Showing papers on "Markov random field published in 2001"

Markov Random Field Modeling in Image Analysis

Abstract: Markov random field (MRF) theory provides a basis for modeling contextual constraints in visual processing and interpretation. It enables systematic development of optimal vision algorithms when used with optimization principles. This detailed and thoroughly enhanced third edition presents a comprehensive study / reference to theories, methodologies and recent developments in solving computer vision problems based on MRFs, statistics and optimisation. It treats various problems in low- and high-level computational vision in a systematic and unified way within the MAP-MRF framework. Among the main issues covered are: how to use MRFs to encode contextual constraints that are indispensable to image understanding; how to derive the objective function for the optimal solution to a problem; and how to design computational algorithms for finding an optimal solution. Easy-to-follow and coherent, the revised edition is accessible, includes the most recent advances, and has new and expanded sections on such topics as: Discriminative Random Fields (DRF) Strong Random Fields (SRF) Spatial-Temporal Models Total Variation Models Learning MRF for Classification (motivation + DRF) Relation to Graphic Models Graph Cuts Belief Propagation Features: Focuses on the application of Markov random fields to computer vision problems, such as image restoration and edge detection in the low-level domain, and object matching and recognition in the high-level domain Presents various vision models in a unified framework, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation Uses a variety of examples to illustrate how to convert a specific vision problem involving uncertainties and constraints into essentially an optimization problem under the MRF setting Introduces readers to the basic concepts, important models and various special classes of MRFs on the regular image lattice and MRFs on relational graphs derived from images Examines the problems of parameter estimation and function optimization Includes an extensive list of references This broad-ranging and comprehensive volume is an excellent reference for researchers working in computer vision, image processing, statistical pattern recognition and applications of MRFs. It has been class-tested and is suitable as a textbook for advanced courses relating to these areas.

Classification Methods for Remotely Sensed Data

Abstract: Preface to the Second Edition Preface to the First Edition Author Biographies Chapter 1: Remote Sensing in the Optical and Microwave Regions 1.1 Introduction to Remote Sensing 1.1.1 Atmospheric Interactions 1.1.2 Surface Material Reflectance 1.1.3 Spatial and Radiometric Resolution 1.2 Optical Remote Sensing Systems 1.3 Atmospheric Correction 1.3.1 Dark Object Subtraction 1.3.2 Modeling Techniques 1.3.2.1 Modeling the Atmospheric Effect 1.3.2.2 Steps in Atmospheric Correction 1.4 Correction for Topographic Effects 1.5 Remote Sensing in the Microwave Region 1.6 Radar Fundamentals 1.6.1 SLAR Image Resolution 1.6.2 Geometric Effects on Radar Images 1.6.3 Factors Affecting Radar Backscatter 1.6.3.1 Surface Roughness 1.6.3.2 Surface Conductivity 1.6.3.3 Parameters of the Radar Equation 1.7 Imaging Radar Polarimetry 1.7.1 Radar Polarization State 1.7.2 Polarization Synthesis 1.7.3 Polarization Signatures 1.8 Radar Speckle Suppression 1.8.1 Multilook Processing 1.8.2 Filters for Speckle Suppression Chapter 2: Pattern Recognition Principles 2.1 Feature Space Manipulation 2.1.1 Tasseled Cap Transform 2.1.2 Principal Components Analysis 2.1.3 Minimum/Maximum Autocorrelation Factors (MAF) 2.1.4 Maximum Noise Fraction Transformation 2.2 Feature Selection 2.3 Fundamental Pattern Recognition Techniques 2.3.1 Unsupervised Methods 2.3.1.1 The k-means Algorithm 2.3.1.2 Fuzzy Clustering 2.3.2 Supervised Methods 2.3.2.1 Parallelepiped Method 2.3.2.2 Minimum Distance Classifier 2.3.2.3 Maximum Likelihood Classifier 2.4 Combining Classifiers 2.5 Incorporation of Ancillary Information 2.5.1 Use of Texture and Context 2.5.2 Using Ancillary Multisource Data 2.6 Sampling Scheme and Sample Size 2.6.1 Sampling Scheme 2.6.2 Sample Size, Scale, and Spatial Variability 2.6.3 Adequacy of Training Data 2.7 Estimation of Classification Accuracy Epilogue Chapter 3: Artificial Neural Networks 3.1 Multilayer Perceptron 3.1.1 Back-Propagation 3.1.2 Parameter Choice, Network Architecture, and Input/Output Coding 3.1.3 Decision Boundaries in Feature Space 3.1.4 Overtraining and Network Pruning 3.2 Kohonen's Self-Organizing Feature Map 3.2.1 SOM Network Construction and Training 3.2.1.1 Unsupervised Training 3.2.1.2 Supervised Training 3.2.2 Examples of Self-Organization 3.3 Counter-Propagation Networks 3.3.1 Counter-Propagation Network Training 3.3.2 Training Issues 3.4 Hopfield Networks 3.4.1 Hopfield Network Structure 3.4.2 Hopfield Network Dynamics 3.4.3 Network Convergence 3.4.4 Issues Relating to Hopfield Networks 3.4.5 Energy and Weight Coding: An Example 3.5 Adaptive Resonance Theory (ART) 3.5.1 Fundamentals of the ART Model 3.5.2 Choice of Parameters 3.5.3 Fuzzy ARTMAP 3.6 Neural Networks in Remote Sensing Image Classification 3.6.1 An Overview 3.6.2 A Comparative Study Chapter 4: Support Vector Machines 4.1 Linear Classification 4.1.1 The Separable Case4.1.2 The Nonseparable Case 4.2 Nonlinear Classification and Kernel Functions 4.2.1 Nonlinear SVMs 4.2.2 Kernel Functions 4.3 Parameter Determination 4.3.1 t-fold Cross-Validations 4.3.2 Bound on Leave-One-Out Error 4.3.3 Grid Search 4.3.4 Gradient Descent Method 4.4 Multiclass Classification 4.4.1 One-against-One, One-against-Others, and DAG 4.4.2 Multiclass SVMs 4.4.2.1 Vapnik's Approach 4.4.2.2 Methodology of Crammer and Singer 4.5 Feature Selection 4.6 SVM Classification of Remotely Sensed Data 4.7 Concluding Remarks Chapter 5: Methods Based on Fuzzy Set Theory 5.1 Introduction to Fuzzy Set Theory 5.1.1 Fuzzy Sets: Definition 5.1.2 Fuzzy Set Operations 5.2 Fuzzy C-Means Clustering Algorithm 5.3 Fuzzy Maximum Likelihood Classification 5.4 Fuzzy Rule Base 5.4.1 Fuzzification 5.4.2 Inference 5.4.3 Defuzzification 5.5 Image Classification Using Fuzzy Rules 5.5.1 Introductory Methodology 5.5.2 Experimental Results Chapter 6: Decision Trees 6.1 Feature Selection Measures for Tree Induction 6.1.1 Information Gain 6.1.2 Gini Impurity Index 6.2 ID3, C4.5, and SEE5.0 Decision Trees 6.2.1 ID3 6.2.2 C4.5 6.2.3 SEE5.0 6.3 CHAID 6.4 CART 6.5 QUEST 6.5.1 Split Point Selection 6.5.2 Attribute Selection 6.6 Tree Induction from Artificial Neural Networks 6.7 Pruning Decision Trees 6.7.1 Reduced Error Pruning (REP) 6.7.2 Pessimistic Error Pruning (PEP) 6.7.3 Error-Based Pruning (EBP) 6.7.4 Cost Complexity Pruning (CCP) 6.7.5 Minimal Error Pruning (MEP) 6.8 Boosting and Random Forest 6.8.1 Boosting 6.8.2 Random Forest 6.9 Decision Trees in Remotely Sensed Data Classification 6.10 Concluding Remarks Chapter 7: Texture Quantization 7.1 Fractal Dimensions 7.1.1 Introduction to Fractals 7.1.2 Estimation of the Fractal Dimension 7.1.2.1 Fractal Brownian Motion (FBM) 7.1.2.2 Box-Counting Methods and Multifractal Dimension 7.2 Frequency Domain Filtering 7.2.1 Fourier Power Spectrum 7.2.2 Wavelet Transform 7.3 Gray-Level Co-occurrence Matrix (GLCM) 7.3.1 Introduction to the GLCM 7.3.2 Texture Features Derived from the GLCM 7.4 Multiplicative Autoregressive Random Fields 7.4.1 MAR Model: Definition 7.4.2 Estimation of the Parameters of the MAR Model 7.5 The Semivariogram and Window Size Determination 7.6 Experimental Analysis 7.6.1 Test Image Generation 7.6.2 Choice of Texture Features 7.6.2.1 Multifractal Dimension 7.6.2.2 Fourier Power Spectrum 7.6.2.3 Wavelet Transform 7.6.2.4 Gray-Level Co-occurrence Matrix 7.6.2.5 Multiplicative Autoregressive Random Field 7.6.3 Segmentation Results 7.6.4 Texture Measure of Remote Sensing Patterns Chapter 8: Modeling Context Using Markov Random Fields 8.1 Markov Random Fields and Gibbs Random Fields 8.1.1 Markov Random Fields 8.1.2 Gibbs Random Fields 8.1.3 MRF-GRF Equivalence 8.1.4 Simplified Form of MRF 8.1.5 Generation of Texture Patterns Using MRF 8.2 Posterior Energy for Image Classification 8.3 Parameter Estimation 8.3.1 Least Squares Fit Method 8.3.2 Results of Parameter Estimations 8.4 MAP-MRF Classification Algorithms 8.4.1 Iterated Conditional Modes 8.4.2 Simulated Annealing 8.4.3 Maximizer of Posterior Marginals 8.5 Experimental Results Chapter 9: Multisource Classification 9.1 Image Fusion 9.1.1 Image Fusion Methods 9.1.2 Assessment of Fused Image Quality in the Spectral Domain 9.1.3 Performance Overview of Fusion Methods 9.2 Multisource Classification Using the Stacked-Vector Method 9.3 The Extension of Bayesian Classification Theory 9.3.1 An Overview 9.3.1.1 Feature Extraction 9.3.1.2 Probability or Evidence Generation 9.3.1.3 Multisource Consensus 9.3.2 Bayesian Multisource Classification Mechanism 9.3.3 A Refined Multisource Bayesian Model 9.3.4 Multisource Classification Using the Markov Random Field 9.3.5 Assumption of Intersource Independence 9.4 Evidential Reasoning 9.4.1 Concept Development 9.4.2 Belief Function and Belief Interval 9.4.3 Evidence Combination 9.4.4 Decision Rules for Evidential Reasoning 9.5 Dealing with Source Reliability 9.5.1 Using Classification Accuracy 9.5.2 Use of Class Separability 9.5.3 Data Information Class Correspondence Matrix 9.5.4 The Genetic Algorithm 9.6 Experimental Results Bibliography Index

Automated segmentation of multiple sclerosis lesions by model outlier detection

Abstract: This paper presents a fully automated algorithm for segmentation of multiple sclerosis (MS) lesions from multispectral magnetic resonance (MR) images. The method performs intensity-based tissue classification using a stochastic model for normal brain images and simultaneously detects MS lesions as outliers that are not well explained by the model. It corrects for MR field inhomogeneities, estimates tissue-specific intensity models from the data itself, and incorporates contextual information in the classification using a Markov random field. The results of the automated method are compared with lesion delineations by human experts, showing a high total lesion load correlation. When the degree of spatial correspondence between segmentations is taken into account, considerable disagreement is found, both between expect segmentations, and between expert and automatic measurements.

Bayesian inference for generalized additive mixed models based on Markov random field priors

Abstract: Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo (MCMC) simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as usual covariates with fixed effects, metrical covariates with nonlinear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates are all treated within the same general framework by assigning appropriate priors with different forms and degrees of smoothness. The approach is particularly appropriate for discrete and other fundamentally non-Gaussian responses, where Gibbs sampling techniques developed for Gaussian models cannot be applied, but it also works well for Gaussian responses. We use the close relation between nonparametric regression and dynamic or state space models to develop posterior sampling procedures, based on Markov random field priors. They include recent Metropolis-Hastings block move algorithms for dynamic generalized linear models and extensions for spatial covariates as building blocks. We illustrate the approach with a number of applications that arose out of consulting cases, showing that the methods are computionally feasible also in problems with many covariates and large data sets.

An efficient algorithm for image segmentation, Markov random fields and related problems

Abstract: Problems of statistical inference involve the adjustment of sample observations so they fit some a priori rank requirements, or order constraints. In such problems, the objective is to minimize the deviation cost function that depends on the distance between the observed value and the modify value. In Markov random field problems, there is also a pairwise relationship between the objects. The objective in Markov random field problem is to minimize the sum of the deviation cost function and a penalty function that grows with the distance between the values of related pairs---separation function.We discuss Markov random fields problems in the context of a representative application---the image segmentation problem. In this problem, the goal is to modify color shades assigned to pixels of an image so that the penalty function consisting of one term due to the deviation from the initial color shade and a second term that penalizes differences in assigned values to neighboring pixels is minimized. We present here an algorithm that solves the problem in polynomial time when the deviation function is convex and separation function is linear; and in strongly polynomial time when the deviation cost function is linear, quadratic or piecewise linear convex with few pieces (where “few” means a number exponential in a polynomial function of the number of variables and constraints). The complexity of the algorithm for a problem on n pixels or variables, m adjacency relations or constraints, and range of variable values (colors) U, is O(T(n,m) + n log U) where T(n,m) is the complexity of solving the minimum s, t cut problem on a graph with n nodes and m arcs. Furthermore, other algorithms are shown to solve the problem with convex deviation and convex separation in running time O(mn log n log nU) and the problem with nonconvex deviation and convex separation in running time O(T(nU, mU). The nonconvex separation problem is NP-hard even for fixed value of U.For the family of problems with convex deviation functions and linear separation function, the algorithm described here runs in polynomial time which is demonstrated to be fastest possible.

Video segmentation by MAP labeling of watershed segments

Abstract: This paper addresses the problem of spatio-temporal segmentation of video sequences. An initial intensity segmentation method (watershed segmentation) provides a number of initial segments which are subsequently labeled, with a known number of labels, according to motion information. The label field is modeled as a Markov random field where the statistical spatial and and temporal interactions are expressed on the basis of the initial watershed segments. The labeling criterion is the maximization of the conditional a posteriori probability of the label field given the motion hypotheses, the estimate of the label field of the previous frame, and the image intensities. For the optimization, an iterative motion estimation-labeling algorithm is proposed and experimental results are presented.

Endocardial Boundary E timation and Tracking in Echocardiographic Images using Deformable Template and Markov Random Fields

Abstract: We present a new approach to shape-based segmentation and tracking of deformable anatomical structures in medical images, and validate this approach by detecting and tracking the endocardial contour in an echocardiographic image sequence. To this end, some global prior shape knowledge of the endocardial boundary is captured by a prototype template with a set of predefined global and local deformations to take into account its inherent natural variability over time. In this deformable model-based Bayesian segmentation, the data likelihood model relies on an accurate statistical modelling of the grey level distribution of each class present in the ultrasound image. The parameters of this distribution mixture are given by a preliminary iterative estimation step. This estimation scheme relies on a Markov Random Field prior model, and takes into account the imaging process as well as the distribution shape of each class present in the image. Then the detection and the tracking problem is stated in a Bayesian framework, where it ends up as a cost function minimisation problem for each image of the sequence. In our application, this energy optimisation problem is efficiently solved by a genetic algorithm combined with a steepest ascent procedure. This technique has been successfully applied on synthetic images, and on a real echocardiographic image sequence.

Bayesian approach to segmentation of statistical parametric maps

Abstract: A contextual segmentation technique to detect brain activation from functional brain images is presented in the Bayesian framework. Unlike earlier similar approaches [Holmes and Ford (1993) and Descombes et al. (1998)], a Markov random field (MRF) is used to represent configurations of activated brain voxels, and likelihoods given by statistical parametric maps (SPM's) are directly used to find the maximum a posteriori (MAP) estimation of segmentation. The iterative segmentation algorithm, which is based on a simulated annealing scheme, is fully data-driven and capable of analyzing experiments involving multiple-input stimuli. Simulation results and comparisons with the simple thresholding and the statistical parametric mapping (SPM) approaches are presented with synthetic images, and functional MR images acquired in memory retrieval and event-related working memory tasks. The experiments show that an MRF Is a valid representation of the activation patterns obtained in functional brain images, and the present technique renders a superior segmentation scheme to the context-free approach and the SPM approach.

Markov Random Field Models for Segmentation of PET Images

Abstract: This paper investigates the segmentation of different regions in PET images based on the feature vector extracted from the time-activity curve for each voxel. PET image segmentation has applications in PET reference region analysis and activation studies. The segmentation algorithm presented uses a Markov random field model for the voxel class labels. By including the Markov random field model in the expectation-maximisation iteration, the algorithm can be used to simultaneously estimate parameters and segment the image. Hence, the algorithm is able to combine both feature and spatial information for the purpose of segmentation. Experimental results on synthetic and real PET data are presented to demonstrate the performance of the algorithm. The algorithms used in this paper can be used to segment other functional images.

Contextual clustering for analysis of functional MRI data

Abstract: Presents 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 the authors' 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.

Empirical Bayesian motion segmentation

Abstract: We introduce an empirical Bayesian procedure for the simultaneous segmentation of an observed motion field and estimation of the hyperparameters of a Markov random field prior. The new approach exhibits the Bayesian appeal of incorporating prior beliefs, but requires only a qualitative description of the prior, avoiding the requirement for a quantitative specification of its parameters. This eliminates the need for trial-and-error strategies for the determination of these parameters and leads to better segmentations.

A spectral mixture process conditioned by Gibbs-based partitioning

Abstract: An enhanced method of spectral mixture analysis is investigated for hyperspectral imagery of moderate-to-high scene complexity, where either a large set of fundamental materials may exist throughout, or where some of the fundamental members have spectra that are similar to each other. For a complex scene, the use of one large set of fundamental materials as the set of "endmembers" for performing spectral unmixing can cause unreliable estimates of material compositions at sites within the scene. In such cases, partitioning this large set of endmembers into a number of smaller sets is appropriate, where the smaller sets are associated with certain regions in a scene. Herein, a Gibbs-based algorithm is developed to partition hyperspectral imagery into regions of similarity. This partitioning algorithm provides an estimator of an underlying and unobserved process called a "partition process" that coexists with other underlying (and unobserved) processes, one of which is called a "spectral mixing process." The algorithm exploits the properties of a Markov random field (MRF) and the associated Gibbs equivalence theorem, using a suitably defined graph structure and a Gibbs distribution to model the partition process. Consequently, spatial consistency is imposed on the spectral content of sites in each partition. The enhanced spectral mixing process is then computed as a linear mixture model that is conditioned on the partition process. Experiments are performed using scenes of HYDICE imagery to validate the algorithm, where spectral mixture analysis is performed with and without conditioning on the partitioning process.

Vehicle tracking in low-angle and front-view images based on spatio-temporal markov random field model

Abstract: One of the most important research in intelligent transportation systems (ITS) is the development of systems that automatically analyze or monitor traffic activities. For that purpose, it is necessary to achieve reliable vehicle tracking in traffic images. However, occlusion effect among vehicles had impeded such reliable tracking for a long time. In order to solve this problem the authors have developed the dedicated tracking algorithm, referred to as Spatio-Temporal Markov Random Field in the year of 2000. 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. And it was proved that the algorithm has performed 95% success of tracking in middle-angle image. However, most of images actually captured by cameras on infrastructures are low-angle image, and many of them are front-view image. Since vehicles severely occlude each other in such images, segmentations of vehicle region through spatio-temporal images will be unsuccessful. In order to resolve such a problem, the authors have improved this ST-MRF model to re-optimize segmentation boundaries through accumulated spatio-temporal images. As a result, the improved algorithm were able to track vehicles at 91:2% success rate against such severe occlusions in low-angle and front view images at a highway junction. This successful result would lead precise analyses of severely complicated traffic.

A Hierarchical Markov Random Field Model for Figure-Ground Segregation

Abstract: To segregate overlapping objects into depth layers requires the integration of local occlusion cues distributed over the entire image into a global percept. We propose to model this process using hierarchical Markov random field (HMRF), and suggest a broader view that clique potentials in MRF models can be used to encode any local decision rules. A topology-dependent multiscale hierarchy is used to introduce long range interaction. The operations within each level are identical across the hierarchy. The clique parameters that encode the relative importance of these decision rules are estimated using an optimization technique called learning from rehearsals based on 2-object training samples. We find that this model generalizes successfully to 5-object test images, and that depth segregation can be completed within two traversals across the hierarchy. This computational framework therefore provides an interesting platform for us to investigate the interaction of local decision rules and global representations, as well as to reason about the rationales underlying some of recent psychological and neurophysiological findings related to figure-ground segregation.

Texture replacement in real images

Abstract: Texture replacement in real images has many applications, such as interior design, digital movie making and computer graphics. The goal is to replace some specified texture patterns in an image while preserving lighting effects, shadows and occlusions. To achieve convincing replacement results we have to detect texture patterns and estimate the lighting map from a given image. Near regular planar texture patterns are considered in this paper. Given a sample texture patch, a standard tile is computed. Candidate texture regions are determined by mutual information between the standard tile and each image patch. Regions with high mutual information scores are used to estimate the admissible lighting distributions, which is represented by cached statistics. Spatial lighting change constraints are represented by a Markov random field model. Maximum a posteriori estimation of the texture segmentation and lighting map is solved in a stochastic annealing fashion, namely, the Markov chain Monte Carlo method. Visually satisfactory result is achieved using this statistical sampling model.

Magnetic resonance image analysis by information theoretic criteria and stochastic site models

Abstract: Quantitative analysis of magnetic resonance (MR) images is a powerful tool for image-guided diagnosis, monitoring, and intervention. The major tasks involve tissue quantification and image segmentation where both the pixel and context images are considered. To extract clinically useful information from images that might be lacking in prior knowledge, the authors introduce an unsupervised tissue characterization algorithm that is both statistically principled and patient specific. The method uses adaptive standard finite normal mixture and inhomogeneous Markov random field models, whose parameters are estimated using expectation-maximization and relaxation labeling algorithms under information theoretic criteria. The authors demonstrate the successful applications of the approach with synthetic data sets and then with real MR brain images.

Bayesian Approach to Image Interpretation

Abstract: List of Figures. List of Tables. Preface. Acknowledgments. 1: Overview. 1. Introduction. 2. Image Interpretation. 3. Literature Review. 4. Approaches. 5. Layout of the Monograph. 2: Background. 1. Introduction. 2. Markov Random Field Models. 3. Multiresolution. 3: MRF Framework For Image Interpretation. 1. MRF on a Graph. 4. Bayesian Net Approach To Interpretation. 1. Introduction. 2. MRF model leading to Bayesian Network Formulation. 3. Bayesian Networks and Probabilistic Inference. 4. Probability Updating in Bayesian Networks. 5. Bayesian Networks for Gibbsian Image Interpretation. 6. Experimental Results. 7. Conclusions. 5: Joint Segmentation And Image Interpretation. 1. Introduction. 2. Image Interpretation using Integration. 3. The Joint Segmentation and Image Interpretation Scheme. 4. Experimental Results. 5. Conclusions. 6: Conclusions. Appendices: Appendix A. Bayesian Reconstruction. Appendix B. Proof of Hammersley-Clifford Theorem. Appendix C. Simulated Annealing Algorithm - Selecting Toin practise. Appendix D. Custom Made Pyramids. Appendix E. Proof of Theorem 4.6. Appendix F. k-means clustering. Appendix G. Features used in Image Interpretation. Appendix H. Knowledge Acquisition. Appendix I. HMM for Clique Functions. References. Index.

A MAP framework for tag line detection in SPAMM data using Markov random fields on the B-spline solid

Abstract: Magnetic resonance (MR) tagging is a technique for measuring heart deformations through creation of a stripe grid pattern on cardiac images. Typically, sets of tag surfaces are encoded in the tissue appearing as dark lines on 2D images. The B-spline solid model for tagged MRI has the advantage of tracking myocardial tissue with material coordinates. This makes it an effective model in the analysis of heart deformation. In this paper, we present a Maximum A Posteriori (MAP) framework for detecting tags with a Markov random field (MRF) defined on a sampled B-spline solid model. We formulate the tag tracking problem as MAP estimation, finding the optimal solid for the tag features present in the current image set given an initial solid for the previous frame. The framework also allows the parameters of the solid model, number of knots, and spline order to be adjusted. In this approach, fitting can start with a solid with less knots and lower spline order, and proceed to one with more knots and/or higher order to achieve more accuracy. The approach has been validated on two sets of in-vivo heart data.

A region-based MRF model for unsupervised segmentation of moving objects in image sequences

Abstract: This paper addresses the problem of segmentation of moving objects in image sequences, which is of key importance in content-based applications. We transform the problem into a graph labeling problem over a region adjacency graph (RAG), by introducing a Markov random field (MRF) model based on spatio-temporal information. The initial partition is obtained by fast, color-based watershed segmentation. The motion of each region is estimated and validated in a hierarchical framework. A dynamic memory, based on object tracking, is incorporated into the segmentation process to maintain temporal coherence. The performance of the algorithm is evaluated on several real-world image sequences.

A Markov Random Field Image Segmentation Model Using Combined Color and Texture Features

Abstract: In this paper, we propose a Markov random field (MRF) image segmentation model which aims at combining color and texture features. The theoretical framework relies on Bayesian estimation associated with combinatorial optimization (Simulated Annealing). The segmentation is obtained by classifying the pixels into different pixel classes. These classes are represented by multi-variate Gaussian distributions. Thus, the only hypothesis about the nature of the features is that an additive white noise model is suitable to describe the feature values belonging to a given class. Herein, we use the perceptually uniform CIE-L*u*v* color values as color features and a set of Gabor filters as texture features. We provide experimental results that illustrate the performance of our method on both synthetic and natural color images. Due to the local nature of our MRF model, the algorithm can be highly parallelized.

Robust fast extraction of video objects combining frame differences and adaptive reference image

Abstract: This paper introduces a video object segmentation algorithm developed in the context of the European project Art.live where constraints on the quality of segmentation and the processing rate (at least 10 images/second) are required. In order to obtain a fine segmentation (no blocking effect, boundaries precision, temporal stability without flickering), the segmentation process is based on Markov random field (MRF) modelling which involves consecutive frame difference and a reference image in a unified way. Temporal changes of the luminance are predominant when the reference image is not yet available whereas the reference image prevails for low textured moving objects or for objects which stop moving for a while. The increased processing rate comes from the substitution of some Markovian iterations with morphological operations without loss of quality. Simulation results show the efficiency of the proposed method in term of accuracy and complexity (/spl sime/6 images/second for 352/spl times/288 pixels YUV images on a low-end processor).

Markov face models

Abstract: The spatial distribution of gray level intensities in an image can be naturally modeled using Markov random field (MRF) models. We develop and investigate the performance of face detection algorithms derived from MRF considerations. For enhanced detection, the MRF models are defined for every permutation of site indices (pixels) in the image. We find the optimal permutation that provides maximum discriminatory power to identify faces from nonfaces. The methodology presented here is a generalization of the face detection algorithm described previously where a most discriminating Markov chain model was used. The MRF models successfully detect faces in a number of test images.

Image restoration using recursive Markov random field models driven by Cauchy distributed noise

Abstract: A recursive restoration algorithm based on a Markov random field model driven by Cauchy noise is described and demonstrated to provide better edge preservation than similar algorithms using Gaussian or Laplacian noises without increased computational cost.

Segmentations of Spatio-Temporal Images by Spatio-Temporal Markov Random Field Model

Abstract: There have been many successful researches on image segmentations that employ Markov Random Field model. However, most of them were interested in two-dimensional MRF, or spatial MRF, and very few researches are interested in three-dimensional MRF model. Generally, 'three-dimensional' have two meaning, that are spatially three-dimensional and spatio-temporal. In this paper, we especially are interested in segmentations of spatio-temporal images which appears to be equivalent to tracking problem of moving objects such as vehicles etc. For that purpose, by extending usual two-dimensional MRF, we defined a dedicated three-dimensional MRF which we defined as Spatio-Temporal MRF model(S-T MRF). This S-T MRF models a tracking problem by determining labels of groups of pixels by referring to their texture and labeling correlations along the temporal axis as well as the x-y image axes. Although vehicles severely occlude each other in general traffic images, segmentation boundaries of vehicle regions will be determined precisely by this S-T MRF optimizing such boundaries through spatio-temporal images. Consequently, it was proved that the algorithm has performed 95% success of tracking in middle-angle image at an intersection and 91% success in low-angle and front-view images at a highway junction.

Markov Random Field Modelling of Royal Road Genetic Algorithms

Abstract: Markov Random Fields (MRFs) [5] are a class of probabalistic models that have been applied for many years to the analysis of visual patterns or textures. In this paper, our objective is to establish MRFs as an interesting approach to modelling genetic algorithms. Our approach bears strong similarities to recent work on the Bayesian Optimisation Algorithm [9], but there are also some significant differences. We establish a theoretical result that every genetic algorithm problem can be characterised in terms of a MRF model. This allows us to construct an explicit probabilistic model of the GA fitness function. The model can be used to generate chromosomes, and derive a MRF fitness measure for the population. We then use a specific MRF model to analyse two Royal Road problems, relating our analysis to that of Mitchell et al. [7].

Relaxing Symmetric Multiple Windows Stereo Using Markov Random Fields

Abstract: This paper introduces R-SMW, a new algorithm for stereo matching. The main aspect is the introduction of a Markov Random Field (MRF) model in the Symmetric Multiple Windows (SMW) stereo algorithm in order to obtain a non-deterministic relaxation. The SMW algorithm is an adaptive, multiple window scheme using left-right consistency to compute disparity. The MRF approach allows to combine in a single functional the disparity values coming from different windows, the left-right consistency constraint and regularization hypotheses. The optimal estimate of the disparity is obtained by minimizing an energy functional with simulated annealing. Results with both synthetic and real stereo pairs demonstrate the improvement over the original SMW algorithm, which was already proven to perform better than state-of-the-art algorithms.