Iterated Conditional Modes Research Articles

A Multiresolution Approach Based on MRF and Bak–Sneppen Models for Image Segmentation

The two major Markov Random Fields (MRF) based algorithms for image segmentation are the Simulated Annealing (SA) and Iterated Conditional Modes (ICM). In practice, compared to the SA, the ICM provides reasonable segmentation and shows robust behavior in most of the cases. However, the ICM strongly depends on the initialization phase. In this paper, we combine Bak-Sneppen model and Markov Random Fields to define a new image segmentation approach. We introduce a multiresolution technique in order to speed up the segmentation process and to improve the restoration process. Image pixels are viewed as lattice species of Bak-Sneppen model. The a-posteriori probability corresponds to a local fitness. At each cycle, some objectionable species are chosen for a random change in their fitness values. Furthermore, the change in the fitness of each species engenders fitness changes for its neighboring species. After a certain number of iteration, the system converges to a Maximum A Posteriori estimate. In this multireolution approach, we use a wavelet transform to reduce the size of the system.

Effectiveness of neuro-fuzzy recognition approach in evaluating steel bridge paint conditions

The development of digital image recognition techniques has contributed to increased precision in pattern recognition and led to numerous applications in industries. In September 1999, the Indiana Department of Transportation (INDOT) first tried out digital image recognition techniques to steel bridge coating assessment. The purpose of this tryout was to obtain a rust percentage, which was required in the INDOT bridge painting warranty contract, when conducting steel bridge coating investigation. Despite the advantages of digital image recognition, some problems that may cause inaccurate recognition results still exist. Nonuniform illumination (i.e., brightness or darkness or shadow) is one of them. The neuro-fuzzy recognition approach (NFRA) was developed to minimize the effect of nonuniform illumination. In this technical note, the framework of NFRA, its application to steel bridge coating assessment, and its performance comparison to three other image recognition methods will be presented.Key words: neuro-fuzzy recognition approach (NFRA), artificial neural network (ANN), double sampling plan, multiresolution pattern classification (MPC), iterated conditional modes (ICM).

Initialization of Markov random field clustering of large remote sensing images

Markov random field (MRF) clustering, utilizing both spectral and spatial interpixel dependency information, often improves classification accuracy for remote sensing images, such as multichannel polarimetric synthetic aperture radar (SAR) images. However, it is heavily sensitive to initial conditions such as the choice of the number of clusters and their parameters. In this paper, an initialization scheme for MRF clustering approaches is suggested for remote sensing images. The proposed method derives suitable initial cluster parameters from a set of homogeneous regions, and estimates the number of clusters using the pseudolikelihood information criterion (PLIC). The method works best for an image consisting of many large homogeneous regions, such as agricultural crops areas. It is illustrated using a well-known polarimetric SAR image of Flevoland in the Netherlands. The experiment shows a superior performance compared to several other methods, such as fuzzy C-means and iterated conditional modes (ICM) clustering.

A comparative study of markovian and variational image-matching techniques in application to mammograms

In this paper, we focus our interest on the image-matching problem. This major problem in Image Processing has received a considerable attention in the last decade. However, contrarily to other image-processing problems such as image restoration, the image-matching problem have been mainly tackled using a single approach based on variational principles. In this paper, our motivation is to investigate the feasibility of another famous image-processing approach based on Markov random fields (MRF). For that, we propose a discrete and stochastic image-matching framework which is equivalent to an usual variational one and suitable for an MRF-based approach. In this framework, we describe multigrid implementations of two algorithms: an iterated conditional modes (ICM) and a simulated annealing. We apply these algorithms for the registration of mammograms and compare their performances to those of an usual variational algorithm. We come to the conclusion that MRF-based techniques are optimization techniques which are relevant for the mammogram application. We also point out some of their specific properties and mention interesting perspectives offered by the markovian approach.

Optimisation of spatial allocation of forestry activities within a forest stand

Forest management planning usually takes place at the stand, enterprise or regional level. To maintain and conserve forest ecological processes, management operations should be transformed to an individual tree scale. This paper describes a method for supporting decision making at the level of individual trees following an approach based on close-to-nature forestry. An iterated conditional mode algorithm, as a relaxation of simulated annealing optimisation, was used to find an optimal solution. Using the principles of close-to-nature silviculture, a value function assigns management actions at the tree level. The reference conditions for optimisation are the decision-maker's preferences. The method was applied to an uneven-aged stand of Pinus sylvestris in the Guadarrama Mountains of Madrid (Spain) to find an optimal combination of individual trees to be harvested. An energy function is used to find an economic maximum for the remaining trees in the stand, in terms of the amount of low and high-quality timber to be harvested using the constraints: forest cover, biodiversity and regeneration. The optimal solution achieved an increased value for the stand of €321.32/ha (€96,396 for the 300 ha forest), while the residual diameter distribution favoured ecosystem services and regeneration. Even though this type of model is adaptable to a variety of decision-maker preferences and optimisation constraints, its data requirements limit application to small, intensively managed properties.

A bayesian approach to classification of multiresolution remote sensing data

Several earth observation satellites acquire image bands with different spatial resolutions, e.g., a panchromatic band with high resolution and spectral bands with lower resolution. Likewise, we often face the problem of different resolutions when performing joint analysis of images acquired by different satellites. This work presents models and methods for classification of multiresolution images. The approach is based on the concept of a reference resolution, corresponding to the highest resolution in the dataset. Prior knowledge about the spatial characteristics of the classes is specified through a Markov random field model at the reference resolution. Data at coarser scales are modeled as mixed pixels by relating the observations to the classes at the reference resolution. A Bayesian framework for classification based on this multiscale model is proposed. The classification is realized by an iterative conditional modes (ICM) algorithm. The parameter estimation can be based both on a training set and on pixels with unknown class. A computationally efficient scheme based on a combination of the ICM and the expectation-maximization algorithm is proposed. Results obtained on simulated and real satellite images are presented.

Evolutionary Optimization With Markov Random Field Prior

This work discusses an evolutionary algorithm in which the constituent variables of a solution are modeled by a Markov random field (MRF). We maintain a population of potential solutions at every generation and for each solution a fitness value is calculated. The evolution, however, is not achieved through genetic recombination. Instead, each variable in a solution will be updated by sampling from its probability distribution. According to the MRF prior, local exploitation is encoded in the conditional probabilities. For evolutionary exploration, we estimate the probabilities as fitness-weighted statistics. These two kinds of search are combined smoothly in our algorithm. We compare it with two representative algorithms [iterated conditional modes (ICM) and simulated annealing (SA)] on noisy and textured image segmentation. Remarkable performance is observed.

Automatic detection of change direction of multi-temporal ERS-2 SAR images using two-threshold EM and MRF algorithms

An algorithm of two-threshold expectation maximum (EM) and Markov random field (MRF) is developed to detect the change in direction in urban surfaces from multitemporal synthetic aperture radar (SAR) images. The difference in the SAR images demonstrates a variation in backscattering caused by the surface change over all image pixels. Two thresholds are derived by the EM iterative process and are applied to change the direction of three classes: enhanced scattering, reduced scattering and unchanged regimes. Initializing from the EM result, the iterated conditional modes (ICM) algorithm of the MRF is then applied to analyse the detection of contexture change in the urban area. As an example, two images of ERS-2 SAR in 1996 and 2002 over Shanghai City are studied.

Nonlinear sinogram smoothing for low-dose X-ray CT

When excessive quantum noise is present in extremely low dose X-ray CT imaging, statistical properties of the data has to be considered to achieve a satisfactory image reconstruction. Statistical iterative reconstruction with accurate modeling of the noise, rather than a filtered back-projection (FBP) with low-pass filtering, is one way to deal with the problem. Estimating a noise-free sinogram to satisfy the FBP reconstruction for the Radon transform is another way. The benefits of the latter include a higher computation efficiency, more uniform spatial resolution in the reconstructed image, and less modification of the current machine configurations. In a clinic X-ray CT system, the acquired raw data must be calibrated, in addition to the logarithmic transform, to achieve the high diagnostic image quality. The calibrated projection data or sinogram no longer follow a compound Poisson distribution in general, but are close to a Gaussian distribution with signal-dependent variance. In this paper, we first investigated a relatively accurate statistical model for the sinogram data, based on several phantom experiments. Then we developed a penalized likelihood method to smooth the sinogram, which led to a set of nonlinear equations that can be solved by iterated conditional mode (ICM) algorithm within a reasonable computing time. The method was applied to several experimental datasets acquired at 120 kVp, 10 mA/20 mA/50 mA protocols with a GE HiSpeed multi-slice detector CT scanner and demonstrated a significant noise suppression without noticeable sacrifice of the spatial resolution.

Contextual classification of Landsat TM images to forest inventory cover types

In the context of Landsat TM images forest stands are a cluster of homogeneous pixels. Contextual classification of forest cover types exploits relationships between neighbouring pixels in the pursuit of an increase in classification accuracy. Results with six contextual classifiers from two sites in Canada were compared to results with a maximum likelihood (ML) classifier. The comparisons were done at three levels of spectral class separation. Training and validation data were obtained from single-stage cluster sampling of 2 km×2 km primary sampling units (PSU) located on a 20 km×20 km grid. A strong relationship between contextual and ML classification accuracy was explored with logistic regression analysis. Effects of contextual classification were predicted for given levels of ML accuracy. Estimates of the spatial autocorrelation of reflectance values within a PSU were deemed consistent with a first-order autoregressive process. Iterative Conditional Modes (ICM) was the best contextual method; it improved the overall accuracy by four to six percentage points (statistically significant) when ML accuracy was between 50% and 80%. A relaxed ICM and a smoothing algorithm were second and third best. Contextual classification is most promising when an ML accuracy is around 70%. ICM results were sensitive to the level of spatial autocorrelation of ML classification errors and to the homogeneity of a PSU.

Automatic analysis of change detection of multi-temporal ERS-2 SAR images by using two-threshold EM and MRF algorithms*

Abstract To automatically detect and analyze the surface change in the urban area from multi-temporal SAR images, an algorithm of two-threshold expectation maximum (EM) and Markov random field (MRF) is developed. Difference of the SAR images demonstrates variation of backscattering caused by the surface change all over the image pixels. Two thresholds are obtained by the EM iterative process and categorized to three classes: enhanced scattering, reduced scattering and unchanged regimes. Initializing from the EM result, the iterated conditional modes (ICM) algorithm of the MRF is then used to analyze the detection of contexture change in the urban area. As an example, two images of the ERS-2 SAR in 1996 and 2002 over the Shanghai City are studied.

MRF model and FRAME model-based unsupervised image segmentation

This paper presents a method for unsupervised segmentation of images consisting of multiple textures. The images under study are modeled by a proposed hierarchical random field model, which has two layers. The first layer is modeled as a Markov Random Field (MRF) representing an unobservable region image and the second layer uses “Filters, Random and Maximum Entropy (Abb. FRAME)” model to represent multiple textures which cover each region. Compared with the traditional Hierarchical Markov Random Field (HMRF), the FRAME can use a bigger neighborhood system and model more complex patterns. The segmentation problem is formulated as Maximum a Posteriori (MAP) estimation according to the Bayesian rule. The iterated conditional modes (ICM) algorithm is carried out to find the solution of the MAP estimation. An algorithm based on the local entropy rate is proposed to simplify the estimation of the parameters of MRF. The parameters of FRAME are estimated by the Expectation-Maximum (EM) algorithm. Finally, an experiment with synthesized and real images is given, which shows that the method can segment images with complex textures efficiently and is robust to noise.

Pseudo-optical flow estimation for medical image sequence

In this paper, a statistical method is used to accomplish pseudo-optical flow estimation of medical image sequence. The optical flow field are modelled by a two-dimensional Gibbs random field (GRF). An estimation algorithm. based on the statistical model, approximately can find the maximum a posteriori (MAP) estimation of the optical flow field. The algorithm utilized for estimation is based on the iterative conditional modes (ICM) algorithm, which converges to the solution that maximizes the local conditional probabilities. Application of the algorithm can greatly reduce the inter-frame redundancies. thus faciliates the medical image compression.

Automatic land cover analysis for Tenerife by supervised classification using remotely sensed data

Automatic land cover classification from satellite images is an important topic in many remote sensing applications. In this paper, we consider three different statistical approaches to tackle this problem: two of them, namely the well-known maximum likelihood classification (ML) and the support vector machine (SVM), are noncontextual methods. The third one, iterated conditional modes (ICM), exploits spatial context by using a Markov random field. We apply these methods to Landsat 5 Thematic Mapper (TM) data from Tenerife, the largest of the Canary Islands. Due to the size and the strong relief of the island, ground truth data could be collected only sparsely by examination of test areas for previously defined land cover classes. We show that after application of an unsupervised clustering method to identify subclasses, all classification algorithms give satisfactory results (with statistical overall accuracy of about 90%) if the model parameters are selected appropriately. Although being superior to ML theoretically, both SVM and ICM have to be used carefully: ICM is able to improve ML, but when applied for too many iterations, spatially small sample areas are smoothed away, leading to statistically slightly worse classification results. SVM yields better statistical results than ML, but when investigated visually, the classification result is not completely satisfying. This is due to the fact that no a priori information on the frequency of occurrence of a class was used in this context, which helps ML to limit the unlikely classes.

Artificial intelligence application to bridge painting assessment

Digital image recognition has been experimented for steel bridge painting assessment by the Indiana Department of Transportation (INDOT) in September 1999. Although the application was successfully carried out as a whole, there are still some minor problems left to be improved. Nonuniform illumination is one of the problems that affect the accuracy of recognition results. To address this problem, the neuro-fuzzy recognition approach (NFRA) is proposed, which segments an image into three areas based on illumination and conducts area-based thresholding with the help of an artificial neural network (ANN) and a fuzzy adjustment system. In this paper, the framework of NFRA will be presented, followed by the application of NFRA to steel bridge painting assessment and its performance comparison with the multiresolution pattern classification (MPC) method and the iterated conditional modes (ICM) algorithm. The conclusions will be presented last.

A peak preserving algorithm for the removal of colored noise from signals

We employ the simulated annealing method in order to restore signals that may contain peaks we wish to preserve but, otherwise, are smooth and buried in colored noise. The problem is formulated as a global optimization one. We propose a piecewise linear model for the noise-free signal that is appropriate for preserving peaks that are often encountered in biomedical or industrial signals. An iterative algorithm is proposed. The restored signal is used to estimate the model parameters that are subsequently used to improve the signal estimation. The algorithm stops when self-consistency has been achieved, i.e., the estimated values of the noise model parameters agree to within the accuracy of their estimation with the parameters used to restore the signal. Application of the method to simulated data with various levels of noise showed that the underlying signal can be restored sufficiently well. The algorithm is also applied to some evoked-response magneto-encephalographic data, as well as to some signals from an automatic industrial inspection problem. Our results are compared with those obtained by using the iterative conditional modes algorithm and shown to be better in terms of preserving the peaks in the signals.

The ZπM algorithm: a method for interferometric image reconstruction in SAR/SAS

This paper presents an effective algorithm for absolute phase (not simply modulo-2-pi) estimation from incomplete, noisy and modulo-2pi observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical interferometry, magnetic resonance imaging and diffraction tomography. The Bayesian viewpoint is adopted; the observation density is 2-pi-periodic and accounts for the interferometric pair decorrelation and system noise; the a priori probability of the absolute phase is modeled by a compound Gauss-Markov random field (CGMRF) tailored to piecewise smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) absolute phase estimate. Each iteration embodies a discrete optimization step (Z-step), implemented by network programming techniques and an iterative conditional modes (ICM) step (pi-step). Accordingly, the algorithm is termed ZpiM, where the letter M stands for maximization. An important contribution of the paper is the simultaneous implementation of phase unwrapping (inference of the 2pi-multiples) and smoothing (denoising of the observations). This improves considerably the accuracy of the absolute phase estimates compared to methods in which the data is low-pass filtered prior to unwrapping. A set of experimental results, comparing the proposed algorithm with alternative methods, illustrates the effectiveness of our approach.

Multisource classification using ICM and Dempster-Shafer theory

We propose to use evidential reasoning in order to relax Bayesian decisions given by a Markovian classification algorithm, the multiscale iterated conditional mode (ICM) algorithm. The Dempster-Shafer rule of combination enables us to fuse decisions in a local spatial neighborhood which we further extend to be multisource. This approach enables us to more directly fuse information. Application to the classification of very noisy images produces interesting results.

Bayesian Smoothing and Regression Splines for Measurement Error Problems

In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely difficult, the problem being related to deconvolution. Various frequentist approaches exist for this problem, but to date there has been no Bayesian treatment. In this article we describe Bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error. The regression function is modeled with smoothing splines and regression P-splines. Two methods are described for exploration of the posterior. The first, called the iterative conditional modes (ICM), is only partially Bayesian. ICM uses a componentwise maximization routine to find the mode of the posterior. It also serves to create starting values for the second method, which is fully Bayesian and uses Markov chain Monte Carlo (MCMC) techniques to generate observations from the joint posterior distribution. Use of the MCMC approach has the advantage that interval estimates that directly model and adjust for the measurement error are easily calculated. We provide simulations with several nonlinear regression functions and provide an illustrative example. Our simulations indicate that the frequentist mean squared error properties of the fully Bayesian method are better than those of ICM and also of previously proposed frequentist methods, at least in the examples that we have studied.

Contextual clustering for analysis of functional MRI data.

We present a contextual clustering procedure for statistical parametric maps (SPM) calculated from time varying three-dimensional images. The algorithm can be used for the detection of neural activations from functional magnetic resonance images (fMRI). An important characteristic of SPM is that the intensity distribution of background (nonactive area) is known whereas the distributions of activation areas are not. The developed contextual clustering algorithm divides an SPM into background and activation areas so that the probability of detecting false activations by chance is controlled, i.e., hypothesis testing is performed. Unlike the much used voxel-by-voxel testing, neighborhood information is utilized, an important difference. This is achieved by using a Markov random field prior and iterated conditional modes (ICM) algorithm. However, unlike in the conventional use of ICM algorithm, the classification is based only on the distribution of background. The results from our simulations and human fMRI experiments using visual stimulation demonstrate that a better sensitivity is achieved with a given specificity in comparison to the voxel-by-voxel thresholding technique. The algorithm is computationally efficient and can be used to detect and delineate objects from a noisy background in other applications.