on quantitative values of the second order statistics, on region characteristics and consequently deciding upon the action of merging neighboring regions using the F-statistic. The effectiveness of our approach is demonstrated with wide variety of real life examples viz., indoor, outdoor and satellite and a comparison of its output with that of a previous work in the literature has been provided.

Probabilistic modeling of single-trial fMRI data

Abstract: Describes a probabilistic framework for modeling single-trial functional magnetic resonance (fMR) images based on a parametric model for the hemodynamic response and Markov random field (MRF) image models. The model is fitted to image data by maximizing a lower bound on the log likelihood. The result is an approximate maximum a posteriori estimate of the joint distribution over the model parameters and pixel labels. Examples show how this technique can used to segment two-dimensional (2-D) fMR images, or parts thereof, into regions with different characteristics of their hemodynamic response.

Real-time Defect Inspection of Textured Surfaces

Abstract: Texture analysis plays an important role in the automated visual inspection of textured images to detect their defects. For this purpose, model-based and feature-based methods are implemented and tested for textile images in a laboratory environment. The methods are compared in terms of their success rates in determining the defects. The Markov Random Field model is applied on different DSP systems for real-time inspection.

On block updating in Markov random field models for disease mapping. (REVISED, May 2001)

Abstract: Gaussian Markov random field (GMRF) models are commonly used to model spatial correlation in disease mapping applications. For Bayesian inference by MCMC, so far mainly single-site updating algorithms have been considered. However, convergence and mixing properties of such algorithms can be extremely bad due to strong dependencies of parameters in the posterior distribution. In this paper, we propose various block sampling algorithms in order to improve the MCMC performance. The methodology is rather general, allows for non-standard full conditionals, and can be applied in a modular fashion in a large number of different scenarios. For illustration we consider three different models: two formulations for spatial modelling of a single disease (with and without additional unstructured parameters respectively), and one formulation for the joint analysis of two diseases. We apply the proposed algorithms to two datasets known from the literature. The results indicate that the largest benefits are obtained if parameters and the corresponding hyperparameter are updated jointly in one large block. In certain situations, even updating of all or nearly all parameters in one block may be necessary. Implementation of such block algorithms is surprisingly easy using methods for fast sampling of Gaussian Markov random fields (Rue, 2000). By comparison, estimates of the relative risk and related quantities, such as the posterior probability of an exceedence relative risk, based on single-site updating, can be rather misleading, even for very long runs. Our results may have wider relevance for efficient MCMC simulation in hierarchical models with Markov random field components.

A genetic algorithm-based segmentation of Markov random field modeled images

Abstract: An unsupervised method is presented for segmenting video sequences degraded by noise. Each frame in a sequence is modeled using a Markov random field (MRF), and the energy function of each MRF is minimized by chromosomes that evolve using distributed genetic algorithms. To improve the computational efficiency, only unstable chromosomes corresponding to moving object parts are evolved. Experimental results show the effectiveness of the proposed method.

Image Segmentation Using Markov Random Field Model in Fully Parallel Cellular Network Architectures

Abstract: Markovian approaches to early vision processes need a huge amount of computing power. These algorithms can usually be implemented on parallel computing structures. Herein, we show that the Markovian labeling approach can be implemented in fully parallel cellular network architectures, using simple functions and data representations. This makes possible to implement our model in parallel imaging VLSI chips.As an example, we have developed a simplified statistical image segmentation algorithm for the Cellular Neural/Nonlinear Networks Universal Machine (CNN-UM), which is a new image processing tool, containing thousands of cells with analog dynamics, local memories and processing units. The Modified Metropolis Dynamics (MMD) optimization method can be implemented into the raw analog architecture of the CNN-UM. We can introduce the whole pseudo-stochastic segmentation process in the CNN architecture using 8 memories/cell. We use simple arithmetic functions (addition, multiplication), equality-test between neighboring pixels and very simple nonlinear output functions (step, jigsaw). With this architecture, the proposed VLSI CNN chip can execute a pseudo-stochastic relaxation algorithm of about 100 iterations in about 100 ?s.In the suggested solution the segmentation is unsupervised, where a pixel-level statistical estimation model is used. We have tested different monogrid and multigrid architectures.In our CNN-UM model several complex preprocessing steps can be involved, such as texture-classification or anisotropic diffusion. With these preprocessing steps, our fully parallel cellular system may work as a high-level image segmentation machine, using only simple functions based on the close-neighborhood of a pixel.

A concealment method for shape information in MPEG-4 coded video sequences

Abstract: We propose a new method for error concealment of shape information in MPEG-4 video bit streams that are transmitted over error prone channels. The proposed method employs a MAP estimator with a Markov random field (MRF) as the image a priori model. The MRF is designed for binary shape information and its parameters are adapted based on the information of neighboring blocks. Our experimental results show that the proposed concealment method restores missing shape blocks with high accuracy. Compared to the median filtering method, our method restores 20% more missing shape data, with a much greater subjective improvement. The proposed algorithm requires a relatively small number of integer multiplications and additions and simple logic operations, making it suitable for real-time implementations.

Hidden Markov random field model for segmentation of brain MR image

Abstract: The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain MR images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogram-based model, the FM has an intrinsic limitation -- no spatial information is taken into account. This causes the FM model to work only on well-defined images with low noise level. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a Markov random field whose state sequence cannot be observed directly but which can be observed through observations. Mathematically, it can be shown that the FM model is a degenerate version of the HMRF model. The advantage of the HMRF model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites. To fit the HMRF model, an expectation-maximization (EM) algorithm is used. We show that by incorporating both the HMRF model and the EM algorithm into an HMRF-EM framework, an accurate and robust segmentation can be achieved, which is demonstrated by comparison experiments with the FM model-based segmentation.

Image Segmentation Based on the Integration of Markov Random Fields and Deformable Models

Abstract: This paper proposes a new methodology for image segmentation based on the integration of deformable and Markov Random Field models. Our method makes use of Markov Random Field theory to build a Gibbs Prior model of medical images with arbitrary initial parameters to estimate the boundary of organs with low signal to noise ratio (SNR). Then we use a deformable model to fit the estimated boundary. The result of the deformable model fit is used to update the Gibbs prior model parameters, such as the gradient threshold of a boundary. Based on the updated parameters we restart the Gibbs prior models. By iteratively integrating these processes we achieve an automated segmentation of the initial images. By careful choice of the method used for the Gibbs prior models, and based on the above method of integration with deformable model our segmentation solution runs in close to real time. Results of the method are presented for several examples, including some MRI images with significant amount of noise.

Using circulant symmetry to model featureless objects

Abstract: SUMMARY Grenander & Miller (1994) describe a model for representing amorphous twodimensional objects with no obvious landmark. Each object is represented by n vertices around its perimeter, and is described by deforming an n-sided regular polygon using edge transformations. A multivariate normal distribution with a block circulant covariance matrix is used to model these edge transformations. The purpose of this paper is to describe in detail the statistical properties of this multivariate model and the eigenstructure of the covariance matrix. Various special cases of the model are considered, including articulated models and conditional Markov random field models. We consider maximum likelihood based inference and the model is applied to some datasets to explore shape variability.

Markov Random Field and Fuzzy Logic Modeling in Sonar Imagery

Abstract: This paper proposes an original method for the classification of seafloors from high resolution sidescan sonar images. We aim at classifying the sonar images into five kinds of regions: sand, pebbles, rocks, ripples, and dunes. The proposed method adopts a pattern recognition approach based on the extraction and the analysis of the cast shadows exhibited by each seabottom type. This method consists of three stages of processing. First, the original image is segmented into two kinds of regions: shadow (corresponding to a lack of acoustic reverberation behind each “object” lying on the seabed) and seabottom reverberation. Second, based on the extracted shadows, shape parameter vectors are computed on subimages and classified with a fuzzy classifier. This preliminary classification is finally refined thanks to a Markov random field model which allows to incorporate spatial homogeneity properties one would expect for the final classification map. Experiments on a variety of real high-resolution sonar images are reported.

Probabilistic models for query approximation with large sparse binary data sets

Abstract: Large sparse sets of binary transaction data with millions of records and thousands of attributes occur in various domains: customers purchasing products, users visiting web pages, and documents containing words are just three typical examples. Real-time query selectivity estimation (the problem of estimating the number of rows in the data satisfying a given predicate) is an important practical problem for such databases. We investigate the application of probabilistic models to this problem. In particular, we study a Markov random field (MRF) approach based on frequent sets and maximum entropy, and compare it to the independence model and the Chow-Liu tree model. We find that the MRF model provides substantially more accurate probability estimates than the other methods but is more expensive from a computational and memory viewpoint. To alleviate the computational requirements we show how one can apply bucket elimination and clique tree approaches to take advantage of structure in the models and in the queries. We provide experimental results on two large real-world transaction datasets.

Lagrangian-based methods for finding MAP solutions for MRF models

Abstract: Finding maximum a posteriori (MAP) solutions from noisy images based on a prior Markov random field (MRF) model is a huge computational task. In this paper, we transform the computational problem into an integer linear programming (ILP) problem. We explore the use of Lagrange relaxation (LR) methods for solving the MAP problem. In particular, three different algorithms based on LR are presented. All the methods are competitive alternatives to the commonly used simulation-based algorithms based on Markov Chain Monte Carlo techniques. In all the examples (including both simulated and real images) that have been tested, the best method essentially finds a MAP solution in a small number of iterations. In addition, LR methods provide lower and upper bounds for the posterior, which makes it possible to evaluate the quality of solutions and to construct a stopping criterion for the algorithm. Although additive Gaussian noise models have been applied, any additive noise model fits into the framework.

Roof-edge preserving image smoothing based on MRFs

Abstract: A novel Markov random field (MRF) model is proposed for roof-edge (as well as step-edge) preserving image smoothing. Image surfaces containing roof-edges are represented by piecewise continuous polynomial functions governed by a few parameters. Piecewise smoothness constraint is imposed on these parameters rather than on the surface heights as is in traditional models for step-edges. In this way, roof edges are preserved without the necessity to deal with unstable higher order derivatives.