Visualization

Understanding the relationships between pathways and the altered expression of their components in disease conditions can be addressed in a visual data analysis process. Caleydo uses novel visualization techniques to support life science experts in their analysis of gene expression data in the context of pathways and functions of individual genes. Pathways and gene expression visualizations are placed in a 3D scene where selected entities (i.e. genes) are visually connected. This allows Caleydo to seamlessly integrate interactive gene expression visualization with cross-database pathway exploration.

This paper presents a visual data mining approach using the combination of clinical data, pathways and gene-expression data. The visual exploration of medical data using pathways to navigate and filter the data allows a more systematic and efficient investigation of problems in modern life science. A multiplicity of hypothesis can be evaluated in the same period of time, enabling a much better exploitation of the data. We present a system for data preprocessing and automatic classification, a set of visualization views and finally the integration in the Caleydo visualization framework, which enables the "coupling" of genetic and a broad spectrum of clinical data. With the help of the Caleydo framework the medical expert can identify connections between genetic parameters, patient subgroups, and drug responses.

As the complexity and amount of real world data continuously grows, modern visualization systems are changing. Traditional information visualization techniques are often not sufficient to allow an in-depth visual data exploration process. Multiple view systems combined with linking & brushing are only one building block of a successful InfoVis system. In this paper we propose the incorporation of cheap and simple gaze-based interaction. We employ the tracking information not for selecting data (i.e. mouse interaction) but for an intelligent adaption of 2D and 3D visualizations. Derived from the focus+context paradigm, we call this gaze-focus. The proposed methods are demonstrated by means of three different visualizations.

In the field of comparative genomics, scientists seek to answer questions about evolution and genomic function by comparing the genomes of species to find regions of shared sequences. Conserved syntenic blocks are an important biological data abstraction for indicating regions of shared sequences. The goal of this work is to show multiple types of relationships at multiple scales in a way that is visually comprehensible in accordance with known perceptual principles. We present a task analysis for this domain where the fundamental questions asked by biologists can be understood by a characterization of relationships into the four types of proximity/location, size, orientation, and similarity/strength, and the four scales of genome, chromosome, block, and genomic feature. We also propose a new taxonomy of the design space for visually encoding conservation data. We present MizBee, a multiscale synteny browser with the unique property of providing interactive side-by-side views of the data across the range of scales supporting exploration of all of these relationship types. We conclude with case studies from two biologists who used MizBee to augment their previous automatic analysis work flow, providing anecdotal evidence about the efficacy of the system for the visualization of syntenic data, the analysis of conservation relationships, and the communication of scientific insights.

One of the central challenges facing visualization research is how to effectively enable knowledge discovery. An effective approach will likely combine application architectures that are capable of running on today's largest platforms to address the challenges posed by large data with visual data analysis techniques that help find, represent, and effectively convey scientifically interesting features and phenomena.

Polynomial chaos methods (and generalized polynomial chaos methods) have been extensively applied to analyze PDEs that contain uncertainties. However this approach is rarely applied to hyperbolic systems. In this paper we analyze the properties of the resulting deterministic system of equations obtained by stochastic Galerkin projection. We consider a simple model of a scalar wave equation with random wave speed. We show that when uncertainty causes the change of characteristic directions, the resulting deterministic system of equations is a symmetric hyperbolic system with both positive and negative eigenvalues. A consistent method of imposing the boundary conditions is proposed and its convergence is established. Numerical examples are presented to support the analysis.

Keywords: Generalized polynomial chaos, stochastic PDE, Galerkin method, hyperbolic equation, uncertainty quantification

The method of Moving Least Squares (MLS) is a popular framework for reconstructing continuous functions from scattered data due to its rich mathematical properties and well-understood theoretical foundations. This paper applies MLS to volume rendering, providing a unified mathematical framework for ray casting of scalar data stored over regular as well as irregular grids. We use the MLS reconstruction to render smooth isosurfaces and to compute accurate derivatives for high-quality shading effects. We also present a novel, adaptive preintegration scheme to improve the efficiency of the ray casting algorithm by reducing the overall number of function evaluations, and an efficient implementation of our framework exploiting modern graphics hardware. The resulting system enables high-quality volume integration and shaded isosurface rendering for regular and irregular volume data.

A ubiquitous requirement in many mathematical and computational problems is a set of well-placed point samples. For producing very even distributions of samples across complex surfaces, a dynamic particle system is a controllable mechanism that naturally accommodates strict sampling requirements. The systemfirst constrains particles to a surface, and then moves the particles across the surface until they are arranged in minimal energy configurations. Adaptivity is added into the system by scaling the distance between particles, causing higher densities of points around surface features. In this dissertation we explore and refine the dynamics of particle systems for generating efficient and adaptive point samples of implicit surfaces.

Throughout this dissertation, we apply the adaptive particle system framework to several application areas. First, efficient visualizations of high-order finite element datasets are generated by developing adaptivity metrics of surfaces that exist in the presence of curvilinear coordinate transformation. Second, a framework is proposed that meets fundamental sampling constraints of Delaunay-based surface reconstruction algorithms. In meeting these constraints, the particle distributions produce nearly-regular, efficient isosurface tessellation that are geometrically and topologically accurate. And third, a novel analytic representation of material boundaries in multimaterial volume datasets is developed, as well as a set of projection operators, that allow for explicit sampling of nonmanifold material intersections. Using a tetrahedral labeling algorithm, the material intersections are extracted as watertight, nonmanifold meshes that are well-suited for simulations.