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Dissertations / Theses on the topic 'MRF, Markov Random Fields'

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Published: 1 June 2024

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1

Samuel, Kegan. "Gradient based MRF learning for image restoration and segmentation." Doctoral diss., University of Central Florida, 2012. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5480.

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The undirected graphical model or Markov Random Field (MRF) is one of the more popular models used in computer vision and is the type of model with which this work is concerned. Models based on these methods have proven to be particularly useful in low-level vision systems and have led to state-of-the-art results for MRF-based systems. The research presented will describe a new discriminative training algorithm and its implementation. The MRF model will be trained by optimizing its parameters so that the minimum energy solution of the model is as similar as possible to the ground-truth. While previous work has relied on time-consuming iterative approximations or stochastic approximations, this work will demonstrate how implicit differentiation can be used to analytically differentiate the overall training loss with respect to the MRF parameters. This framework leads to an efficient, flexible learning algorithm that can be applied to a number of different models. The effectiveness of the proposed learning method will then be demonstrated by learning the parameters of two related models applied to the task of denoising images. The experimental results will demonstrate that the proposed learning algorithm is comparable and, at times, better than previous training methods applied to the same tasks. A new segmentation model will also be introduced and trained using the proposed learning method. The proposed segmentation model is based on an energy minimization framework that is novel in how it incorporates priors on the size of the segments in a way that is straightforward to implement. While other methods, such as normalized cuts, tend to produce segmentations of similar sizes, this method is able to overcome that problem and produce more realistic segmentations.
Ph.D.
Doctorate
Computer Science
Engineering and Computer Science
Computer Science
2

Kato, Jien, Toyohide Watanabe, Sébastien Joga, Liu Ying, Hiroyuki Hase, ジェーン 加藤, and 豊英 渡邉. "An HMM/MRF-based stochastic framework for robust vehicle tracking." IEEE, 2004. http://hdl.handle.net/2237/6743.

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3

Karci, Mehmet Haydar. "Higher Order Levelable Mrf Energy Minimization Via Graph Cuts." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609408/index.pdf.

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A feature of minimizing images of a class of binary Markov random field energies is introduced and proved. Using this, the collection of minimizing images of levels of higher order, levelable MRF energies is shown to be a monotone collection. This implies that these images can be combined to give minimizing images of the MRF energy itself. Due to the recent developments, second and third order binary MRF energies of the mentioned class are known to be exactly minimized by maximum flow/minimum cut computations on appropriately constructed graphs. With the aid of these developments an exact and efficient algorithm to minimize levelable second and third order MRF energies, which is composed of a series of maximum flow/minimum cut computations, is proposed and applications of the proposed algorithm to image restoration are given.
4

Gasnier, Nicolas. "Use of multi-temporal and multi-sensor data for continental water body extraction in the context of the SWOT mission." Electronic Thesis or Diss., Institut polytechnique de Paris, 2022. http://www.theses.fr/2022IPPAT002.

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La télédétection spatiale fournit aux hydrologues et aux décideurs des données indispensables à la compréhension du cycle de l’eau et à la gestion des ressources et risques associés. Le satellite SWOT, qui est une collaboration entre les agences spatiales françaises (CNES) et américaine (NASA, JPL), et dont le lancement est prévu en 2022 vise à mesurer la hauteur des lacs, rivières et océans avec une grande résolution spatiale. Il complétera ainsi les capteurs existants, comme les constellations SAR et optique Sentinel-1 et 2 et les relevés in situ. SWOT représente une rupture technologique car il est le premier satellite qui embarque un altimètre de fauchée quasi-nadir. Le calcul des hauteurs d’eau est fait par interférométrie sur les images SAR acquises par SWOT. La détection d’eau dans ces images est donc une étape essentielle du traitement des données SWOT, mais qui peut être difficile, en particulier avec un faible rapport signal sur bruit ou en présence de radiométries inhabituelles. Dans cette thèse, nous cherchons à développer de nouvelles méthodes pour rendre la détection d’eau plus robustes. Pour cela, nous nous intéressons à l’utilisation de données exogènes pour guider la détection, à la combinaison de données multi-temporelles et multi-capteurs et à des approches de débruitage. La première méthode proposée exploite les informations de la base de donnée des rivières utilisée par SWOT pour détecter les rivières fines dans l’image de façon robuste à la fois aux bruit dans l’image, aux erreurs éventuelles de la base de données et aux changements survenus. Cette méthode s’appuie sur un nouveau détecteur de structures linéiques, un algorithme de chemin de moindre coût et une nouvelle méthode de segmentation par CRF qui combine des termes d’attache aux données et de régularisation adaptés au problème. Nous avons également proposé une méthode dérivée des GrabCut qui utilise un polygone a priori contenant un lac pour le détecter sur une image SAR ou une série temporelle. Dans ce cadre, nous avons également étudié le recours à une combinaison multi-temporelle et multi-capteurs (optique et SAR). Enfin, dans le cadre d’une étude préliminaire sur les méthodes de débruitage pour la détection d’eau nous avons étudié les propriétés statistiques de la moyenne géométrique temporelle et proposé une adaptation de la méthode variationnelle MuLoG pour la débruiter
Spaceborne remote sensing provides hydrologists and decision-makers with data that are essential for understanding the water cycle and managing the associated resources and risks. The SWOT satellite, which is a collaboration between the French (CNES) and American (NASA, JPL) space agencies, is scheduled for launch in 2022 and will measure the height of lakes, rivers, and oceans with high spatial resolution. It will complement existing sensors, such as the SAR and optical constellations Sentinel-1 and 2, and in situ measurements. SWOT represents a technological breakthrough as it is the first satellite to carry a near-nadir swath altimeter. The estimation of water levels is done by interferometry on the SAR images acquired by SWOT. Detecting water in these images is therefore an essential step in processing SWOT data, but it can be very difficult, especially with low signal-to-noise ratios, or in the presence of unusual radiometries. In this thesis, we seek to develop new methods to make water detection more robust. To this end, we focus on the use of exogenous data to guide detection, the combination of multi-temporal and multi-sensor data and denoising approaches. The first proposed method exploits information from the river database used by SWOT (derived from GRWL) to detect narrow rivers in the image in a way that is robust to both noise in the image, potential errors in the database, and temporal changes. This method relies on a new linear structure detector, a least-cost path algorithm, and a new Conditional Random Field segmentation method that combines data attachment and regularization terms adapted to the problem. We also proposed a method derived from GrabCut that uses an a priori polygon containing a lake to detect it on a SAR image or a time series of SAR images. Within this framework, we also studied the use of a multi-temporal and multi-sensor combination between Sentinel-1 SAR and Sentinel-2 optical images. Finally, as part of a preliminary study on denoising methods applied to water detection, we studied the statistical properties of the geometric temporal mean and proposed an adaptation of the variational method MuLoG to denoise it
5

Besbes, Ahmed. "Image segmentation using MRFs and statistical shape modeling." Phd thesis, Ecole Centrale Paris, 2010. http://tel.archives-ouvertes.fr/tel-00594246.

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Nous présentons dans cette thèse un nouveau modèle statistique de forme et l'utilisons pour la segmentation d'images avec a priori. Ce modèle est représenté par un champ de Markov. Les noeuds du graphe correspondent aux points de contrôle situés sur le contour de la forme géométrique, et les arêtes du graphe représentent les dépendances entre les points de contrôle. La structure du champ de Markov est déterminée à partir d'un ensemble de formes, en utilisant des techniques d'apprentissage de variétés et de groupement non-supervisé. Les contraintes entre les points sont assurées par l'estimation des fonctions de densité de probabilité des longueurs de cordes normalisées. Dans une deuxième étape, nous construisons un algorithme de segmentation qui intègre le modèle statistique de forme, et qui le relie à l'image grâce à un terme région, à travers l'utilisation de diagrammes de Voronoi. Dans cette approche, un contour de forme déformable évolue vers l'objet à segmenter. Nous formulons aussi un algorithme de segmentation basé sur des détecteurs de points d'intérêt, où le terme de régularisation est lié à l'apriori de forme. Dans ce cas, on cherche à faire correspondre le modèle aux meilleurs points candidats extraits de l'image par le détecteur. L'optimisation pour les deux algorithmes est faite en utilisant des méthodes récentes et efficaces. Nous validons notre approche à travers plusieurs jeux de données en 2D et en 3D, pour des applications de vision par ordinateur ainsi que l'analyse d'images médicales.
6

Kale, Hikmet Emre. "Segmentation Of Human Facial Muscles On Ct And Mri Data Using Level Set And Bayesian Methods." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613352/index.pdf.

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Medical image segmentation is a challenging problem, and is studied widely. In this thesis, the main goal is to develop automatic segmentation techniques of human mimic muscles and to compare them with ground truth data in order to determine the method that provides best segmentation results. The segmentation methods are based on Bayesian with Markov Random Field (MRF) and Level Set (Active Contour) models. Proposed segmentation methods are multi step processes including preprocess, main muscle segmentation step and post process, and are applied on three types of data: Magnetic Resonance Imaging (MRI) data, Computerized Tomography (CT) data and unified data, in which case, information coming from both modalities are utilized. The methods are applied both in three dimensions (3D) and two dimensions (2D) data cases. A simulation data and two patient data are utilized for tests. The patient data results are compared statistically with ground truth data which was labeled by an expert radiologist.
7

Wang, Siying. "Segmentation of magnetic resonance images for assessing neonatal brain maturation." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:96db1546-16c1-4e37-9fd2-6431b385b516.

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In this thesis, we aim to investigate the correlation between myelination and the gestational age for preterm infants, with the former being an important developmental process during human brain maturation. Quantification of myelin requires dedicated imaging, but the conventional magnetic resonance images routinely acquired during clinical imaging of neonates carry signatures that are thought to be associated with myelination. This thesis thus focuses on structural segmentation and spatio-temporal modelling of the so-called myelin-like signals on T2-weighted scans for early prognostic evaluation of the preterm brain. The segmentation part poses the major challenges of this task: insufficient spatial prior information of myelination and the presence of substantial partial volume voxels in clinical data. Specific spatial priors for the developing brain are obtained from either probabilistic atlases or manually annotated training images, but none of them currently include myelin as an individual tissue type. This causes further difficulties in partial volume estimation which depends on the probabilistic atlases of the composing pure tissues. Our key contribution is the development of an expectation-maximisation framework that incorporates an explicit partial volume class whose locations are configured in relation to the composing pure tissues in a predefined region of interest via second-order Markov random fields. This approach resolves the above challenges without requiring any probabilistic atlas of myelin. We also investigate atlas-based whole brain segmentation that generates the binary mask for the region of interest. We then construct a spatio-temporal growth model for myelin-like signals using logistic regression based on the automatic segmentations of 114 preterm infants aged between 29 and 44 gestational weeks. Lastly, we demonstrate the ability of age estimation using the normal growth model in a leave-one-out procedure.
8

Stien, Marita. "Sequential Markov random fields and Markov mesh random fields for modelling of geological structures." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2006. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9326.

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We have been given a two-dimensional image of a geological structure. This structure is used to construct a three-dimensional statistical model, to be used as prior knowledge in the analysis of seismic data. We consider two classes of discrete lattice models for which efficient simulation is possible; sequential Markov random field (sMRF) and Markov mesh random field (MMRF). We first explore models from these two classes in two dimensions, using the maximum likelihood estimator (MLE). The results indicate that a larger neighbourhood should be considered for all the models. We also develop a second estimator, which is designed to match the model with the observation with respect to a set of specified functions. This estimator is only considered for the sMRF model, since that model proved to be flexible enough to give satisfying results. Due to time limitation of this thesis, we could not wait for the optimization of the estimator to converge. Thus, we can not evaluate this estimator. Finally, we extract useful information from the two-dimensional models and specify a sMRF model in three dimensions. Parameter estimation for this model needs approximative techniques, since we only have given observations in two dimensions. Such techniques have not been investigated in this report, however, we have adjusted the parameters manually and observed that the model is very flexible and might give very satisfying results.

9

Austad, Haakon Michael. "Approximations of Binary Markov Random Fields." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-14922.

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10

Drouin, Simon. "Digital rotoscoping using Markov random fields." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=32535.

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This thesis presents a statistical framework and its implementation in a user-assisted rotoscoping program intended for the production of animation movies. User-assisted video segmentation of scenes with well-defined foreground and background, a special case of the general problem of rotoscoping, is used to analyze the properties of the framework and its implementation. The statistical model used in the framework is built from pairs of training images composed of a frame from the sequence to segment and of a binary image representing the associated user-specified segmentation. The segmentation for a new frame is generated by pasting in, for each image patch, the nearest neighbor from the training set. A mechanism inspired by belief propagation is used to insure consistency between neighboring patches. The algorithm is applied at different scale levels of the input images to take into account longer range interactions. A performance metric is defined for the automatic segmentation and the segmentation results are compared with a set of video sequences that have been entirely traced by hand. A new technique is also presented to automatically choose the optimal training data for the statistical model. A crude segmentation is computed from the smallest possible training set (one frame). A statistical analysis of this segmentation is then used to determine which other frames should be added to the training set in order to get the best possible segmentation. Finally, it is shown how the technique used for segmentation can be extended to perform example-based filtering of video and thus allow the creation of general-purpose rotoscoping systems.
Ce mémoire présente un modèle statistique ainsi que son implantation dans un programme de rotoscopie qui peut être utilisé pour la production de films d'animation. Le problème de la segmentation assistée de scènes video contenant un avant-plan et un arrière-plan distincts, un sous-ensemble du problème plus général que constitue la rotoscopie, est utilisé pour analyser les propriétés du modèle statistique et de son implantation. Le modèle statistique utilisé est construit à partir d'un découpage de paires d'images d'entraînement composées d'un cadre de la séquence video à segmenter et d'une image binaire qui défini la segmentation associée. La segmentation de chaque cadre de la sequence est obtenue en collant, pour chaque portion d'image, la portion d'image la plus similaire de l'ensemble d'entraînement. Un mécanisme inspiré de la "propagation de conviction"(belief propagation) est utilisé pour assurer la cohérence entre les portions de l'image de sortie qui sont voisines. L'algorithme est appliqué à plusieurs niveaux d'échelle afin de considérer la dépendance statistique de plus longue portée qui existe entre les pixels d'une image. Une métrique est définie pour mesurer la performance de la segmentation automatique. Les résultats de la segmentation sont analysés à l'aide d'une série de séquences vidéo qui ont préalablement été segmentées manuellement. Une nouvelle technique est également présentée pour permettre au logiciel de segmentation de choisir automatiquement l'ensemble d'entraînement optimal. Une segmentation grossière est d'abord obtenue en ulitisant le plus petit ensemble d'entraînement possible (1 cadre)
11

Kirkland, Mark. "Simulation methods for Markov random fields." Thesis, University of Strathclyde, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.278512.

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12

Arnesen, Petter. "Approximate recursive calculations of discrete Markov random fields." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2010. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-10806.

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In this thesis we present an approximate recursive algorithm for calculations of discrete Markov random fields defined on graphs. We write the probability distribution of a Markov random field as a function of interaction parameters, a representation well suited for approximations. The algorithm we establish is a forward-backward algorithm, where the forward part recursively decomposes the probability distribution into a product of conditional distributions. Next we establish two different backward parts to our algorithm. In the first one we are able to simulate from the probability distribution, using the decomposed system. The second one enables us to calculate the marginal distributions for all the nodes in the Markov random field. All the approximations in our algorithm are controlled by a positive parameter, and when this parameter is equal to 0, our algorithm is by definition an exact algorithm. We investigate the performance of our algorithm by the CPU time, and by evaluating the quality of the approximations in various ways. As an example of the usage of our algorithm, we estimate an unknown picture from a degenerated version, using the marginal posterior mode estimate. This is a classical Bayesian problem.

13

Dror, Mizrahi Yariv. "Linear and parallel learning of Markov random fields." Thesis, University of British Columbia, 2014. http://hdl.handle.net/2429/51458.

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In this thesis, we introduce a new class of embarrassingly parallel parameter learning algorithms for Markov random fields (MRFs) with untied parameters, which are efficient for a large class of practical models. The algorithms parallelize naturally over cliques and, for graphs of bounded degree, have complexity that is linear in the number of cliques. We refer to these algorithms with the acronym LAP, which stands for Linear And Parallel. Unlike their competitors, the marginal versions of the proposed algorithms are fully parallel and for log-linear models they are also data efficient, requiring only the local sufficient statistics of the data to estimate parameters. LAP algorithms are ideal for parameter learning in big graphs and big data applications. The correctness of the newly proposed algorithms relies heavily on the existence and uniqueness of the normalized potential representation of an MRF. We capitalize on this theoretical result to develop a new theory of correctness and consistency of LAP estimators corresponding to different local graph neighbourhoods. This theory also establishes a general condition on composite likelihood decompositions of MRFs that guarantees the global consistency of distributed estimators, provided the local estimators are consistent. We introduce a conditional variant of LAP that enables us to attack parameter estimation of fully-observed models of arbitrary connectivity, including fully connected Boltzmann distributions. Once again, we show consistency for this distributed estimator, and relate it to distributed pseudo-likelihood estimators. Finally, for linear and non-linear inverse problems with a sparse forward operator, we present a new algorithm, named iLAP, which decomposes the inverse problem into a set of smaller dimensional inverse problems that can be solved independently. This parallel estimation strategy is also memory efficient.
Science, Faculty of
Mathematics, Department of
Graduate
14

Chandgotia, Nishant. "Markov random fields, Gibbs states and entropy minimality." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/52913.

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The well-known Hammersley-Clifford Theorem states (under certain conditions) that any Markov random field is a Gibbs state for a nearest neighbour interaction. Following Petersen and Schmidt we utilise the formalism of cocycles for the homoclinic relation and introduce "Markov cocycles", reparametrisations of Markov specifications. We exploit this formalism to deduce the conclusion of the Hammersley-Clifford Theorem for a family of Markov random fields which are outside the theorem's purview (including Markov random fields whose support is the d-dimensional "3-colored chessboard"). On the other extreme, we construct a family of shift-invariant Markov random fields which are not given by any finite range shift-invariant interaction. The techniques that we use for this problem are further expanded upon to obtain the following results: Given a "four-cycle free" finite undirected graph H without self-loops, consider the corresponding 'vertex' shift, H ơm(Zd,H) denoted by X(H). We prove that X(H) has the pivot property, meaning that for all distinct configurations x,y ∈ X(H) which differ only at finitely many sites there is a sequence of configurations (x=x¹),x²,...,(xn =y) ∈ X(H) for which the successive configurations (xi,xi+1) differ exactly at a single site. Further if H is connected we prove that X(H) is entropy minimal, meaning that every shift space strictly contained in X(H) has strictly smaller entropy. The proofs of these seemingly disparate statements are related by the use of the 'lifts' of the configurations in X(H) to their universal cover and the introduction of 'height functions' in this context. Further we generalise the Hammersley-Clifford theorem with an added condition that the underlying graph is bipartite. Taking inspiration from Brightwell and Winkler we introduce a notion of folding for configuration spaces called strong config-folding to prove that if all Markov random fields supported on X are Gibbs with some nearest neighbour interaction so are Markov random fields supported on the "strong config-folds" and "strong config-unfolds" of X.
Science, Faculty of
Mathematics, Department of
Graduate
15

Sánchez-Ordoñez, Andrés E. "A Markov random fields approach to modelling habitat." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/54553.

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Habitat modelling presents a challenge due to the variety of data available and their corresponding accuracy. One option is to use Markov random fields as a way to incorporate these distinct types of data for habitat modelling. In this work, I provide a brief overview of the intuition, mathematical theory, and application considerations behind modelling habitat under this framework. In particular, an auto-logistic model is built and applied to modelling sea lion habitat using synthetic data. First, we explore modelling one sample of data. Afterwards, the framework is extended to the multi-sample scenario. Finally, the theory for the methodology is presented, the results of the applied implementation are presented.
Science, Faculty of
Statistics, Department of
Graduate
16

Li, Chang-Tsun. "Unsupervised texture segmentation using multiresolution Markov random fields." Thesis, University of Warwick, 1998. http://wrap.warwick.ac.uk/39307/.

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In this thesis, a multiresolution Markov Random Field (MMRF) model for segmenting textured images without supervision is proposed. Stochastic relaxation labelling is adopted to assign the class label with highest probability to the block (site) being visited. Class information is propagated from low spatial resolution to high spatial resolution, via appropriate modifications to the interaction energies defining the field, to minimise class-position uncertainty. The thesis contains novel ideas presented in Chapter 4 and 5, respectively. In Chapter 4, the Multiresolution Fourier Transform (MFT) is used to provide a set of spatially localised texture descriptors, which are based on a two-component model of texture, in which one component is a deformation, representing the structural or deterministic elements and the other is a stochastic one. Experiments show that the algorithm is efficient in alleviating class-position uncertainty via data propagation across resolutions. However, the blocking artifacts of the segmentation results show that it is preferable to combine both class and position information so as to achieve smoother and more accurate boundary estimation. In Chapter 5, based on the same MFT-MMRF framework, a boundary process is proposed to refine the segmentation result of the region process proposed in Chapter 4. At each resolution, all the image blocks on either sides of the preliminary boundary detected in the region process are treated as potential boundary-containing blocks (PBCB's). The orientation and the centroid of the boundary-segment contained in each PBCB are calculated. The sequence of PBCB's are then modelled as a MRF and the interaction energy between each pair of neighbouring blocks is defined as a function of the 'distance' D between the centroids of the two boundary segments. During the stochastic relaxation process boundary/non-boundary labels are assigned to the PBCB's. Once the algorithm converges, the centroids of the identified true boundary blocks are connected to form the refined boundary which is propagated down to the next resolution for further refinement.
17

Lienart, Thibaut. "Inference on Markov random fields : methods and applications." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:3095b14c-98fb-4bda-affc-a1fa1708f628.

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This thesis considers the problem of performing inference on undirected graphical models with continuous state spaces. These models represent conditional independence structures that can appear in the context of Bayesian Machine Learning. In the thesis, we focus on computational methods and applications. The aim of the thesis is to demonstrate that the factorisation structure corresponding to the conditional independence structure present in high-dimensional models can be exploited to decrease the computational complexity of inference algorithms. First, we consider the smoothing problem on Hidden Markov Models (HMMs) and discuss novel algorithms that have sub-quadratic computational complexity in the number of particles used. We show they perform on par with existing state-of-the-art algorithms with a quadratic complexity. Further, a novel class of rejection free samplers for graphical models known as the Local Bouncy Particle Sampler (LBPS) is explored and applied on a very large instance of the Probabilistic Matrix Factorisation (PMF) problem. We show the method performs slightly better than Hamiltonian Monte Carlo methods (HMC). It is also the first such practical application of the method to a statistical model with hundreds of thousands of dimensions. In a second part of the thesis, we consider approximate Bayesian inference methods and in particular the Expectation Propagation (EP) algorithm. We show it can be applied as the backbone of a novel distributed Bayesian inference mechanism. Further, we discuss novel variants of the EP algorithms and show that a specific type of update mechanism, analogous to the mirror descent algorithm outperforms all existing variants and is robust to Monte Carlo noise. Lastly, we show that EP can be used to help the Particle Belief Propagation (PBP) algorithm in order to form cheap and adaptive proposals and significantly outperform classical PBP.
18

Olsen, Jessica Lyn. "An Applied Investigation of Gaussian Markov Random Fields." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3273.

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Recently, Bayesian methods have become the essence of modern statistics, specifically, the ability to incorporate hierarchical models. In particular, correlated data, such as the data found in spatial and temporal applications, have benefited greatly from the development and application of Bayesian statistics. One particular application of Bayesian modeling is Gaussian Markov Random Fields. These methods have proven to be very useful in providing a framework for correlated data. I will demonstrate the power of GMRFs by applying this method to two sets of data; a set of temporal data involving car accidents in the UK and a set of spatial data involving Provo area apartment complexes. For the first set of data, I will examine how including a seatbelt covariate effects our estimates for the number of car accidents. In the second set of data, we will scrutinize the effect of BYU approval on apartment complexes. In both applications we will investigate Laplacian approximations when normal distribution assumptions do not hold.
19

Islam, Mofakharul University of Ballarat. "Unsupervised Color Image Segmentation Using Markov Random Fields Model." University of Ballarat, 2008. http://archimedes.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/12827.

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We propose a novel approach to investigate and implement unsupervised segmentation of color images particularly natural color images. The aim is to devise a robust unsu- pervised segmentation approach that can segment a color textured image accurately. Here, the color and texture information of each individual pixel along with the pixel's spatial relationship within its neighborhood have been considered for producing precise segmentation of color images. Precise segmentation of images has tremendous potential in various application domains like bioinformatics, forensics, security and surveillance, the mining and material industry and medical imaging where subtle information related to color and texture is required to analyze an image accurately. We intend to implement a robust unsupervised segmentation approach for color im- ages using a newly developed multidimensional spatially variant ¯nite mixture model (MSVFMM) using a Markov Random Fields (MRF) model for improving the over- all accuracy in segmentation and Haar wavelet transform for increasing the texture sensitivity of the proposed approach. [...]
Master of Computing
20

Frondana, Iara Moreira. "Model selection for discrete Markov random fields on graphs." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-02022018-151123/.

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In this thesis we propose to use a penalized maximum conditional likelihood criterion to estimate the graph of a general discrete Markov random field. We prove the almost sure convergence of the estimator of the graph in the case of a finite or countable infinite set of variables. Our method requires minimal assumptions on the probability distribution and contrary to other approaches in the literature, the usual positivity condition is not needed. We present several examples with a finite set of vertices and study the performance of the estimator on simulated data from theses examples. We also introduce an empirical procedure based on k-fold cross validation to select the best value of the constant in the estimators definition and show the application of this method in two real datasets.
Nesta tese propomos um critério de máxima verossimilhança penalizada para estimar o grafo de dependência condicional de um campo aleatório Markoviano discreto. Provamos a convergência quase certa do estimador do grafo no caso de um conjunto finito ou infinito enumerável de variáveis. Nosso método requer condições mínimas na distribuição de probabilidade e contrariamente a outras abordagens da literatura, a condição usual de positividade não é necessária. Introduzimos alguns exemplos com um conjunto finito de vértices e estudamos o desempenho do estimador em dados simulados desses exemplos. Também propomos um procedimento empírico baseado no método de validação cruzada para selecionar o melhor valor da constante na definição do estimador, e mostramos a aplicação deste procedimento em dois conjuntos de dados reais.
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Dharmagunawardhana, Chathurika. "Image texture analysis based on Gaussian Markov Random Fields." Thesis, University of Southampton, 2014. https://eprints.soton.ac.uk/372489/.

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Texture analysis is one of the key techniques of image understanding and processing with widespread applications from low level image segmentation to high level object recognition. Gaussian Markov random field (GMRF) is a particular model based texture feature extraction scheme which uses model parameters as texture features. In this thesis a novel robust texture descriptor based on GMRF is proposed specially for texture segmentation and classification. For these tasks, descriptive features are more favourable relative to the generative features. Therefore, in order to achieve more descriptive features, with the GMRFs, a localized parameter estimation technique is introduced here. The issues arising in the localized parameter estimation process, due to the associated small sample size, are addressed by applying Tikhonov regularization and an estimation window size selection criterion. The localized parameter estimation process proposed here can overcome the problem of parameter smoothing that occurs in traditional GMRF parameter estimation. Such a parameter smoothing disregards some important structural and statistical information for texture discrimination. The normalized distributions of local parameter estimates are proposed as the new texture features and are named as Local Parameter Histogram (LPH) descriptors. Two new rotation invariant texture descriptors based on LPH features are also introduced, namely Rotation Invariant LPH (RI-LPH) and Isotropic LPH (I-LPH)descriptors. The segmentation and classification results on large texture datasets demonstrate that these descriptors significantly improve the performance of traditional GMRF features and also demonstrate better performance in comparison with the state-of-the-art texture descriptors. Satisfactory natural image segmentation is also carried out based on the novel features. Furthermore, proposed features are employed in a real world medical application involving tissue recognition for emphysema, a critical lung disease causing lung tissue destruction. Features extracted from High Resolution Computed Tomography (HRCT) data are used in effective tissue recognition and pathology distribution diagnosis. Moreover, preliminary work on a Bayesian framework for integrating prior knowledge into the parameter estimation process is undertaken to introduce further improved texture features.
22

Islam, Mofakharul. "Unsupervised color image segmentation using Markov Random Fields Model." Thesis, University of Ballarat, 2008. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/53709.

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We propose a novel approach to investigate and implement unsupervised segmentation of color images particularly natural color images. The aim is to devise a robust unsu- pervised segmentation approach that can segment a color textured image accurately. Here, the color and texture information of each individual pixel along with the pixel's spatial relationship within its neighborhood have been considered for producing precise segmentation of color images. Precise segmentation of images has tremendous potential in various application domains like bioinformatics, forensics, security and surveillance, the mining and material industry and medical imaging where subtle information related to color and texture is required to analyze an image accurately. We intend to implement a robust unsupervised segmentation approach for color im- ages using a newly developed multidimensional spatially variant ¯nite mixture model (MSVFMM) using a Markov Random Fields (MRF) model for improving the over- all accuracy in segmentation and Haar wavelet transform for increasing the texture sensitivity of the proposed approach. [...]
Master of Computing
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Islam, Mofakharul. "Unsupervised color image segmentation using Markov Random Fields Model." University of Ballarat, 2008. http://archimedes.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/15694.

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We propose a novel approach to investigate and implement unsupervised segmentation of color images particularly natural color images. The aim is to devise a robust unsu- pervised segmentation approach that can segment a color textured image accurately. Here, the color and texture information of each individual pixel along with the pixel's spatial relationship within its neighborhood have been considered for producing precise segmentation of color images. Precise segmentation of images has tremendous potential in various application domains like bioinformatics, forensics, security and surveillance, the mining and material industry and medical imaging where subtle information related to color and texture is required to analyze an image accurately. We intend to implement a robust unsupervised segmentation approach for color im- ages using a newly developed multidimensional spatially variant ¯nite mixture model (MSVFMM) using a Markov Random Fields (MRF) model for improving the over- all accuracy in segmentation and Haar wavelet transform for increasing the texture sensitivity of the proposed approach. [...]
Master of Computing
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Chandgotia, Nishant. "Markov random fields and measures with nearest neighbour Gibbs potential." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/37000.

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This thesis will discuss the relationship between stationary Markov random fields and probability measures with a nearest neighbour Gibbs potential. While the relationship has been well explored when the measures are fully supported, we shall discuss what happens when we weaken this assumption.
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Milun, Davin. "Generating Markov random field image analysis systems from examples." Buffalo, N.Y. : Dept. of Computer Science, State University of New York at Buffalo, 1995. http://www.cse.buffalo.edu/tech%2Dreports/95%2D23.ps.Z.

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26

Caputo, Barbara. "A new kernel method for object recognition:spin glass-Markov random fields." Doctoral thesis, KTH, Numerical Analysis and Computer Science, NADA, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-58.

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Recognizing objects through vision is an important part of our lives: we recognize people when we talk to them, we recognize our cup on the breakfast table, our car in a parking lot, and so on. While this task is performed with great accuracy and apparently little effort by humans, it is still unclear how this performance is achieved. Creating computer methods for automatic object recognition gives rise to challenging theoretical problems such as how to model the visual appearance of the objects or categories we want to recognize, so that the resulting algorithm will perform robustly in realistic scenarios; to this end, how to use effectively multiple cues (such as shape, color, textural properties and many others), so that the algorithm uses uses the best subset of cues in the most effective manner; how to use specific features and/or specific strategies for different classes.

The present work is devoted to the above issues. We propose to model the visual appearance of objects and visual categories via probability density functions. The model is developed on the basis of concepts and results obtained in three different research areas: computer vision, machine learning and statistical physics of spin glasses. It consists of a fully connected Markov random field with energy function derived from results of statistical physics of spin glasses. Markov random fields and spin glass energy functions are combined together via nonlinear kernel functions; we call the model Spin Glass-Markov Random Fields. Full connectivity enables to take into account the global appearance of the object, and its specific local characteristics at the same time, resulting in robustness to noise, occlusions and cluttered background. Because of properties of some classes of spin glasslike energy functions, our model allows to use easily and effectively multiple cues, and to employ class specific strategies. We show with theoretical analysis and experiments that this new model is competitive with state-of-the-art algorithms for object recognition.

27

Altaye, Endale Berhane. "Approximate recursive algorithm for finding MAP of binary Markov random fields." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2010. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-10824.

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The purpose of this study was to develop a recursive algorithm for computing a maximum a posteriori (MAP) estimate of a binary Markov random field (MRF) by using the MAP-MRF framework. We also discuss how to include an approximation in the recursive scheme, so that the algorithm becomes computationally feasible also for larger problems. In particular, we discuss how our algorithm can be used in an image analysis setting. We consider a situation where an unobserved latent field is assumed to follow a Markov random field prior model, a Gaussian noise-corrupted version of the latent field is observed, and we estimate the unobserved field by the MAP estimator.

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Siksik, Ola. "Markov random fields in visual reconstruction : a transputer-based multicomputer implementation." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/28863.

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Markov Random Fields (MRFs) are used in computer vision as an effective method for reconstructing a function starting from a set of noisy, or sparse data, or in the integration of early vision processes to label physical discontinuities. The MRF formalism is attractive because it enables the assumptions used to be explicitly stated in the energy function. The drawbacks of such models have been the computational complexity of the implementation, and the difficulty in estimating the parameters of the model. In this thesis, the deterministic approximation to the MRF models derived by Girosi and Geiger[10] is investigated, and following that approach, a MIMD based algorithm is developed and implemented on a network of T800 transputers under the Trollius operating system. A serial version of the algorithm has also been implemented on a SUN 4 under Unix. The network of transputers is configured as a 2-dimensional mesh of processors (currently 16 configured as a 4 x 4 mesh), and the input partitioning method is used to distribute the original image across the network. The implementation of the algorithm is described, and the suitability of the transputer for image processing tasks is discussed. The algorithm was applied to a number of images for edge detection, and produced good results in a small number of iterations.
Science, Faculty of
Computer Science, Department of
Graduate
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Fernandez-Duran, Juan Jose. "Statistical techniques for clutter removal and attentuation detection in weather radar data." Thesis, University of Essex, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243358.

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Toftaker, Håkon. "Automatic Parametrisation and Block pseudo Likelihood Estimation for binary Markov random Fields." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9705.

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Discrete Markov random fields play an important role in spatial statistics, and are applied in many different areas. Models which consider only pairwise interaction between sites such as the Ising model often perform well as a prior in a Bayesian setting but are generally unable to provide a realistic representation of a typical scene. Models which are defined by considering more than only two points have been shown to do well in describing many different types of textures. The specification of such models is often rather tedious, both in defining the parametric model, and in estimating the parameters. In this paper we present a procedure which in an automatic fashion defines a parametric model from a training image. On the basis of the frequencies of the different types of local configurations we define the potential function of all the different clique configurations from a relatively small number of parameters. Then we make use of a forward-backward algorithm to compute a maximum block pseudo likelihood estimator for the parametric models resulting from the automatic procedure. Then this set of methods is used to define Markov random field models from three different training images. The same algorithm which is used to calculate the block pseudo likelihood is used to implement a block Gibbs sampler. This is used to explore the properties of the models through simulation. The procedure is tested for a set of different input values. The analysis shows that the procedure is quite able to produce a reasonable presentation for one of the training images but performs insufficiently on the others. The main problem seems to be the ratio between black and white, and this seems to be a problem caused mainly by the estimator. It is therefore difficult to make a conclusion about the quality of the parametric model. We also show that by modifying the estimated potential function slightly we can get a model which is able to describe the second training image quite well.

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Altay, Suhan. "On Forward Interest Rate Models: Via Random Fields And Markov Jump Processes." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608342/index.pdf.

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The essence of the interest rate modeling by using Heath-Jarrow-Morton framework is to find the drift condition of the instantaneous forward rate dynamics so that the entire term structure is arbitrage free. In this study, instantaneous forward interest rates are modeled using random fields and Markov Jump processes and the drift conditions of the forward rate dynamics are given. Moreover, the methodology presented in this study is extended to certain financial settings and instruments such as multi-country interest rate models, term structure of defaultable bond prices and forward measures. Also a general framework for bond prices via nuclear space valued semi-martingales is introduced.
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Caputo, Barbara. "A new kernel method for object recognition : spin glass-Markov random fields /." Stockholm, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-58.

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Muffert, Maximilian [Verfasser]. "Incremental Map Building with Markov Random Fields and its Evaluation / Maximilian Muffert." Bonn : Universitäts- und Landesbibliothek Bonn, 2018. http://d-nb.info/1155302990/34.

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Dai, Zhenwen, and 戴振文. "A Markov random field approach for multi-view normal integration." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B4308588X.

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Dai, Zhenwen. "A Markov random field approach for multi-view normal integration." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B4308588X.

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Wehmann, Adam. "A Spatial-Temporal Contextual Kernel Method for Generating High-Quality Land-Cover Time Series." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1398866264.

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37

Minin, Volodymyr. "Exploring evolutionary heterogeneity with change-point models, Gaussian Markov random fields, and Markov chain induced counting processes." Diss., Restricted to subscribing institutions, 2007. http://proquest.umi.com/pqdweb?did=1320942721&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.

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38

Fauske, Johannes. "An empirical study of the maximum pseudo-likelihood for discrete Markov random fields." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2009. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9949.

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In this text we will look at two parameter estimation methods for Markov random fields on a lattice. They are maximum pseudo-likelihood estimation and maximum general pseudo-likelihood estimation, which we abbreviate MPLE and MGPLE. The idea behind them is that by maximizing an approximation of the likelihood function, we avoid computing cumbersome normalising constants. In MPLE we maximize the product of the conditional distributions for each variable given all the other variables. In MGPLE we use a compromise between pseudo-likelihood and the likelihood function as the approximation. We evaluate and compare the performance of MPLE and MGPLE on three different spatial models, which we have generated observations of. We are specially interested to see what happens with the quality of the estimates when the number of observations increases. The models we use are the Ising model, the extended Ising model and the Sisim model. All the random variables in the models have two possible states, black or white. For the Ising and extended Ising model we have one and three parameters respectively. For Sisim we have $13$ parameters. The quality of both methods get better when the number of observations grow, and MGPLE gives better results than MPLE. However certain parameter combinations of the extended Ising model give worse results.

39

Villanueva-Morales, Antonio. "Modified pseudo-likelihood estimation for Markov random fields with Winsorized Poisson conditional distributions." [Ames, Iowa : Iowa State University], 2008.

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40

Tang, Kam-Lun. "A Markov random field formulation for dense photometric stereo : theory, practice and applications /." View abstract or full-text, 2005. http://library.ust.hk/cgi/db/thesis.pl?COMP%202005%20TANG.

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41

Shakya, Siddhartha. "DEUM : a framework for an estimation of distribution algorithm based on Markov random fields." Thesis, Robert Gordon University, 2006. http://hdl.handle.net/10059/39.

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Estimation of Distribution Algorithms (EDAs) belong to the class of population based optimisation algorithms. They are motivated by the idea of discovering and exploiting the interaction between variables in the solution. They estimate a probability distribution from population of solutions, and sample it to generate the next population. Many EDAs use probabilistic graphical modelling techniques for this purpose. In particular, directed graphical models (Bayesian networks) have been widely used in EDA. This thesis proposes an undirected graphical model (Markov Random Field (MRF)) approach to estimate and sample the distribution in EDAs. The interaction between variables in the solution is modelled as an undirected graph and the joint probability of a solution is factorised as a Gibbs distribution. The thesis describes a model of fitness function that approximates the energy in the Gibbs distribution, and shows how this model can be fitted to a population of solutions to estimate the parameters of the MRF. The estimated MRF is then sampled to generate the next population. This approach is applied to estimation of distribution in a general framework of an EDA, called Distribution Estimation using Markov Random Fields (DEUM). The thesis then proposes several variants of DEUM using different sampling techniques and tests their performance on a range of optimisation problems. The results show that, for most of the tested problems, the DEUM algorithms significantly outperform other EDAs, both in terms of number of fitness evaluations and the quality of the solutions found by them. There are two main explanations for the success of DEUM algorithms. Firstly, DEUM builds a model of fitness function to approximate the MRF. This contrasts with other EDAs, which build a model of selected solutions. This allows DEUM to use fitness in variation part of the evolution. Secondly, DEUM exploits the temperature coefficient in the Gibbs distribution to regulate the behaviour of the algorithm. In particular, with higher temperature, the distribution is closer to being uniform and with lower temperature it concentrates near some global optima. This gives DEUM an explicit control over the convergence of the algorithm, resulting in better optimisation.
42

Wang, Shiyun. "Connection between Graphical Potential Games and Markov Random Fields with an Extension to Bayesian Networks." Thesis, California State University, Long Beach, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10785804.

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A probabilistic graphical model is a graphical representation of a joint probability distribution, in which the conditional independencies among random variables are specified via an underlying graph. We connect the probabilistic graphical models to some special types of games. Graphical potential games are the intersection of potential games and graphical games. They have characteristics from both of these two classes of games, namely, potential functions of potential games and graphical structure of graphical games. We review that there is a bijection between the normalized graphical potential games and the corresponding Markov Random Fields. We use a similar method to study the structure of Bayesian networks and define two types of games on directed graphs whose nodes are players. One is the directed graphical game, which is defined based on the assumption that the utility of player i only depends on the parent of i in the graph. The other one is the Bayesian-factorable potential game. The potential function of the game gives rise to the probability distribution, which can be factorized as in a Bayesian network. We explore the connections between such games and Bayesian networks.

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Marqués, Acosta Fernando. "Multiresolution image segmentation based on camporend random fields: Application to image coding." Doctoral thesis, Universitat Politècnica de Catalunya, 1992. http://hdl.handle.net/10803/6910.

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La segmentación de imágenes es una técnica que tiene como finalidad dividir una imagen en un conjunto de regiones, asignando a cada objeto en la escena una o varias regiones. Para obtener una segmentación correcta, cada una de las regiones debe cumplir con un criterio de homogeneidad impuesto a priori. Cuando se fija un criterio de homogeneidad, lo que implícitamente se esta haciendo es asumir un modelo matemático que caracteriza las regiones.

En esta tesis se introduce un nuevo tipo de modelo denominado modelo jerárquico, ya que tiene dos niveles diferentes sobrepuestos uno sobre el otro. El nivel inferior (o subyacente) modela la posición que ocupa cada una de las regiones dentro de la imagen; mientras que, por su parte, el nivel superior (u observable) esta compuesto por un conjunto de submodelos independientes (un submodelo por región) que caracterizan el comportamiento del interior de las regiones. Para el primero se usa un campo aleatorio Markoviano de orden dos que modelara los contornos de las regiones, mientras que para el segundo nivel se usa un modelo Gausiano.

En el trabajo se estudian los mejores potenciales que deben asignarse a los tipos de agrupaciones que permiten definir los contornos. Con todo ello la segmentación se realiza buscando la partición más probable (criterio MAP) para una realización concreta (imagen observable).

El proceso de búsqueda de la partición optima para imágenes del tamaño habitual seria prácticamente inviable desde un punto de vista de tiempo de cálculo. Para que se pueda realizar debe partirse de una estimación inicial suficientemente buena y de una algoritmo rápido de mejora como es una búsqueda local. Para ello se introduce la técnica de segmentación piramidal (multirresolucion). La pirámide se genera con filtrado Gausiano y diezmado. En el nivel mas alto de la pirámide, al tener pocos píxels, si que se puede encontrar la partición óptima.
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Kornak, John. "Bayesian spatial inference from haemodynamic response parameters in functional magnetic resonance imaging." Thesis, University of Nottingham, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325718.

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Kim, Kyu-Heon. "Segmentation of natural texture images using a robust stochastic image model." Thesis, University of Newcastle Upon Tyne, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307927.

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46

Zhang, Xiaodan Hu Xiaohua. "Exploiting external/domain knowledge to enhance traditional text mining using graph-based methods /." Philadelphia, Pa. : Drexel University, 2009. http://hdl.handle.net/1860/3076.

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Liang, Dong. "Issues in Bayesian Gaussian Markov random field models with application to intersensor calibration." Diss., University of Iowa, 2009. https://ir.uiowa.edu/etd/400.

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A long term record of the earth's vegetation is important in studies of global climate change. Over the last three decades, multiple data sets on vegetation have been collected using different satellite-based sensors. There is a need for methods that combine these data into a long term earth system data record. The Advanced Very High Resolution Radiometer (AVHRR) has provided reflectance measures of the entire earth since 1978. Physical and statistical models have been used to improve the consistency and reliability of this record. The Moderated Resolution Imaging Spectroradiometer (MODIS) has provided measurements with superior radiometric properties and geolocation accuracy. However, this record is available only since 2000. In this thesis, we perform statistical calibration of AVHRR to MODIS. We aim to: (1) fill in gaps in the ongoing MODIS record; (2) extend MODIS values back to 1982. We propose Bayesian mixed models to predict MODIS values using snow cover and AVHRR values as covariates. Random effects are used to account for spatiotemporal correlation in the data. We estimate the parameters based on the data after 2000, using Markov chain Monte Carlo methods. We then back-predict MODIS data between 1978 and 1999, using the posterior samples of the parameter estimates. We develop new Conditional Autoregressive (CAR) models for seasonal data. We also develop new sampling methods for CAR models. Our approach enables filling in gaps in the MODIS record and back-predicting these values to construct a consistent historical record. The Bayesian framework incorporates multiple sources of variation in estimating the accuracy of the obtained data. The approach is illustrated using vegetation data over a region in Minnesota.
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Zhu, Ying. "Signal detection on two-dimensional intersymbol interference channels correlated sources and reduced complexity algorithms /." [Pullman, Wash.] : Washington State University, 2008. http://www.dissertations.wsu.edu/Dissertations/Fall2008/y_zhu_081408.pdf.

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Thesis (Ph. D.)--Washington State University, December 2008.
Title from PDF title page (viewed on Sept. 23, 2008) "School of Electrical Engineering and Computer Science." Includes bibliographical references (p. 83-90).
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Tran, The Truyen. "On conditional random fields: applications, feature selection, parameter estimation and hierarchical modelling." Thesis, Curtin University, 2008. http://hdl.handle.net/20.500.11937/436.

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There has been a growing interest in stochastic modelling and learning with complex data, whose elements are structured and interdependent. One of the most successful methods to model data dependencies is graphical models, which is a combination of graph theory and probability theory. This thesis focuses on a special type of graphical models known as Conditional Random Fields (CRFs) (Lafferty et al., 2001), in which the output state spaces, when conditioned on some observational input data, are represented by undirected graphical models. The contributions of thesis involve both (a) broadening the current applicability of CRFs in the real world and (b) deepening the understanding of theoretical aspects of CRFs. On the application side, we empirically investigate the applications of CRFs in two real world settings. The first application is on a novel domain of Vietnamese accent restoration, in which we need to restore accents of an accent-less Vietnamese sentence. Experiments on half a million sentences of news articles show that the CRF-based approach is highly accurate. In the second application, we develop a new CRF-based movie recommendation system called Preference Network (PN). The PN jointly integrates various sources of domain knowledge into a large and densely connected Markov network. We obtained competitive results against well-established methods in the recommendation field.On the theory side, the thesis addresses three important theoretical issues of CRFs: feature selection, parameter estimation and modelling recursive sequential data. These issues are all addressed under a general setting of partial supervision in that training labels are not fully available. For feature selection, we introduce a novel learning algorithm called AdaBoost.CRF that incrementally selects features out of a large feature pool as learning proceeds. AdaBoost.CRF is an extension of the standard boosting methodology to structured and partially observed data. We demonstrate that the AdaBoost.CRF is able to eliminate irrelevant features and as a result, returns a very compact feature set without significant loss of accuracy. Parameter estimation of CRFs is generally intractable in arbitrary network structures. This thesis contributes to this area by proposing a learning method called AdaBoost.MRF (which stands for AdaBoosted Markov Random Forests). As learning proceeds AdaBoost.MRF incrementally builds a tree ensemble (a forest) that cover the original network by selecting the best spanning tree at a time. As a result, we can approximately learn many rich classes of CRFs in linear time. The third theoretical work is on modelling recursive, sequential data in that each level of resolution is a Markov sequence, where each state in the sequence is also a Markov sequence at the finer grain. One of the key contributions of this thesis is Hierarchical Conditional Random Fields (HCRF), which is an extension to the currently popular sequential CRF and the recent semi-Markov CRF (Sarawagi and Cohen, 2004). Unlike previous CRF work, the HCRF does not assume any fixed graphical structures.Rather, it treats structure as an uncertain aspect and it can estimate the structure automatically from the data. The HCRF is motivated by Hierarchical Hidden Markov Model (HHMM) (Fine et al., 1998). Importantly, the thesis shows that the HHMM is a special case of HCRF with slight modification, and the semi-Markov CRF is essentially a flat version of the HCRF. Central to our contribution in HCRF is a polynomial-time algorithm based on the Asymmetric Inside Outside (AIO) family developed in (Bui et al., 2004) for learning and inference. Another important contribution is to extend the AIO family to address learning with missing data and inference under partially observed labels. We also derive methods to deal with practical concerns associated with the AIO family, including numerical overflow and cubic-time complexity. Finally, we demonstrate good performance of HCRF against rivals on two applications: indoor video surveillance and noun-phrase chunking.
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Kutarnia, Jason Francis. "A Markov Random Field Based Approach to 3D Mosaicing and Registration Applied to Ultrasound Simulation." Digital WPI, 2014. https://digitalcommons.wpi.edu/etd-dissertations/369.

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" A novel Markov Random Field (MRF) based method for the mosaicing of 3D ultrasound volumes is presented in this dissertation. The motivation for this work is the production of training volumes for an affordable ultrasound simulator, which offers a low-cost/portable training solution for new users of diagnostic ultrasound, by providing the scanning experience essential for developing the necessary psycho-motor skills. It also has the potential for introducing ultrasound instruction into medical education curriculums. The interest in ultrasound training stems in part from the widespread adoption of point-of-care scanners, i.e. low cost portable ultrasound scanning systems in the medical community. This work develops a novel approach for producing 3D composite image volumes and validates the approach using clinically acquired fetal images from the obstetrics department at the University of Massachusetts Medical School (UMMS). Results using the Visible Human Female dataset as well as an abdominal trauma phantom are also presented. The process is broken down into five distinct steps, which include individual 3D volume acquisition, rigid registration, calculation of a mosaicing function, group-wise non-rigid registration, and finally blending. Each of these steps, common in medical image processing, has been investigated in the context of ultrasound mosaicing and has resulted in improved algorithms. Rigid and non-rigid registration methods are analyzed in a probabilistic framework and their sensitivity to ultrasound shadowing artifacts is studied. The group-wise non-rigid registration problem is initially formulated as a maximum likelihood estimation, where the joint probability density function is comprised of the partially overlapping ultrasound image volumes. This expression is simplified using a block-matching methodology and the resulting discrete registration energy is shown to be equivalent to a Markov Random Field. Graph based methods common in computer vision are then used for optimization, resulting in a set of transformations that bring the overlapping volumes into alignment. This optimization is parallelized using a fusion approach, where the registration problem is divided into 8 independent sub-problems whose solutions are fused together at the end of each iteration. This method provided a speedup factor of 3.91 over the single threaded approach with no noticeable reduction in accuracy during our simulations. Furthermore, the registration problem is simplified by introducing a mosaicing function, which partitions the composite volume into regions filled with data from unique partially overlapping source volumes. This mosaicing functions attempts to minimize intensity and gradient differences between adjacent sources in the composite volume. Experimental results to demonstrate the performance of the group-wise registration algorithm are also presented. This algorithm is initially tested on deformed abdominal image volumes generated using a finite element model of the Visible Human Female to show the accuracy of its calculated displacement fields. In addition, the algorithm is evaluated using real ultrasound data from an abdominal phantom. Finally, composite obstetrics image volumes are constructed using clinical scans of pregnant subjects, where fetal movement makes registration/mosaicing especially difficult. Our solution to blending, which is the final step of the mosaicing process, is also discussed. The trainee will have a better experience if the volume boundaries are visually seamless, and this usually requires some blending prior to stitching. Also, regions of the volume where no data was collected during scanning should have an ultrasound-like appearance before being displayed in the simulator. This ensures the trainee's visual experience isn't degraded by unrealistic images. A discrete Poisson approach has been adapted to accomplish these tasks. Following this, we will describe how a 4D fetal heart image volume can be constructed from swept 2D ultrasound. A 4D probe, such as the Philips X6-1 xMATRIX Array, would make this task simpler as it can acquire 3D ultrasound volumes of the fetal heart in real-time; However, probes such as these aren't widespread yet. Once the theory has been introduced, we will describe the clinical component of this dissertation. For the purpose of acquiring actual clinical ultrasound data, from which training datasets were produced, 11 pregnant subjects were scanned by experienced sonographers at the UMMS following an approved IRB protocol. First, we will discuss the software/hardware configuration that was used to conduct these scans, which included some custom mechanical design. With the data collected using this arrangement we generated seamless 3D fetal mosaics, that is, the training datasets, loaded them into our ultrasound training simulator, and then subsequently had them evaluated by the sonographers at the UMMS for accuracy. These mosaics were constructed from the raw scan data using the techniques previously introduced. Specific training objectives were established based on the input from our collaborators in the obstetrics sonography group. Important fetal measurements are reviewed, which form the basis for training in obstetrics ultrasound. Finally clinical images demonstrating the sonographer making fetal measurements in practice, which were acquired directly by the Philips iU22 ultrasound machine from one of our 11 subjects, are compared with screenshots of corresponding images produced by our simulator. "
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