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"Patients with repaired tetralogy of Fallot (TOF) account for the majority of cases with late onset right ventricle (RV) failure. The current surgical approach, which includes pulmonary valve replacement/insertion (PVR), has yielded mixed results in terms of RV functional recovery. Therefore, it is of great interest for clinicians to identify parameters, which may be used to predict post-PVR outcome. Pre- and post-PVR cardiac magnetic resonance (CMR) data were obtained from 60 repaired TOF patients with consent obtained for analysis. RV ejection fraction (RVEF) change (post-PVR RVEF minus pre-PVR RVEF) was used to measure post-PVR improvement. The patients were divided into Group 1(optimal outcome) and Group 2 (poor outcome) for comparison. RV wall thickness (WT) and curvature were obtained from CMR data for statistical analysis. Using mean quarter values (one CMR slice = 4 quarters), statistically significant differences in circumferential curvature (C-curvature) and longitudinal curvature (L-curvature) at end-diastole (maximum RV volume) and WT and C-curvature at end-systole (minimum RV volume) between Group 1 and Group 2 were found. Correlations between average WT at systole and between L-curvature at diastole and the change of RVEF were statistically significant. Specifically, the correlation coefficient between average WT at systole and change of RVEF was – 0.2715, (p = 0.036) and between L-curvature at diastole and change of RVEF 0.3297 (p = 0.01). This initial study suggests that the RV longitudinal curvature and wall thickness may be used as a marker/predictor for PVR surgical outcome. "

Discrete shapes can be described and analyzed using Lie groups, which are mathematical structures having both algebraic and geometrical properties. These structures, borrowed from mathematical physics, are both algebraic groups and smooth manifolds. A key property of a Lie group is that a curved space can be studied, using linear algebra, by local linearization with an exponential map. Here, a discrete shape was a Euclidean-invariant computer representation of an object. Highly variable shapes are known to exist in non-linear spaces where linear analysis tools, such as Pearson's decomposition of principal components, are inadequate. The novel method proposed herein represented a shape as an ensemble of homogenous matrix transforms. The Lie group of homogenous transforms has elements that both represented a local shape and acted as matrix operators on other local shapes. For the manifold, a matrix transform was found to be equivalent to a vector transform in a linear space. This combination of representation and linearization gave a simple implementation for solving a computationally expensive problem. Two medical datasets were analyzed: 2D contours of femoral head-neck cross-sections and 3D surfaces of proximal femurs. The Lie-group method outperformed the established principal-component analysis by capturing higher variability with fewer components. Lie groups are promising tools for medical imaging and data analysis. / Thesis (Ph.D, Computing) -- Queen's University, 2014-01-30 09:49:03.293

Geometric modeling of biomolecules plays an important role in the study of biochemical processes. Many simulation methods depend heavily on the geometric models of biomolecules. Among various studies, shape analysis is one of the most important topics, which reveals the functionalities of biomolecules.

Objectives: About 2% of the US population suffers from severe malocclusion discrepancies that are beyond the limits of orthodontics alone. This study explores correlations between 3D malocclusion phenotypes and craniofacial development genes. Methods: CBCTs (124) or digital casts (161) of 285 subjects with skeletal Class I (n=60), II (n=143) and III (n=82) malocclusion were digitized with 48 dental landmarks. 3D coordinates were superimposed prior to Principal Component (PC) analyses to identify symmetric (sym) and asymmetric (asym) aspects of shape variation related to malocclusion. PCs explaining 51%-67% of total shape variation were regressed on 200 variants genotyped within 75 genes adjusting for race, gender, age and data source. Results: Significant correlations (p<0.01) were found for sym variation with BMP3, PITX2, MAFB, SNAl3, FGF8, ABCA4-ARHGAP29, FOXL2 and asym variation PAX7, TBX1, LEFTY1, SATB2, SOX2, TP63 and the 400Kb region containing D1S435. Conclusion: Results suggest genetic pathways associated with malocclusion.

Aggregate shape and texture are important parameters that have a direct influence on the strength and durability of the asphalt and concrete products made from these materials. Shape is characterized in terms of elongated and flat particles. Typically, a given batch of material is rejected if more than a specific percentage of particles have elongation and flatness ratios which exceed some limiting value. Present procedures for determining these ratios rely heavily on manual measurements which are time consuming and limit the sample size. A recently developed rapid shape analysis system can significantly reduce the time required for this procedure. The new system can determine elongation and flatness for a standard batch of 100 particles in under 10 minutes. The system consists of a PC-based image analyzer. Samples of crushed stone are imaged by two video cameras and the images are processed by the computer to determine the flatness and elongation distributions within the sample. Validation procedures indicate an excellent agreement between the rapid analysis system and standard manual techniques. Additionally, the system can provide two quantitative measures of particle roughness which are not measurable by current manual techniques. Preliminary analysis of shape distributions from a sampling campaign indicate that it is possible to determine the effects of crusher type and material type on shape by examining the feed and product shape distributions. Introductory work with manufactured sands indicates that the analyzer can effectively measure all four shape attributes, none of which can currently be measured by manual techniques. / Master of Science

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The functional properties of nanoparticles highly depend on the surface morphology of the particles, so precise measurements of a particle's morphology enable reliable characterizing of the nanoparticle's properties. Obtaining the measurements requires image analysis of electron microscopic pictures of nanoparticles. Today's labor-intensive image analysis of electron micrographs of nanoparticles is a significant bottleneck for efficient material characterization. The objective of this dissertation is to develop automated morphology analysis methods. Morphology analysis is comprised of three tasks: separate individual particles from an agglomerate of overlapping nano-objects (image segmentation); infer the particle's missing contours (shape inference); and ultimately, classify the particles by shape based on their complete contours (shape classification). Two approaches are proposed in this dissertation: the divide-and-conquer approach and the convex shape analysis approach. The divide-and-conquer approach solves each task separately, taking less than one minute to complete the required analysis, even for the largest-sized micrograph. However, its separating capability of particle overlaps is limited, meaning that it is able to split only touching particles. The convex shape analysis approach solves shape inference and classification simultaneously for better accuracy, but it requires more computation time, ten minutes for the biggest-sized electron micrograph. However, with a little sacrifice of time efficiency, the second approach achieves far superior separation than the divide-and-conquer approach, and it handles the chain-linked structure of particle overlaps well. The capabilities of the two proposed methods cannot be substituted by generic image processing and bio-imaging methods. This is due to the unique features that the electron microscopic pictures of nanoparticles have, including special particle overlap structures, and large number of particles to be processed. The application of the proposed methods to real electron microscopic pictures showed that the two proposed methods were more capable of extracting the morphology information than the state-of-the-art methods. When nanoparticles do not have many overlaps, the divide-and-conquer approach performed adequately. When nanoparticles have many overlaps, forming chain-linked clusters, the convex shape analysis approach performed much better than the state-of-the-art alternatives in bio-imaging. The author believes that the capabilities of the proposed methods expedite the morphology characterization process of nanoparticles. The author further conjectures that the technical generality of the proposed methods could even be a competent alternative to the current methods analyzing general overlapping convex-shaped objects other than nanoparticles.

This thesis deals with the problem of tracking highly deformable objects in the presence of noise, clutter and occlusions. The contributions of this thesis are threefold: A novel technique is proposed to perform filtering on an infinite dimensional space of curves for the purpose of tracking deforming objects. The algorithm combines the advantages of particle filter and geometric active contours to track deformable objects in the presence of noise and clutter. Shape information is quite useful in tracking deformable objects, especially if the objects under consideration get partially occluded. A nonlinear technique to perform shape analysis, called kernelized locally linear embedding, is proposed. Furthermore, a new algebraic method is proposed to compute the pre-image of the projection in the context of kernel PCA. This is further utilized in a parametric method to perform segmentation of medical images in the kernel PCA basis. The above mentioned shape learning methods are then incorporated into a generalized tracking algorithm to provide dynamic shape prior for tracking highly deformable objects. The tracker can also model image information like intensity moments or the output of a feature detector and can handle vector-valued (color) images.