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**11 - 19**of**19**### Segmenting Lumbar Vertebrae in Digital Video Fluoroscopic Images through Edge Enhancement

"... Video fluoroscopy provides a cost effective way for the diagnosis of low back pain. Backbones or vertebrae are usually segmented manually from fluoroscopic images of low quality during such a diagnosis. In this paper, we try to reduce human workload by performing automatic vertebrae detection and se ..."

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Video fluoroscopy provides a cost effective way for the diagnosis of low back pain. Backbones or vertebrae are usually segmented manually from fluoroscopic images of low quality during such a diagnosis. In this paper, we try to reduce human workload by performing automatic vertebrae detection and segmentation. Operators need to provide the rough location of landmarks only. The proposed algorithm will perform edge detection, which is based on pattern recognition of texture, along the snake formed from the landmarks. The snake will then attach to the edge detected. Experimental results show that the proposed system can segment vertebrae from video fluoroscopic image automatically and accurately. 1

### Hidden Markov Multiresolution Texture Segmentation

"... A texture segmentation algorithm is developed, utilizing a wavelet-based multi-resolution analysis of general imagery. The wavelet analysis yields a set of quadtrees, each composed of highhigh (HH), high-low (HL) and low-high (LH) wavelet coefficients. Hidden Markov trees (HMTs) are designed for the ..."

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A texture segmentation algorithm is developed, utilizing a wavelet-based multi-resolution analysis of general imagery. The wavelet analysis yields a set of quadtrees, each composed of highhigh (HH), high-low (HL) and low-high (LH) wavelet coefficients. Hidden Markov trees (HMTs) are designed for the quadtree HH, HL and LH wavelet coefficients. Many textures have intricate structure, extending beyond the support of a single quadtree. Therefore, for a given texture we define a set of states, each characterized by unique statistics. The state occupied by a given quadtree is "hidden", and a hidden Markov model (HMM) is developed to characterize the statistics of a given quadtree with respect to the statistics of surrounding quadtrees. Each HMM state is characterized by a unique set of HMTs (one each for the HH, HL and LH wavelet coefficients). An HMM-HMT model is developed for each texture of interest, with which texture segmentation is achieved. Several numerical examples are presented to demonstrate the model, with comparisons to alternative approaches.

### Certified by..........................................................

, 2003

"... This thesis develops the novel method of recursive cavity modeling as a tractable approach to approximate inference in large Gauss-Markov random fields. The main idea is to recursively dissect the field, constructing a cavity model for each subfield at each level of dissection. The cavity model prov ..."

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This thesis develops the novel method of recursive cavity modeling as a tractable approach to approximate inference in large Gauss-Markov random fields. The main idea is to recursively dissect the field, constructing a cavity model for each subfield at each level of dissection. The cavity model provides a compact yet (nearly) faithful model for the surface of one subfield sufficient for inferring other parts of the field. This basic idea is developed into a two-pass inference/modeling procedure which recursively builds cavity models by an “upward ” pass and then builds complementary blanket models by a “downward ” pass. Marginal models are then constructed at the finest level of dissection. Information-theoretic principles are employed for model thinning so as to develop compact yet faithful cavity and blanket models thereby providing tractable yet near-optimal inference. In this regard, recursive cavity modeling blends recursive inference and iterative modeling methodologies. While the main focus is on Gaussian processes, general principles are emphasized throughout suggesting the applicability of the basic framework for more general families of Markov random fields.

### 1 Estimation in Gaussian Graphical Models using Tractable Subgraphs: A Walk-Sum Analysis

"... Abstract — Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a ge ..."

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Abstract — Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure. These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as Embedded Trees, serial iterations such as block Gauss-Seidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walk-sum interpretation of Gaussian inference. We describe the walks “computed ” by the algorithms using walk-sum diagrams, and show that for iterations based on a very large and flexible set of sequences of subgraphs, convergence is guaranteed in walksummable models. Consequently, we are free to choose spanning trees and subsets of variables adaptively at each iteration. This leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error. Simulation results demonstrate that these non-stationary algorithms provide a significant speedup in convergence over traditional one-tree and two-tree iterations. Index Terms — Graphical models, Gauss-Markov Random Fields, walk-sums, distributed estimation, walk-sum diagrams,

### Tree-Structured Graphical Models

, 2010

"... on December 13, 2010, in partial fulfilment of the requirements for the degree of ..."

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on December 13, 2010, in partial fulfilment of the requirements for the degree of

### Sparse Ising Models with Covariates

, 2014

"... There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the binary data, and may influence the dependence relationships. M ..."

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There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the binary data, and may influence the dependence relationships. Motivated by such a dataset on genomic instability collected from tumor samples of several types, we propose a sparse covariate dependent Ising model to study both the conditional dependency within the binary data and its relationship with the additional covariates. This results in subject-specific Ising models, where the subject’s covariates influence the strength of association between the genes. As in all exploratory data analysis, interpretability of results is important, and we use `1 penalties to induce sparsity in the fitted graphs and in the number of selected covariates. Two algorithms to fit the model are proposed and compared on a set of simulated data, and asymptotic results are established. The results on the tumor dataset and their biological significance are discussed in detail.

### CONDITIONAL MARKOV MODELS

"... We are interested in developing digital image restoration algorithms using a class of spatial interaction models known as conditional Markov models. Our approach is to represent the images by Markov models on toroidal lattices and develop minimum mean square error (MMSE) restoration algorithms. The ..."

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We are interested in developing digital image restoration algorithms using a class of spatial interaction models known as conditional Markov models. Our approach is to represent the images by Markov models on toroidal lattices and develop minimum mean square error (MMSE) restoration algorithms. The algorithms are non-recursive in structure and due to the under-lying representation on toroidal lattices can be implemented using FFT algorithms. We give two types of algorithms. First we assume that a prototype of the original image is available and develop algorithms for restoration of degraded images. The degradation is assumed to be due to a known space invariant, non-separable, Speriodic point spread function and additive white noise. Secondly, we consider the more general situation when a proto-type image is not available and give algorithms for MMSE filtering of no'- y images. Experimental results are given for the above cases.

### Robust Gaussian Graphical Modeling with the Trimmed Graphical Lasso

"... Gaussian Graphical Models (GGMs) are popular tools for studying network struc-tures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with out-liers or heavier tails than the Gaussian distribution. In this pap ..."

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Gaussian Graphical Models (GGMs) are popular tools for studying network struc-tures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with out-liers or heavier tails than the Gaussian distribution. In this paper, we propose the Trimmed Graphical Lasso for robust estimation of sparse GGMs. Our method guards against outliers by an implicit trimming mechanism akin to the popular Least Trimmed Squares method used for linear regression. We provide a rigorous statistical analysis of our estimator in the high-dimensional setting. In contrast, existing approaches for robust sparse GGMs estimation lack statistical guaran-tees. Our theoretical results are complemented by experiments on simulated and real gene expression data which further demonstrate the value of our approach. 1

### Methods for Inference in Graphical Models

, 2014

"... Graphical models provide a flexible, powerful and compact way to model relationships between random variables, and have been applied with great success in many domains. Combining prior beliefs with observed evidence to form a prediction is called inference. Prob-lems of great interest include findin ..."

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Graphical models provide a flexible, powerful and compact way to model relationships between random variables, and have been applied with great success in many domains. Combining prior beliefs with observed evidence to form a prediction is called inference. Prob-lems of great interest include finding a configuration with highest probability (MAP inference) or solving for the distribution over a subset of variables (marginal inference). Further, these methods are often critical subroutines for learning the relationships. However, inference is computationally intractable in general. Hence, much effort has focused on two themes: finding subdomains where exact inference is solvable efficiently, or identifying approximate methods that work well. We ex-plore both these themes, restricting attention to undirected graphical models with discrete variables. First we address exact MAP inference by advancing the recent method of reducing the problem to finding a maximum weight stable set (MWSS) on a derived graph, which, if perfect, admits poly-nomial time inference. We derive new results for this approach, including a general decomposition theorem for models of any order and number of labels, extensions of results for binary pairwise models with submodular cost functions to higher order, and a characterization of which binary pair-wise models can be efficiently solved with this method. This clarifies the power of the approach on