Iterated Conditional Modes Research Articles

Effective Image Segmentation with Flexible ICM-Based Markov Random Fields in Distributed Systems of Personal Computers

This paper presents the implementation of modified Markov Random Fields (MRFs) in distributed systems of personal computers. Gibbs Random Fields (GRFs) operating in the iterated conditional mode (ICM), modified to incorporate the flexibility of selecting from a continuum of configurations ranging from greater fidelity to the original image to more contextual influence (and enhanced smoothing), are presented, implemented in a distributed system of personal computers, and assessed for image segmentation. The characteristics of the distributed system, the message interchange mechanisms, the strategy for the implementation of the MRF, as well as the statistical characterization of the performance in terms of hardware utilization, bottlenecks and speed-up are presented and discussed. The results indicate that, despite their relative computational complexity, the developed concurrent system presents good potential for allowing MRFs to be executed in real-time for many applications in image processing and computer vision.

Restoration of severely blurred high range images using stochastic and deterministic relaxation algorithms in compound Gauss–Markov random fields

Over the last few years, a growing number of researchers from varied disciplines have been utilizing Markov random fields (MRF) models for developing optimal, robust algorithms for various problems, such as texture analysis, image synthesis, classification and segmentation, surface reconstruction, integration of several low level vision modules, sensor fusion and image restoration. However, no much work has been reported on the use of Simulated Annealing (SA) and Iterative Conditional Mode (ICM) algorithms for maximum a posteriori estimation in image restoration problems when severe blurring is present. In this paper we examine the use of compound Gauss–Markov random fields (CGMRF) to restore severely blurred high range images. For this deblurring problem, the convergence of the SA and ICM algorithms has not been established. We propose two new iterative restoration algorithms which can be considered as extensions of the classical SA and ICM approaches and whose convergence is established. Finally, they are tested on real and synthetic images and the results compared with the restorations obtained by other iterative schemes.

Unsupervised parallel image classification using Markovian models

This paper deals with the problem of unsupervised classification of images modeled by Markov random fields (MRF). If the model parameters are known then we have various methods to solve the segmentation problem (simulated annealing (SA), iterated conditional modes (ICM), etc). However, when the parameters are unknown, the problem becomes more difficult. One has to estimate the hidden label field parameters only from the observed image. Herein, we are interested in parameter estimation methods related to monogrid and hierarchical MRF models. The basic idea is similar to the expectation–maximization (EM) algorithm: we recursively look at the maximum a posteriori (MAP) estimate of the label field given the estimated parameters, then we look at the maximum likelihood (ML) estimate of the parameters given a tentative labeling obtained at the previous step. The only parameter supposed to be known is the number of classes, all the other parameters are estimated. The proposed algorithms have been implemented on a Connection Machine CM200. Comparative experiments have been performed on both noisy synthetic data and real images.

Bayesian detection of the fovea in eye fundus angiographies

This paper is concerned with the automatic detection of the avascular foveal zone (fovea), in eye fundus angiographies. Fluorescein angiography is used in ophthalmic practice to evaluate vascular retinopathies and choroidopathies: sodium fluorescein is injected in the arm's cubital vein of the patient and its distribution along retinal vessels at certain times is observed. The proposed methodology is based on Bayesian statistical methods that allow to incorporate the previous knowledge about the eye fundus in the model. The contour of the fovea is modeled by means of a unidimensional Markov chain and the observed intensities are assumed Gaussian and statistically independent between pixels. Two approximations are used in order to estimate the model's parameters: Empirical and Fully Bayesian. Two algorithms have been used in order to estimate the fovea contour: Simulated Annealing (SA) and Iterated Conditional Modes (ICM). This procedure is applied to different cases of diabetic retinopathy and vein occlusions.

Adaptive detection and localization of moving objects in image sequences

In this paper we address two important problems in motion analysis: the detection of moving objects and their localization. A statistical approach is adopted in order to formulate these problems. For the first, the inter-frame difference is modelized by a mixture of two zero-mean generalized Gaussian distributions, and a Gibbs random field is used for describing the label set. A new method to determine the regularization parameter is proposed, based on a voting technique. This method is also modelized using a statistical framework. The solution of the second problem is based on the observation of only two successive frames. Using the results of change detection an adaptive statistical model for the couple of image intensities is identified. For each problem two different multiscale algorithms are evaluated, and the labeling problem is solved using either iterated conditional modes (ICM) or highest confidence first (HCF) algorithms. For illustrating the efficiency of the proposed approach, experimental results are presented using synthetic and real video sequences.

Mean fields and two-dimensional Markov random fields in image analysis

In this paper we compare two iterative approaches to the problem of pixel-level image restoration when the model contains unknown parameters. Pairwise interaction models are assumed to represent the local associations in the true scene. The first approach is a variation on the EM algorithm in which Mean-field approximations are used in the E-step and a variational approximation is used in the M-step. In the second approach, each iteration involves first restoring the image using the Iterated Conditional Modes (ICM) algorithm and then updating the parameter estimates by maximising the so-called pseudolikelihood. In addition, refinemenrs are made to the Mean-field approximation, and these are also used for restoration. The methods are compared empirically using both artificial and real noise-corrupted binary scenes. Within the comparisons the effects of using different convergence criteria for deciding when to stop the algorithms are also investigated.

Segmentation of MR images with intensity inhomogeneities

A statistical model to segment clinical magnetic resonance (MR) images in the presence of noise and intensity inhomogeneities is proposed. Inhomogeneities are considered to be multiplicative low-frequency variations of intensities that are due to the anomalies of the magnetic fields of the scanners. The measurements are modeled as a Gaussian mixture where inhomogeneities present a bias field in the distributions. The piecewise contiguous nature of the segmentation is modeled by a Markov random field (MRF). A greedy algorithm based on the iterative conditional modes (ICM) algorithm is used to find an optimal segmentation while estimating the model parameters. Results with simulated and hand-segmented images are presented to compare performance of the algorithm with other statistical methods. Segmentation results with MR head scans acquired from four different clinical scanners are presented.

Color Image Segmentation Using Entropy of Fuzziness and Markov Random Field

This paper presents a color image segmentation algorithm using the fuzzy entropy and Markov Random Fields (MRFs). During an iterative clustering, the fuzzy entropy uses the S-function membership and a suitable window-size vector to minimize the ambiguity of the R, G and B conditional histograms. The main 3D cluster is detected. A local processing clusters and labels the definite pixels coarsely, and masks the ambiguous ones. These ambiguous pixels are further assigned and labeled globally to clusters using the membership function of fuzzy_c means (FCM). As some pixels are misclassified, MRF’s use iterated conditional mode (ICM) to refine the segmentation.

Multiresolution Gauss-Markov random field models for texture segmentation

This paper presents multiresolution models for Gauss-Markov random fields (GMRFs) with applications to texture segmentation. Coarser resolution sample fields are obtained by subsampling the sample field at fine resolution. Although the Markov property is lost under such resolution transformation, coarse resolution non-Markov random fields can be effectively approximated by Markov fields. We present two techniques to estimate the GMRF parameters at coarser resolutions from the fine resolution parameters, one by minimizing the Kullback-Leibler distance and another based on local conditional distribution invariance. We also allude to the fact that different GMRF parameters at the fine resolution can result in the same probability measure after subsampling and present the results for first- and second-order cases. We apply this multiresolution model to texture segmentation. Different texture regions in an image are modeled by GMRFs and the associated parameters are assumed to be known. Parameters at lower resolutions are estimated from the fine resolution parameters. The coarsest resolution data is first segmented and the segmentation results are propagated upward to the finer resolution. We use the iterated conditional mode (ICM) minimization at all resolutions. Our experiments with synthetic, Brodatz texture, and real satellite images show that the multiresolution technique results in a better segmentation and requires lesser computation than the single resolution algorithm.

Minimization of MRF Energy with Relaxation Labeling

Recently, there has been increasing interest in Markov random field (MRF) modeling for solving a variety of computer vision problems formulated in terms of the maximum a posteriori (MAP) probability. When the label set is discrete, such as in image segmentation and matching, the minimization is combinatorial. The objective of this paper is twofold: Firstly, we propose to use the continuous relaxation labeling (RL) as an alternative approach for the minimization. The motivation is that it provides a good compromise between the solution quality and the computational cost. We show how the original combinatorial optimization can be converted into a form suitable for continuous RL. Secondly, we compare various minimization algorithms, namely, the RL algorithms proposed by Rosenfeld et al., and by Hummel and Zucker, the mean field annealing of Peterson and Soderberg, simulated annealing of Kirkpatrick, the iterative conditional modes (ICM) of Besag and an annealing version of ICM proposed in this paper. The comparisons are in terms of the minimized energy value (i.e., the solution quality), the required number of iterations (i.e., the computational cost), and also the dependence of each algorithm on heuristics.

Unsupervised vector image segmentation by a tree structure-ICM algorithm

In recent years, many image segmentation approaches have been based on Markov random fields (MRFs). The main assumption of the MRF approaches is that the class parameters are known or can be obtained from training data. In this paper the authors propose a novel method that relaxes this assumption and allows for simultaneous parameter estimation and vector image segmentation. The method is based on a tree structure (TS) algorithm which is combined with Besag's iterated conditional modes (ICM) procedure. The TS algorithm provides a mechanism for choosing initial cluster centers needed for initialization of the ICM. The authors' method has been tested on various one-dimensional (1-D) and multidimensional medical images and shows excellent performance. In this paper the authors also address the problem of cluster validation. They propose a new maximum a posteriori (MAP) criterion for determination of the number of classes and compare its performance to other approaches by computer simulations.

Image enhancement using the modified ICM method

A generalized version of the iterative conditional modes (ICM) method for image enhancement is developed. The proposed algorithm utilizes the characteristic of Markov random fields (MRF) in modeling the contextual information embedded in image formation. To cope with real images, a new local MRF model with a second-order neighborhood is introduced. This model extracts contextual information not only from the intensity levels but also from the relative position of neighboring cliques. Also, an outlier rejection method is presented. In this method, the rejection depends on each candidate's contribution to the local variance. To cope with a mixed noise case, a hypothesis test is implemented as part of the restoration procedure. The proposed algorithm performs signal adaptive, nonlinear, and recursive filtering. In comparing the performance of the new procedure with several well-known order statistic filters, the superiority of the proposed algorithm is demonstrated both in the mean-square-error (MSE) and the mean-absolute-error (MAE) senses. In addition, the new algorithm preserves the details of the images well. It should be noted that the blurring effect is not considered.

Bayesian image classification using Markov random fields

In this paper, we present three optimisation techniques, Deterministic Pseudo-Annealing (DPA), Game Strategy Approach (GSA), and Modified Metropolis Dynamics (MMD), in order to carry out image classification using a Markov random field model. For the first approach (DPA), the a posteriori probability of a tentative labelling is generalised to a continuous labelling. The merit function thus defined has the same maxima under constraints yielding probability vectors. Changing these constraints convexifies the merit function. The algorithm solves this unambiguous maximisation problem, and then tracks down the solution while the original constraints are restored yielding a good, even if suboptimal, solution to the original labelling assignment problem. In the second method (GSA), the maximisation problem of the a posteriori probability of the labelling is solved by an optimisation algorithm based on game theory. A non-cooperative n-person game with pure strategies is designed such that the set of Nash equilibrium points of the game is identical to the set of local maxima of the a posteriori probability of the labelling. The algorithm converges to a Nash equilibrium. The third method (MMD) is a modified version of the Metropolis algorithm: at each iteration the new state is chosen randomly, but the decision to accept it is purely deterministic. This is also a suboptimal technique but it is much faster than stochastic relaxation. These three methods have been implemented on a Connection Machine CM2. Experimental results are compared to those obtained by the Metropolis algorithm, the Gibbs sampler and ICM (Iterated Conditional Mode).

NOTE: Blind Restoration of Degraded Binary Markov Random Field Images

The problem of restoring binary images degraded by region-dependent flip-flap noises is considered. The real image is described by a Markov random field (MRF). The iterative conditional modes (ICM) algorithm is adopted. It is shown that under certain conditions the ICM algorithm is insensitive to either the MRF model or the noise parameters. Using this property, we propose a blind restoration algorithm that has the following two basic properties: (a) it does not require full knowledge about the model and noise parameters; (b) it can be fully implemented in parallel. To show the effectiveness of the algorithm, simulation results are presented on the applications of the algorithm to degraded hand-drawn and synthetic images.

Artifact reduction in low bit rate DCT-based image compression

This correspondence presents a scheme for artifact reduction of low bit rate discrete-cosine-transform-compressed (DCT-compressed) images. First, the DC coefficients are calibrated using gradient continuity constraints. Then, an improved Huber-Markov-random-field-based (HMRF-based) smoothing is applied. The constrained optimization is implemented by the iterative conditional mode (ICM). Final reconstructions of typical images with improvements in both visual quality and peak signal-to-noise ratio (PSNR) are also shown.

A study of simulated annealing and a revised cascade algorithm for image reconstruction

We describe an image reconstruction problem and the computational difficulties arising in determining the maximum a posteriori (MAP) estimate. Two algorithms for tackling the problem, iterated conditional modes (ICM) and simulated annealing, are usually applied pixel by pixel. The performance of this strategy can be poor, particularly for heavily degraded images, and as a potential improvement Jubb and Jennison (1991) suggest the cascade algorithm in which ICM is initially applied to coarser images formed by blocking squares of pixels. In this paper we attempt to resolve certain criticisms of cascade and present a version of the algorithm extended in definition and implementation. As an illustration we apply our new method to a synthetic aperture radar (SAR) image. We also carry out a study of simulated annealing, with and without cascade, applied to a more tractable minimization problem from which we gain insight into the properties of cascade algorithms.

A Markovian model for contour grouping

Classical methods of contour extraction do not always allow the detection of all the contours. For instance, the contours obtained by a Canny-Deriche filter have some gaps, especially at corners or at T-junctions. In this paper, we present an algorithm which restores incomplete contours. We model the image by a Markov Random Field. In order to complete the contours, several criteria are defined and introduced in an energy function, which has to be optimized. The deterministic ICM (“Iterated Conditional Mode”) relaxation algorithm is implemented to minimize this energy function. The result is a contour image consisting of closed contours. This method has been tested on different images which present different types of difficulties [indoors, outdoors, satellite (SPOT), industrial and medical images].

The application of mean field theory to image motion estimation

Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates.

Maximum-likelihood parameter estimation for unsupervised stochastic model-based image segmentation

An unsupervised stochastic model-based approach to image segmentation is described, and some of its properties investigated. In this approach, the problem of model parameter estimation is formulated as a problem of parameter estimation from incomplete data, and the expectation-maximization (EM) algorithm is used to determine a maximum-likelihood (ML) estimate. Previously, the use of the EM algorithm in this application has encountered difficulties since an analytical expression for the conditional expectations required in the EM procedure is generally unavailable, except for the simplest models. In this paper, two solutions are proposed to solve this problem: a Monte Carlo scheme and a scheme related to Besag's (1986) iterated conditional mode (ICM) method. Both schemes make use of Markov random-field modeling assumptions. Examples are provided to illustrate the implementation of the EM algorithm for several general classes of image models. Experimental results on both synthetic and real images are provided.

Unsupervised image segmentation using an unlabeled region process

The segmentation of a gray scale image of regions of uniform or slowly varying intensity is discussed. A Gibbsian representation is given for a partition of a lattice with no labels. The homogeneity of each segment is measured by the sample variance of observations. In a region merging algorithm, the posterior probability of the segmentation is gradually increased. It is shown how to simulate partitions with the Gibbs sampler and how to combine information in simulated segmentations. When the segments cannot be grouped into genuine classes, the segmentation methods are preferable to classification by Iterated Conditional Modes (ICM) or by the Maximizer of Posterior Marginals (MPM).