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One of the barriers to visualization-enabled scientific discovery is the difficulty in clearly and quantitatively articulating the meaning of a visualization, particularly in the exploration of relationships between multiple variables in large-scale data sets. This issue becomes more complicated in the visualization of three-dimensional turbu- lence, since geometry, topology, and statistics play complicated, intertwined roles in the definitions of the features of interest, making them difficult or impossible to precisely describe.
This dissertation develops and evaluates a novel interactive multivariate volume visualization framework that allows features to be progressively isolated and defined using a combination of global and feature-local properties. I argue that a progressive and interactive multivariate feature-local approach is advantageous when investigating ill-defined features because it provides a physically meaningful, quantitatively rich en- vironment within which to examine the sensitivity of the structure properties to the identification parameters. The efficacy of this approach is demonstrated in the analysis of vortical structures in Taylor-Green turbulence. Through this analysis, two distinct structure populations have been discovered in these data: structures with minimal and maximal local absolute helicity distributions. These populations cannot be distinguished via global distributions; however, they were readily identified by this approach, since their feature-local statistics are distinctive.

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Content uploaded by Kenny Gruchalla

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All content in this area was uploaded by Kenny Gruchalla on Oct 04, 2019

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The volume of data and the velocity with which it is being generated by com-
putational experiments on high performance computing (HPC) systems is quickly
outpacing our ability to effectively store this information in its full
fidelity. There- fore, it is critically important to identify and study
compression methodologies that retain as much information as possible,
particularly in the most salient regions of the simulation space. In this
paper, we cast this in terms of a general decision-theoretic problem and
discuss a wavelet-based compression strategy for its solution. We pro- vide a
heuristic argument as justification and illustrate our methodology on several
examples. Finally, we will discuss how our proposed methodology may be utilized
in an HPC environment on large-scale computational experiments.

Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired particular significance since coherent structures (CS) in turbulent flows are now commonly regarded as vortices. An objective definition of a vortex should permit the use of vortex dynamics concepts to educe CS, to explain formation and evolutionary dynamics of CS, to explore the role of CS in turbulence phenomena, and to develop viable turbulence models and control strategies for turbulence phenomena. We propose a definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor S 2 + a 2 ; here S and 0 are respectively the symmetric and antisymmetric parts of the velocity gradient tensor Vu. This definition captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers, unlike a pressure-minimum criterion. We compare our definition with prior schemes/definitions using exact and numerical solutions of the Euler and Navier-Stokes equations for a variety of laminar and turbulent flows. In contrast to definitions based on the positive second invariant of V u or the complex eigenvalues of Vu, our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.

In this paper we review a variety of neighborhood operators in a way which emphasizes their common form. These operators are useful for image segmentation tasks as well as for the construction of primitives involved in structural image analysis. The common form of the operators suggests the possibility of a large scale integration hardware implementation in the VLSI device technology.

The mathematical description of three dimensional surfaces usually falls in one of two classifications: parametric and algebraic. The form is defined as all points which satisfy some equation: F(x,y,z)=0. This form is ideally suited for image space shaded picture drawing, the pixel coordinates are substituted for x and y and the equation is solved for z. Algorithms for drawing such objects have been developed primarily for first and second order polynomial functions. This paper presents a new algorithm applicable to other functional forms, in particular to the summation of several gaussian density distributions. The algorithm was created to model electron density maps of molecular structures but can be used for other artistically interesting shapes.

Multi-dimensional Transfer Functions (MDTFs) are increasingly used in volume rendering to produce high quality visualizations of complex data sets. A major factor limiting the use of MDTFs is that the available design tools have not been simple enough to reach wide usage outside of the research context, for instance in clinical medical imaging. In this paper we address this problem by defining an MDTF design concept based on improved histogram display and interaction in an exploratory process. To this end we propose sorted histograms, 2D histograms that retain the intuitive appearance of a traditional 1D histogram while conveying a second attribute. We deploy the histograms in medical visualizations using data attributes capturing domain knowledge e.g. in terms of homogeneity and typical surrounding of tissues. The resulting renderings demonstrate that the proposed concept supports a vast number of visualization possibilities based on multi-dimensional attribute data.

This paper describes an automated classification algorithm of RBC's morphological abnormalities, which is one of the examinations of the blood cell differentials. As there are many RBCs in the image (which is called multi-object pattern), one of the important problems for this automation is to develope the segmentation of the multi-object pattern. We developed a new method of the segmentation of the multi-object pattern, which was done only by the local operations based on the wave propagation method. Feature extraction is done only by the local operations, too. Moreover, we developed a logic to detect various kinds of morphological abnormalities by the partition of multidimensional space, which is defined by the feature parameters of RBC's. Classification rate of morphological abnormalities by this method is 92.6%.

This chapter reviews different hardware-accelerated methods and architectures for volume rendering. The discussion focuses on direct volume rendering techniques. Direct volume rendering has the ability to give a qualitative feel for the density changes in the data. It precludes the need to segment the data; indeed, it is particularly adept at showing structurally weak and “fuzzy” information. The chapter also reviews the basics of direct volume rendering and provides background and terminology used throughout this chapter. The chapter describes several approaches to volume rendering that have been successfully accelerated by hardware. The chapter also discusses ray-casting, 3D and 2D texture slicing, shear-warp rendering and its implementation on VolumePro, and splatting. The chapter further focuses on the underlying rendering algorithms and principles and refers to the literature for implementation details.

We present an approach to visualizing correlations in 3D multifield scalar data. The core of our approach is the computation of correlation fields, which are scalar fields containing the local correlations of subsets of the multiple fields. While the visualization of the correlation fields can be done using standard 3D volume visualization techniques, their huge number makes selection and handling a challenge. We introduce the Multifield-Graph to give an overview of which multiple fields correlate and to show the strength of their correlation. This information guides the selection of informative correlation fields for visualization. We use our approach to visually analyze a number of real and synthetic multifield datasets.