Magnetic resonance imaging (MRI) is a highly exible and non-invasive medical imaging modality based on the concept of nuclear magnetic resonance (NMR). Compared to other imaging techniques, major limitation of MRI is the relatively long acquisition time. The slowness of acquisition makes MRI difficult to apply to time-sensitive clinical applications. Acquisition of MRA images with a spatial resolution close to conventional digital subtraction angiography is feasible, but at the expense of reduction in temporal resolution. Parallel MRI employs multiple receiver coils to speed up the MRI acquisition by reducing the number of data points collected. Although, the reconstructed images from undersampled data sets often suffer from different different types of degradation and artifacts. In contrast-enhanced magnetic resonance imaging, information is effectively measured in 3D k-space one line at a time therefore the 3D data acquisition extends over several minutes even using parallel receiver coils. This limits the assessment of high ow lesions and some vascular tumors in patients. To improve spatio-temporal resolution in contrast enhanced magnetic resonance angiography (CE-MRA), the use of incorporating prior knowledge in the image recovery process is considered in this thesis. There are five contributions in this thesis. The first contribution is the modification of generalized unaliasing using support and sensitivity encoding (GUISE). GUISE was introduced by this group to explore incorporating prior knowledge of the image to be reconstructed in parallel MRI. In order to provide improved time-resolved MRA image sequences of the blood vessels, the GUISE method requires an accurate segmentation of the relatively noisy 3D data set into vessel and background. The method that was originally used for definition of the effective region of support was primitive and produced a segmented image with much false detection because of the effect of overlying structures and the relatively noisy background in images. We proposed to use the statistical principle as employed for the modified maximum intensity projection (MIP) to achieve better 3D segmentation and optimal visualization of blood vessels. In comparison with the previous region of support (ROS), the new one enables higher accelerations MRA reconstructions due to the decreased volume of the ROS and leads to less computationally expensive reconstruction. In the second contribution we demonstrated the impact of imposing the Karhunen-Loeve transform (KLT) basis for the temporal changes, based on prior expectation of the changes in contrast concentration with time. In contrast with other transformation, KLT of the temporal variation showed a better contrast to noise ratio (CNR) can be achieved. By incorporating a data ordering step with compressed sensing (CS), an improvement in image quality for reconstructing parallel MR images was exhibited in prior estimate based compressed sensing (PECS). However, this method required a prior estimate of the image to be available. A singular value decomposition (SVD) modification of PECS algorithm (SPECS) to explore ways of utilising the data ordering step without requiring a prior estimate was extended as the third contribution. By employing singular value decomposition as the sparsifying transform in the CS algorithm, the recovered image was used to derive the data ordering in PECS. The preliminary results outperformed the PECS results. The fourth contribution is a novel approach for training a dictionary for sparse recovery in CE-MRA. The experimental results demonstrate improved reconstructions on clinical undersampled dynamic images. A new method recently has been developed to exploit the structure of the signal in sparse representation. Group sparse compressed sensing (GSCS) allows the efficient reconstruction of signals whose support is contained in the union of a small number of groups (sets) from a collection of pre-defined disjoint groups. Exploiting CS applications in dynamic MR imaging, a group sparse method was introduced for our contrast-enhanced data set. Instead of incorporating data ordering resulted from prior information, pre-defined sparsity patterns were used in the PECS recovery algorithm, resulting to a suppression of noise in the reconstruction.

Redwood (Sequoia sempervirens (D. Don) Endl.) has been identified as a species with considerable potential for plantation forestry in New Zealand. Investment decisions in high value alternate species must be based on accurate wood quality and value predictions. There is an opportunity to extend non-destructive evaluation tools available to redwood growers, and to present the outputs of the growth model by log products and sawn timber. A redwood pruned buttlog sawing simulator has been developed however the simulator had not been tested with real data. Twelve redwood trees from Mangatu estate were selected for a sawing study; these logs were reconstructed and run through the sawing simulator. Computerised log processing was used to produce simulated pruned log sawing outturn from the redwood Buttlog Sawing Simulator, and results were compared to real results from a sawing study. The objective of the study was therefore to determine how well the simulator matched volume and grade out-turn from twelve logs. This study found the many inconsistencies between simulated data and real data; particularly related to log size. While this study was unsuccessful in validation of the redwood sawing simulator, it provides initial insight into the simulators strengths and short comings.

Compressed sensing (CS) theory has demonstrated that sparse signals can be reconstructed from far fewer measurements than suggested by the Nyquist sampling theory. CS has received great attention recently as an alternative to the current paradigm of sampling followed by compression. Initial CS operated under the implicit assumption that the sparsity domain coefficients are independently distributed. Recent results, however, show that exploiting statistical dependencies in sparse signals improves the recovery performance of CS. This dissertation proposes model-based CS reconstruction techniques. Statistical dependency models for several CS problems are proposed and incorporated into different CS algorithms. These models allow incorporation of a priori information into the CS reconstruction problems. Firstly, we propose the use of a Bayes least squares-Gaussian scale mixtures (BLS-GSM) model for CS recovery of natural images. The BLS-GSM model is able to exploit dependencies inherent in wavelet coefficients. This model is incorporated into several recent CS algorithms. The resulting methods significantly reduce reconstruction errors and/or the number of measurements required to obtain a desired reconstruction quality, when compared to state-of-the-art model-based CS methods in the literature. The model-based CS reconstruction techniques are then extended to video. In addition to spatial dependencies, video sequences exhibit significant temporal dependencies as well. In this dissertation, a model for jointly exploiting spatial and temporal dependencies in video CS is also proposed. The proposed method enforces structural self-similarity of image blocks within each frame as well as across neighboring frames. By sparsely representing collections of similar blocks, dominant image structures are retained while noise and incoherent undersampling artifacts are eliminated. A new video CS algorithm which incorporates this model is then proposed. The proposed algorithm iterates between enforcement of the self-similarity model and consistency with measurements. By enforcing measurement consistency in residual domain, sparsity is increased and CS reconstruction performance is enhanced. The proposed approach exhibits superior subjective image quality and significantly improves peak-signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM).Finally, a model-based CS framework is proposed for super resolution (SR) reconstruction. The SR reconstruction is formulated as a CS problem and a self-similarity model is incorporated into the reconstruction. The proposed model enforces similarity of collections of blocks through shrinkage of their transform-domain coefficients. A sharpening operation is performed in transform domain to emphasize edge recovery. The proposed method is compared with state-of-the-art SR techniques and provides high-quality SR images, both quantitatively and subjectively.

We introduce new approaches of modeling and synthesizing realistic-looking 2D fire animations using video-based techniques and statistical analysis. Our approaches are based on real footage of various small-scale fire samples with customized motions that we captured for this research, and the final results can be utilized as a sequence of images in video games, motion graphics and cinematic visual effects. Instead of conventional physically-based simulation, we utilize example-based principal component analysis (PCA) and take it to a new level by introducing “Eigenfires”, as a new way to represent the main features of various real fire samples. The visualization of Eigenfires helps animators to design the fire interactively through a more meaningful and convenient way in comparison to known procedural approaches or other video-based synthesis models. Our system enables artists to control real-life fire videos through motion transitions and loops by selecting any desired ranges of any video clips and then the system takes care of the remaining part that best represent a smooth transition. Instead of tricking the eyes with a basic blending only between similar shapes, our flexible fire transitions are capable of connecting various fire styles. Our techniques are also effective for data compressions, they can deliver real-time interactive recognition for high resolution images, very easy to implement, and requires little parameter tuning.

Two types of problems are studied in this thesis: reconstruction and visualization of polygons and polyhedra. <br /><br /> Three problems are considered in reconstruction of polygons and polyhedra, given a set of projection characteristics. The first problem is to reconstruct a closed convex polygon (polyhedron) given the number of visible edges (faces) from each of a set of directions <em>S</em>. The main results for this problem include the necessary and sufficient conditions for the existence of a polygon that realizes the projections. This characterization gives an algorithm to construct a feasible polygon when it exists. The other main result is an algorithm to find the maximum and minimum size of a feasible polygon for the given set <em>S</em>. Some special cases for non-convex polygons and for perspective projections are also studied. <br /><br /> For reconstruction of polyhedra, it is shown that when the projection directions are co-planar, a feasible polyhedron (i. e. a polyhedron satisfying the projection properties) can be constructed from a feasible polygon and vice versa. When the directions are covered by two planes, if the number of visible faces from each of the directions is at least four, then an algorithm is presented to decide the existence of a feasible polyhedron and to construct one, when it exists. When the directions see arbitrary number of faces, the same algorithm works, except for a particular sub-case. <br /><br /> A polyhedron is, in general, called equiprojective, if from any direction the size of the projection or the projection boundary is fixed, where the "size" means the number of vertices, edge, or faces. A special problem on reconstruction of polyhedra is to find all equiprojective polyhedra. For the case when the size is the number of vertices in the projection boundary, main results include the characterization of all equiprojective polyhedra and an algorithm to recognize them, and finding the minimum equiprojective polyhedra. Other measures of equiprojectivity are also studied. <br /><br /> Finally, the problem of efficient visualization of polyhedra under given constraints is considered. A user might wish to find a projection that highlights certain properties of a polyhedron. In particular, the problem considered is given a set of vertices, edges, and/or faces of a convex polyhedron, how to determine all projections of the polyhedron such that the elements of the given set are on the projection boundary. The results include efficient algorithms for both perspective and orthogonal projections, and improved adaptive algorithm when only edges are given and they form disjoint paths. A related problem of finding all projections where the given edges, faces, and/or vertices are not on the projection boundary is also studied.

The aim of this research is to develop a range of procedures for enhancing conversational skills. From a review of theoretical analyses of social encounters a model of conversational process is developed to describe mechanisms by which interactants construct, maintain and revise cognitive models of their social environment. From this model, three dimensions of conversational competence are derived and a training paradigm devised incorporating the process of cognitive reflection by which functional properties of models are displayed to interactants. This paradigm provides a rationale for discrete intervention strategies to effect changes on each dimension of competence. Preliminary studies report attempts to implement the first intervention strategy in a friendship relationship and workshop group. Using the "conversational cycle" and repertory grid techniques, procedures are developed to exhibit critical interpersonal events and their relationship to modelling processes. The main studies investigate the second and third intervention strategies by developing serial repertory grid methods to exhibit the functional properties of centrality to self-cognition and stability of construction. The training paradigm is elaborated to include these properties at three levels of organisation, and a sequential Bayesian analysis is developed to determine the extent of centrality and stability of construction. The training paradigm is tested in two case-studies and evidence of increases in insight, centrality and elaboration of personal construction are found. This methodology is extended to incorporate repertory grids produced by two interactants yoked by element sample and tested in a case-study of a married couple. Evidence of increased insight and self-partner reconstruction is found, but predictions concerning increased self-partner distinctiveness are contraindicated. These findings suggest that evaluative criteria may not be coincident with subjective strategies, and alternative evaluation methodologies are proposed.

Das mediale patello-femorale Ligament (MPFL) wurde in den letzten Jahren und Jahrzehnten als maßgeblicher passiver Stabilisator der Kniescheibe identifiziert und in biomechanischen Studien beschrieben. Auch wurden die verschiedenen Möglichkeiten der operativen Rekonstruktion des MPFL und deren klinisches Outcome bei patellofemoraler Instabilität in zahlreichen Studien beschrieben sowie relevante Ergebnisse für den klinischen Alltag formuliert. Ziel dieser Arbeit war es, die MPFL-Ersatzplastik als Revisionseingriff mit dem Outcome bei Primäreingriffen zu vergleichen und Faktoren zu bestimmen, die das klinische Outcome beeinflussen. Hierzu wurden 61 Patienten, die von Januar 2009 bis Dezember 2012 in der Klinik für Unfall- und Wiederherstellungschirurgie des Diakoniekrankenhauses Friederikenstift gGmbH Hannover operativ mittels MPFL-Ersatzplastik stabilisiert worden sind, untersucht. Retrospektiv nach Aktenlage und im Rahmen einer klinischen Nachuntersuchung wurden anhand eines standardisierten Studienprotokolls verschiedene Ausgangs- und Outcome-Parameter erhoben und mittels IBM SPSS Statistics for Windows, Version 20.0. Armonk, NY: IBM Corp. Released 2011 ausgewertet. Es zeigte sich, dass die Patienten der Primärgruppe eine signifikante Verbesserung durch die Operation erzielen konnten, bei den Patienten der Revisionsgruppe traf dies nicht auf alle Parameter zu. Im Vergleich der Ausgangs- und Outcome-Parameter der Primär- und Revisionsgruppe zeigten sich keine signifikanten Unterschiede. Des Weiteren zeigte sich, dass die Ausgangsparameter Alter bei OP, operativ-versorgte Seite, BMI, Beruf, generelle sportliche Betätigung, verwendete Fadenanker zur Transplantatfixierung an der Patella und Lage der Bohrkanäle in der Patella das Outcome der Operation signifikant beeinflussten.

In many complex water supply systems, the next generation of water resources planning models will require simultaneous probabilistic streamflow inputs at multiple locations on an interconnected network. To make use of the valuable multicentury records provided by tree-ring data, reconstruction models must be able to produce appropriate multisite inputs. Existing streamflow reconstruction models typically focus on one site at a time, not addressing intersite dependencies and potentially misrepresenting uncertainty. To this end, we develop a model for multisite streamflow reconstruction with the ability to capture intersite correlations. The proposed model is a hierarchical Bayesian nonhomogeneous hidden Markov model (NHMM). A NHMM is fit to contemporary streamflow at each location using lognormal component distributions. Leading principal components of tree rings are used as covariates to model nonstationary transition probabilities and the parameters of the lognormal component distributions. Spatial dependence between sites is captured with a Gaussian elliptical copula. Parameters of the model are estimated in a fully Bayesian framework, in that marginal posterior distributions of all the parameters are obtained. The model is applied to reconstruct flows at 20 sites in the Upper Colorado River Basin (UCRB) from 1473 to 1906. Many previous reconstructions are available for this basin, making it ideal for testing this new method. The results show some improvements over regression-based methods in terms of validation statistics. Key advantages of the Bayesian NHMM over traditional approaches are a dynamic representation of uncertainty and the ability to make long multisite simulations that capture at-site statistics and spatial correlations between sites.

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Two Chinese pine (Pinus tabulaeformis) tree-ring width chronologies up to 375 years long were used to reconstruct rainfall from February to early July for the Wu Dangzhao region and from February to mid-July for the La Madong region, Inner Mongolia, China. The predictor variables account for 44.3% and 42.7% of the variance in precipitation, respectively. Both historical records and two other tree-ring based precipitation reconstructions from the environmentally sensitive zone (the northern Helan Mountain range and Baiyinaobao) confirm our results. After applying a 10-year moving average, the trends of four tree-ring based precipitation reconstructions vary synchronously. Periods with below-normal precipitation occurred during the 1720s–1730s, 1740s–1750s, 1790s, early 1810s, late 1830s–1860s, 1880s–1910s, late 1920s–1930s and after the late 1960s–early 1970s. Periods with above-normal precipitation occurred in the 1760s to early 1770s, 1820s to early 1830s, 1870s–1880s, early 1920s, 1940s to early 1960s, and 1990s. The late 1920s period was the most severe drought over a broad area in north China in the last 375 years. In contrast, the wettest period was in the late 1990s.