A Markov Random Field Based Approach to 3D Mosaicing and Registration Applied to Ultrasound Simulation

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\u27s visual experience isn\u27t 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\u27t 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

Modeling Dynamic Swarms

This paper proposes the problem of modeling video sequences of dynamic swarms (DS). We define DS as a large layout of stochastically repetitive spatial configurations of dynamic objects (swarm elements) whose motions exhibit local spatiotemporal interdependency and stationarity, i.e., the motions are similar in any small spatiotemporal neighborhood. Examples of DS abound in nature, e.g., herds of animals and flocks of birds. To capture the local spatiotemporal properties of the DS, we present a probabilistic model that learns both the spatial layout of swarm elements and their joint dynamics that are modeled as linear transformations. To this end, a spatiotemporal neighborhood is associated with each swarm element, in which local stationarity is enforced both spatially and temporally. We assume that the prior on the swarm dynamics is distributed according to an MRF in both space and time. Embedding this model in a MAP framework, we iterate between learning the spatial layout of the swarm and its dynamics. We learn the swarm transformations using ICM, which iterates between estimating these transformations and updating their distribution in the spatiotemporal neighborhoods. We demonstrate the validity of our method by conducting experiments on real video sequences. Real sequences of birds, geese, robot swarms, and pedestrians evaluate the applicability of our model to real world data.Comment: 11 pages, 17 figures, conference paper, computer visio

Multispectral texture synthesis

Synthesizing texture involves the ordering of pixels in a 2D arrangement so as to display certain known spatial correlations, generally as described by a sample texture. In an abstract sense, these pixels could be gray-scale values, RGB color values, or entire spectral curves. The focus of this work is to develop a practical synthesis framework that maintains this abstract view while synthesizing texture with high spectral dimension, effectively achieving spectral invariance. The principle idea is to use a single monochrome texture synthesis step to capture the spatial information in a multispectral texture. The first step is to use a global color space transform to condense the spatial information in a sample texture into a principle luminance channel. Then, a monochrome texture synthesis step generates the corresponding principle band in the synthetic texture. This spatial information is then used to condition the generation of spectral information. A number of variants of this general approach are introduced. The first uses a multiresolution transform to decompose the spatial information in the principle band into an equivalent scale/space representation. This information is encapsulated into a set of low order statistical constraints that are used to iteratively coerce white noise into the desired texture. The residual spectral information is then generated using a non-parametric Markov Ran dom field model (MRF). The remaining variants use a non-parametric MRF to generate the spatial and spectral components simultaneously. In this ap proach, multispectral texture is grown from a seed region by sampling from the set of nearest neighbors in the sample texture as identified by a template matching procedure in the principle band. The effectiveness of both algorithms is demonstrated on a number of texture examples ranging from greyscale to RGB textures, as well as 16, 22, 32 and 63 band spectral images. In addition to the standard visual test that predominates the literature, effort is made to quantify the accuracy of the synthesis using informative and effective metrics. These include first and second order statistical comparisons as well as statistical divergence tests

One-class Support Vector Machines Approach for Trust-Aware Recommendation Systems

As the amount of information users interact with every day continue to grow, filtering it for useful information is increasingly important. One of the most useful tools for this task are recommender systems (RS). These look at past products the user has interacted with and recommends similar products. However, these suffer from a major issue, cold-start, in which there is difficulty in producing recommendations for new users. One of the suggested techniques for mitigating the cold-start issue is the use of trust data. By using the relationships between users such as friendships on social media or following reviewers of movies the recommender system can recommend products that the user’s friend would rate highly as well. We extend previous trust models by applying a One-Class Support Vector Machine model to the known trust relations and predicting distrust relations among users. This is shown to improve the predictions movie ratings in some circumstances.

Identifying functionally and topologically cohesive modules in protein interaction networks

Abstract unavailable please refer to PD

On the Study of Fitness Landscapes and the Max-Cut Problem

The goal of this thesis is to study the complexity of NP-Hard problems, using the Max-Cut and the Max-k-Cut problems, and the study of fitness landscapes. The Max-Cut and Max-k-Cut problems are well studied NP-hard problems specially since the approximation algorithm of Goemans and Williamson (1995) which introduced the use of SDP to solve relaxed problems. In order to prove the existence of a performance guarantee, the rounding step from the SDP solution to a Max-Cut solution is simple and randomized. For the Max-k-Cut problem, there exist several approximation algorithms but many of them have been proved to be equivalent. Similarly as in Max-Cut, these approximation algorithms use a simple randomized rounding to be able to get a performance guarantee. Ignoring for now the performance guarantee, one could ask if there is a rounding process that takes into account the structure of the relaxed solution since it is the result of an optimization problem. In this thesis we answered this question positively by using clustering as a rounding method. In order to compare the performance of both algorithms, a series of experiments were performed using the so-called G-set benchmark for the Max-Cut problem and using the Random Graph Benchmark of Goemans1995 for the Max-k-Cut problem. With this new rounding, larger cut values are found both for the Max-Cut and the Max-k-Cut problems, and always above the value of the performance guarantee of the approximation algorithm. This suggests that taking into account the structure of the problem to design algorithms can lead to better results, possibly at the cost of a worse performance guarantee. An example for the vertex k-center problem can be seen in Garcia-Diaz et al. (2017), where a 3-approximation algorithm performs better than a 2-approximation algorithm despite having a worse performance guarantee. Landscapes over discrete configurations spaces are an important model in evolutionary and structural biology, as well as many other areas of science, from the physics of disordered systems to operations research. A landscape is a function defined on a very large discrete set V that carries an additional metric or at least topological structure into the real numbers R. We will consider landscapes defined on the vertex set of undirected graphs. Thus let G=G(V,E) be an undirected graph and f an arbitrary real-valued function taking values from V . We will refer to the triple (V,E,f) as a landscape over G. We say two configurations x,y in V are neutral if f(x)=f(y). We colloquially refer to a landscape as 'neutral'' if a substantial fraction of adjacent pairs of configurations are neutral. A flat landscape is one where f is constant. The opposite of flatness is ruggedness and it is defined as the number of local optima or by means of pair correlation functions. These two key features of a landscape, ruggedness and neutrality, appear to be two sides of the same coin. Ruggedness can be measured either by correlation properties, which are sensitive to monotonic transformation of the landscape, and by combinatorial properties such as the lengths of downhill paths and the number of local optima, which are invariant under monotonic transformations. The connection between the two views has remained largely unexplored and poorly understood. For this thesis, a survey on fitness landscapes is presented, together with the first steps in the direction to find this connection together with a relation between the covariance matrix of a random landscape model and its ruggedness

Estimation of Distribution Algorithms and Minimum Relative Entropy

In the field of optimization using probabilistic models of the search space, this thesis identifies and elaborates several advancements in which the principles of maximum entropy and minimum relative entropy from information theory are used to estimate a probability distribution. The probability distribution within the search space is represented by a graphical model (factorization, Bayesian network or junction tree). An estimation of distribution algorithm (EDA) is an evolutionary optimization algorithm which uses a graphical model to sample a population within the search space and then estimates a new graphical model from the selected individuals of the population. - So far, the Factorized Distribution Algorithm (FDA) builds a factorization or Bayesian network from a given additive structure of the objective function to be optimized using a greedy algorithm which only considers a subset of the variable dependencies. Important connections can be lost by this method. This thesis presents a heuristic subfunction merge algorithm which is able to consider all dependencies between the variables (as long as the marginal distributions of the model do not become too large). On a 2-D grid structure, this algorithm builds a pentavariate factorization which allows to solve the deceptive grid benchmark problem with a much smaller population size than the conventional factorization. Especially for small population sizes, calculating large marginal distributions from smaller ones using Maximum Entropy and iterative proportional fitting leads to a further improvement. - The second topic is the generalization of graphical models to loopy structures. Using the Bethe-Kikuchi approximation, the loopy graphical model (region graph) can learn the Boltzmann distribution of an objective function by a generalized belief propagation algorithm (GBP). It minimizes the free energy, a notion adopted from statistical physics which is equivalent to the relative entropy to the Boltzmann distribution. Previous attempts to combine the Kikuchi approximation with EDA have relied on an expensive Gibbs sampling procedure for generating a population from this loopy probabilistic model. In this thesis a combination with a factorization is presented which allows more efficient sampling. The free energy is generalized to incorporate the inverse temperature ß. The factorization building algorithm mentioned above can be employed here, too. The dynamics of GBP is investigated, and the method is applied on Ising spin glass ground state search. Small instances (7 x 7) are solved without difficulty. Larger instances (10 x 10 and 15 x 15) do not converge to the true optimum with large ß, but sampling from the factorization can find the optimum with about 1000-10000 sampling attempts, depending on the instance. If GBP does not converge, it can be replaced by a concave-convex procedure which guarantees convergence. - Third, if no probabilistic structure is given for the objective function, a Bayesian network can be learned to capture the dependencies in the population. The relative entropy between the population-induced distribution and the Bayesian network distribution is equivalent to the log-likelihood of the model. The log-likelihood has been generalized to the BIC/MDL score which reduces overfitting by punishing complicated structure of the Bayesian network. A previous information theoretic analysis of BIC/MDL in the context of EDA is continued, and empiric evidence is given that the method is able to learn the correct structure of an objective function, given a sufficiently large population. - Finally, a way to reduce the search space of EDA is presented by combining it with a local search heuristics. The Kernighan Lin hillclimber, known originally for the traveling salesman problem and graph bipartitioning, is generalized to arbitrary binary problems. It can be applied in a stand-alone manner, as an iterative 1+1 search algorithm, or combined with EDA. On the MAXSAT problem it performs in a similar scale to the specialized SAT solver Walksat. An analysis of the Kernighan Lin local optima indicates that the combination with an EDA is favorable. The thesis shows how evolutionary optimization can be improved using interdisciplinary results from information theory, statistics, probability calculus and statistical physics. The principles of information theory for estimating probability distributions are applicable in many areas. EDAs are a good application because an improved estimation affects directly the optimization success.Estimation of Distribution Algorithms und Minimierung der relativen Entropie Im Bereich der Optimierung mit probabilistischen Modellen des Suchraums werden einige Fortschritte identifiziert und herausgearbeitet, in denen die Prinzipien der maximalen Entropie und der minimalen relativen Entropie aus der Informationstheorie verwendet werden, um eine Wahrscheinlichkeitsverteilung zu schätzen. Die Wahrscheinlichkeitsverteilung im Suchraum wird durch ein graphisches Modell beschrieben (Faktorisierung, Bayessches Netz oder Verbindungsbaum). Ein Estimation of Distribution Algorithm (EDA) ist ein evolutionärer Optimierungsalgorithmus, der mit Hilfe eines graphischen Modells eine Population im Suchraum erzeugt und dann anhand der selektierten Individuen dieser Population ein neues graphisches Modell erzeugt. - Bislang baut der Factorized Distribution Algorithm (FDA) eine Faktorisierung oder ein Bayessches Netz aus einer gegebenen additiven Struktur der Zielfunktion durch einen Greedy-Algorithmus, der nur einen Teil der Verbindungen zwischen den Variablen berücksichtigt. Wichtige verbindungen können durch diese Methode verloren gehen. Diese Arbeit stellt einen heuristischen Subfunktionenverschmelzungsalgorithmus vor, der in der Lage ist, alle Abhängigkeiten zwischen den Variablen zu berücksichtigen (wofern die Randverteilungen des Modells nicht zu groß werden). Auf einem 2D-Gitter erzeugt dieser Algorithmus eine pentavariate Faktorisierung, die es ermöglicht, das Deceptive-Grid-Testproblem mit viel kleinerer Populationsgröße zu lösen als mit der konventionellen Faktorisierung. Insbesondere für kleine Populationsgrößen kann das Ergebnis noch verbessert werden, wenn große Randverteilungen aus kleineren vermittels des Prinzips der maximalen Entropie und des Iterative Proportional Fitting- Algorithmus berechnet werden. - Das zweite Thema ist die Verallgemeinerung graphischer Modelle zu zirkulären Strukturen. Mit der Bethe-Kikuchi-Approximation kann das zirkuläre graphische Modell (der Regionen-Graph) die Boltzmannverteilung einer Zielfunktion durch einen generalisierten Belief Propagation-Algorithmus (GBP) lernen. Er minimiert die freie Energie, eine Größe aus der statistischen Physik, die äquivalent zur relativen Entropie zur Boltzmannverteilung ist. Frühere Versuche, die Kikuchi-Approximation mit EDA zu verbinden, benutzen einen aufwendigen Gibbs-Sampling-Algorithmus, um eine Population aus dem zirkulären Wahrscheinlichkeitsmodell zu erzeugen. In dieser Arbeit wird eine Verbindung mit Faktorisierungen vorgestellt, die effizienteres Sampling erlaubt. Die freie Energie wird um die inverse Temperatur ß erweitert. Der oben erwähnte Algorithmus zur Erzeugung einer Faktorisierung kann auch hier angewendet werden. Die Dynamik von GBP wird untersucht und auf Ising-Modelle angewendet. Kleine Probleme (7 x 7) werden ohne Schwierigkeit gelöst. Größere Probleme (10 x 10 und 15 x 15) konvergieren mit großem ß nicht mehr zum wahren Optimum, aber durch Sampling von der Faktorisierung kann das Optimum bei einer Samplegröße von 1000 bis 10000, je nach Probleminstanz, gefunden werden. Wenn GBP nicht konvergiert, kann es durch eine Konkav-Konvex-Prozedur ersetzt werden, die Konvergenz garantiert. - Drittens kann, wenn für die Zielfunktion keine Struktur gegeben ist, ein Bayessches Netz gelernt werden, um die Abhängigkeiten in der Population zu erfassen. Die relative Entropie zwischen der Populationsverteilung und der Verteilung durch das Bayessche Netz ist äquivalent zur Log-Likelihood des Modells. Diese wurde erweitert zum BIC/MDL-Kriterium, das Überanpassung lindert, indem komplizierte Strukturen bestraft werden. Eine vorangegangene informationstheoretische Analyse von BIC/MDL im EDA-Bereich wird erweitert, und empirisch wird belegt, daß die Methode die korrekte Struktur einer Zielfunktion bei genügend großer Population lernen kann. - Schließlich wird vorgestellt, wie durch eine lokale Suchheuristik der Suchraum von EDA reduziert werden kann. Der Kernighan-Lin-Hillclimber, der ursprünglich für das Problem des Handlungsreisenden und Graphen-Bipartitionierung konzipiert ist, wird für beliebige binäre Probleme erweitert. Er kann allein angewandt werden, als iteratives 1+1-Suchverfahren, oder in Kombination mit EDA. Er löst das MAXSAT-Problem in ähnlicher Größenordnung wie der spezialisierte Hillclimber Walksat. Eine Analyse der lokalen Optima von Kernighan-Lin zeigt, daß die Kombination mit EDA vorteilhaft ist. Die Arbeit zeigt, wie evolutionäre Optimierung verbessert werden kann, indem interdisziplinäre Ergebnisse aus Informationstheorie, Statistik, Wahrscheinlichkeitsrechnung und statistischer Physik eingebracht werden. Die Prinzipien der Informationstheorie zur Schätzung von Wahrscheinlichkeitsverteilungen lassen sich in vielen Bereichen anwenden. EDAs sind eine gute Anwendung, denn eine verbesserte Schätzung beeinflußt direkt den Optimierungserfolg