A Variational r-Adaption and Shape-Optimization Method for Finite-Deformation Elasticity

This paper is concerned with the formulation of a variational r-adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configuration forces for isoparametric elements and nonlinear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and nonlinear elastic bodies; and the optimization of the shape of elastic inclusions

Color graph representation for structural analysis of tissue images

Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 71-82.Computer aided image analysis tools are becoming increasingly important in automated cancer diagnosis and grading. They have the potential of assisting pathologists in histopathological examination of tissues, which may lead to a considerable amount of subjectivity. These analysis tools help reduce the subjectivity, providing quantitative information about tissues. In literature, it has been proposed to implement such computational tools using different methods that represent a tissue with different set of image features. One of the most commonly used methods is the structural method that represents a tissue quantifying the spatial relationship of its components. Although previous structural methods lead to promising results for different tissue types, they only use the spatial relations of nuclear tissue components without considering the existence of different components in a tissue. However, additional information that could be obtained from other components of the tissue has an importance in better representing the tissue, and thus, in making more reliable decisions. This thesis introduces a novel structural method to quantify histopathological images for automated cancer diagnosis and grading. Unlike the previous structural methods, it proposes to represent a tissue considering the spatial distribution of different tissue components. To this end, it constructs a graph on multiple tissue components and colors its edges depending on the component types of their end points. Subsequently, a new set of structural features is extracted from these “color graphs” and used in the classification of tissues. Experiments conducted on 3236 photomicrographs of colon tissues that are taken from 258 different patients demonstrate that the color graph approach leads to 94.89 percent training accuracy and 88.63 percent test accuracy. Our experiments also show that the introduction of color edges to represent the spatial relationship of different tissue components and the use of graph features defined on these color edges significantly improve the classification accuracy of the previous structural methods.Altunbay, DoğanM.S

Perceptually Motivated Shape Context Which Uses Shape Interiors

In this paper, we identify some of the limitations of current-day shape matching techniques. We provide examples of how contour-based shape matching techniques cannot provide a good match for certain visually similar shapes. To overcome this limitation, we propose a perceptually motivated variant of the well-known shape context descriptor. We identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties. We show that our method can easily be augmented with any other shape matching algorithm. We also show from our experiments that the use of our descriptor can significantly improve the retrieval rates

Lattice cleaving: a multimaterial tetrahedral meshing algorithm with guarantees

pre-printWe introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach

Construction of boundary element models in bioelectromagnetism

Multisensor electro- and magnetoencephalographic (EEG and MEG) as well as electro- and magnetocardiographic (ECG and MCG) recordings have been proved useful in noninvasively extracting information on bioelectric excitation. The anatomy of the patient needs to be taken into account, when excitation sites are localized by solving the inverse problem. In this work, a methodology has been developed to construct patient specific boundary element models for bioelectromagnetic inverse problems from magnetic resonance (MR) data volumes as well as from two orthogonal X-ray projections. The process consists of three main steps: reconstruction of 3-D geometry, triangulation of reconstructed geometry, and registration of the model with a bioelectromagnetic measurement system. The 3-D geometry is reconstructed from MR data by matching a 3-D deformable boundary element template to images. The deformation is accomplished as an energy minimization process consisting of image and model based terms. The robustness of the matching is improved by multi-resolution and global-to-local approaches as well as using oriented distance maps. A boundary element template is also used when 3-D geometry is reconstructed from X-ray projections. The deformation is first accomplished in 2-D for the contours of simulated, built from the template, and real X-ray projections. The produced 2-D vector field is back-projected and interpolated on the 3-D template surface. A marching cube triangulation is computed for the reconstructed 3-D geometry. Thereafter, a non-iterative mesh-simplification method is applied. The method is based on the Voronoi-Delaunay duality on a 3-D surface with discrete distance measures. Finally, the triangulated surfaces are registered with a bioelectromagnetic measurement utilizing markers. More than fifty boundary element models have been successfully constructed from MR images using the methods developed in this work. A simulation demonstrated the feasibility of X-ray reconstruction; some practical problems of X-ray imaging need to be solved to begin tests with real data.reviewe

Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

Three-Dimensional Modelling of the Terra Nova Bay Sea Floor (Ross Sea - Antarctica)

The importance of gathering data on the Antarctic coastline and its adjacent waters has been widely recognised by the Antarctic Treaty Consultative Meeting (ATCM), the Council of Managers of National Antarctic Programs (COMNAP) and the Scientific Committee on Antarctic Research (SCAR). In particular, both for navigational safety and environmental monitoring, it is very desirable to increase hydrographic activity in those areas which have the most significant importance from a scientific or navigational point of view - such as in the continental shelf and continental slope areas of the western part of the Ross Sea. Quite apart from the safety of navigation requirements, knowledge of the seabed topography is necessary to study and understand the various phenomena taking place in the marine environment. For example, the movement of water masses and their mixing processes depend on the shape of the seabed and adjacent coastline. The sea area surrounding Antarctica is one of the least explored parts of the world’s oceans and the available bathymetric data is only sufficient to allow a very general analysis to be made. With the probable growth of tourism and fishing around Antarctica and with the increasing need to understand the effects on the world’s climate of Antarctic water patterns, it is necessary to consider powerful new techniques - such as threedimensional modelling of the sea floors - in order to build up more quickly an effective and reliable bathymetric data base of Antarctic waters