Allen Sanderson

A Next Step: Visualizing Errors and Uncertainty

The development of formal theoretical frameworks and the creation of new visual representations of error and uncertainty will be fundamental to a better understanding of 3D experimental and simulation data. Such improved understanding will validate new theoretical models, enable better understanding of data, and facilitate better decision making. We urge the scientific visualization research community to take the next step and make visually representing errors and uncertainties the norm rather than the exception.

Display of Vector Fields Using a Reaction-Diffusion Model

Effective visualization of vector fields relies on the ability to control the size and density of the underlying mapping to visual cues used to represent the field. In this paper we introduce the use of a reaction-diffusion model, already well known for its ability to form irregular spatio-temporal patters, to control the size, density, and placement of the vector field representation. We demonstrate that it is possible to encode vector field information (orientation and magnitude) into the parameters governing a reaction-diffusion model to form a spot pattern with the correct orientation, size, and density, creating an effective visualization. To encode direction we texture the spots using a light to dark fading texture. We also show that it is possible to use the reaction-diffusion model to visualize an additional scalar value, such as the uncertainty in the orientation of the vector field. An additional benefit of the reaction-diffusion visualization technique arises from its automatic density distribution. This benefit suggests using the technique to augment other vector visualization techniques. We demonstrate this utility by augmenting a LIC visualization with a reaction-diffusion visualization. Finally, the reaction-diffusion visualization method provides a technique that can be used for streamline and glyph placement.

Advanced Reaction-Diffusion Models for Texture Synthesis

Since the introduction of texture synthesis using a reaction-diffusion model in the early 1990s, their use has not been widespread. This is likely due to both the difficulty in selecting parameters that result in stable, useful patterns as well as the computational costs of producing these patterns. In this paper we present techniques that help overcome the difficult parameter selection process that controls the pattern development. In addition, we expand the basic diffusion model to allow for shaped patterns. Finally, we show that it is possible to create multiple and oscillating patterns by coupling two reaction-diffusion systems together. These techniques have been implemented using both explicit and semi-implicit solutions on a CPU and GPU.We provide sample source code of both implementations online.

Analysis of Recurrent Patterns in Toroidal Magnetic Fields

In the development of magnetic confinement fusion which will potentially be a future source for low cost power, physicists must be able to analyze the magnetic field that confines the burning plasma. While the magnetic field can be described as a vector field, traditional techniques for analyzing the fields topology cannot be used because of its Hamiltonian nature. In this paper we describe a technique developed as a collaboration between physicists and computer scientists that determines the topology of a toroidal magnetic field using fieldlines with near minimal lengths. More specifically, we analyze the Poincaré map of the sampled fieldlines in a Poincaré section including identifying critical points and other topological features of interest to physicists. The technique has been deployed into an interactiveparallel visualization tool which physicists are using to gain new insight into simulations of magnetically confined burning plasmas.

Microscopic Computed Tomography–Based Virtual Histology for Visualization and Morphometry of Atherosclerosis in Diabetic Apolipoprotein E Mutant Mice

Atherosclerosis is a progressive disease characterized by the accumulation of lipids and fibrous elements in the arteries and is a leading cause of heart disease and stroke in developed and developing countries.1 Animal models have become increasingly important tools for addressing key mechanistic and therapeutic questions that cannot be answered from human studies of atherosclerosis. However, the small-scale vascular structures in genetically engineered mice require labor-intensive histomorphometric techniques to quantify lesions. Recently, a new technique has emerged to image ex vivo blocks of soft tissue by staining tissue with metal solutions, then scanning with a microscopic computed tomography (microCT) instrument (Figure I in the online-only Data Supplement).2 This technique was originally applied to the study of the developing heart in embryos3 and fetuses (Figure II in the online-only Data Supplement) but can also be applied to the en bloc imaging of the heart, great vessels, and lesions thereof. By this method, tissues are left intact, but one can employ image analysis to create “virtual” histological …

Visualization of Topological Structures in Area-Preserving Maps

Area-preserving maps are found across a wide range of scientific and engineering problems. Their study is made challenging by the significant computational effort typically required for their inspection but more fundamentally by the fractal complexity of salient structures. The visual inspection of these maps reveals a remarkable topological picture consisting of fixed (or periodic) points embedded in so-called island chains, invariant manifolds, and regions of ergodic behavior. This paper is concerned with the effective visualization and precise topological analysis of area-preserving maps with two degrees of freedom from numerical or analytical data. Specifically, a method is presented for the automatic extraction and characterization of fixed points and the computation of their invariant manifolds, also known as separatrices, to yield a complete picture of the structures present within the scale and complexity bounds selected by the user. This general approach offers a significant improvement over the visual representations that are so far available for area-preserving maps. The technique is demonstrated on a numerical simulation of magnetic confinement in a fusion reactor.

Visualizing Invariant Manifolds in Area-Preserving Maps

Area-preserving maps arise in the study of conservative dynamical systems describing a wide variety of physical phenomena, from the rotation of planets to the dynamics of a fluid. The visual inspection of these maps reveals a remarkable topological picture in which invariant manifolds form the fractal geometric scaffold of both quasi-periodic and chaotic regions. We discuss in this paper the visualization of such maps built upon these invariant manifolds. This approach is in stark contrast with the discrete Poincare plots that are typically used for the visual inspection of maps. We propose to that end several modified definitions of the finite-time Lyapunov exponents that we apply to reveal the underlying structure of the dynamics. We examine the impact of various parameters and the numerical aspects that pertain to the implementation of this method. We apply our technique to a standard analytical example and to a numerical simulation of magnetic confinement in a fusion reactor. In both cases our simple method is able to reveal salient structures across spatial scales and to yield expressive images across application domains.

Visual interrogation of gyrokinetic particle simulations

Gyrokinetic particle simulations are critical to the study of anomalous energy transport associated with plasma microturbulence in magnetic confinement fusion experiments. The simulations are conducted on massively parallel computers and produce large quantities of particles, variables, and time steps, thus presenting a formidable challenge to data analysis tasks. We present two new visualization techniques for scientists to improve their understanding of the time-varying, multivariate particle data. One technique allows scientists to examine correlations in multivariate particle data with tightly coupled views of the data in both physical space and variable space, and to visually identify and track features of interest. The second technique, built into SCIRun, allows scientists to perform range-based queries over a series of time slices and visualize the resulting particles using glyphs. The ability to navigate the multiple dimensions of the particle data, as well as query individual or a collection of particles, enables scientists to not only validate their simulations but also discover new phenomena in their data.

An Alternative Formulation of Lyapunov Exponents for Computing Lagrangian Coherent Structures

Lagrangian coherent structures are time-evolving surfaces that highlight areas in flow fields where neighboring advected particles diverge or converge. The detection and understanding of such structures is an important part of many applications such as in oceanography where there is a need to predict the dispersion of oil and other materials in the ocean. One of the most widely used tools for revealing Lagrangian coherent structures has been to calculate the finite-time Lyapunov exponents, whose maximal values appear as ridgelines to reveal Lagrangian coherent structures. In this paper we explore an alternative formulation of Lyapunov exponents for computing Lagrangian coherent structures.

Occam's razor and petascale visual data analysis

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 todays 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.