Exploring Classification of Topological Priors With Machine Learning for Feature Extraction.

In many scientific endeavors, increasingly abstract representations of data allow for new interpretive methodologies and conceptualization of phenomena. For example, moving from raw imaged pixels to segmented and reconstructed objects allows researchers new insights and means to direct their studies toward relevant areas. Thus, the development of new and improved methods for segmentation remains an active area of research.

Towards replacing physical testing of granular materials with a Topology-based Model.

In the study of packed granular materials, the performance of a sample (e.g., the detonation of a high-energy explosive) often correlates to measurements of a fluid flowing through it.

Improving the Usability of Virtual Reality Neuron Tracing with Topological Elements.

Researchers in the field of connectomics are working to reconstruct a map of neural connections in the brain in order to understand at a fundamental level how the brain processes information. Constructing this wiring diagram is done by tracing neurons through high-resolution image stacks acquired with fluorescence microscopy imaging techniques. While a large number of automatic tracing algorithms have been proposed, these frequently rely on local features in the data and fail on noisy data or ambiguous cases, requiring time-consuming manual correction.

High-throughput feature extraction for measuring attributes of deforming open-cell foams.

Metallic open-cell foams are promising structural materials with applications in multifunctional systems such as biomedical implants, energy absorbers in impact, noise mitigation, and batteries. There is a high demand for means to understand and correlate the design space of material performance metrics to the material structure in terms of attributes such as density, ligament and node properties, void sizes, and alignments. Currently, X-ray Computed Tomography (CT) scans of these materials are segmented either manually or with skeletonization approaches that may not accurately model the variety of shapes present in nodes and ligaments, especially irregularities that arise from manufacturing, image artifacts, or deterioration due to compression.

Toward Localized Topological Data Structures: Querying the Forest for the Tree.

Topological approaches to data analysis can answer complex questions about the number, connectivity, and scale of intrinsic features in scalar data. However, the global nature of many topological structures makes their computation challenging at scale, and thus often limits the size of data that can be processed. One key quality to achieving scalability and performance on modern architectures is data locality, i.

ISAVS: Interactive Scalable Analysis and Visualization System.

Modern science is inundated with ever increasing data sizes as computational capabilities and image acquisition techniques continue to improve. For example, simulations are tackling ever larger domains with higher fidelity, and high-throughput microscopy techniques generate larger data that are fundamental to gather biologically and medically relevant insights. As the image sizes exceed memory, and even sometimes local disk space, each step in a scientific workflow is impacted.

Shared-Memory Parallel Computation of Morse-Smale Complexes with Improved Accuracy.

Topological techniques have proven to be a powerful tool in the analysis and visualization of large-scale scientific data. In particular, the Morse-Smale complex and its various components provide a rich framework for robust feature definition and computation. Consequently, there now exist a number of approaches to compute Morse-Smale complexes for large-scale data in parallel.

TopoMS: Comprehensive topological exploration for molecular and condensed-matter systems.

We introduce TopoMS, a computational tool enabling detailed topological analysis of molecular and condensed-matter systems, including the computation of atomic volumes and charges through the quantum theory of atoms in molecules, as well as the complete molecular graph. With roots in techniques from computational topology, and using a shared-memory parallel approach, TopoMS provides scalable, numerically robust, and topologically consistent analysis. TopoMS can be used as a command-line tool or with a GUI (graphical user interface), where the latter also enables an interactive exploration of the molecular graph.

Interstitial and Interlayer Ion Diffusion Geometry Extraction in Graphitic Nanosphere Battery Materials.

Large-scale molecular dynamics (MD) simulations are commonly used for simulating the synthesis and ion diffusion of battery materials. A good battery anode material is determined by its capacity to store ion or other diffusers. However, modeling of ion diffusion dynamics and transport properties at large length and long time scales would be impossible with current MD codes.

Conforming Morse-Smale Complexes.

Morse-Smale (MS) complexes have been gaining popularity as a tool for feature-driven data analysis and visualization. However, the quality of their geometric embedding and the sole dependence on the input scalar field data can limit their applicability when expressing application-dependent features. In this paper we introduce a new combinatorial technique to compute an MS complex that conforms to both an input scalar field and an additional, prior segmentation of the domain.

Direct Feature Visualization Using Morse-Smale Complexes.

In this paper, we characterize the range of features that can be extracted from an Morse-Smale complex and describe a unified query language to extract them. We provide a visual dictionary to guide users when defining features in terms of these queries. We demonstrate our topology-rich visualization pipeline in a tool that interactively queries the MS complex to extract features at multiple resolutions, assigns rendering attributes, and combines traditional volume visualization with the extracted features.

Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees.

This paper introduces an efficient algorithm for computing the Reeb graph of a scalar function f defined on a volumetric mesh M in R3. We introduce a procedure called "loop surgery" that transforms M into a mesh M' by a sequence of cuts and guarantees the Reeb graph of f(M') to be loop free. Therefore, loop surgery reduces Reeb graph computation to the simpler problem of computing a contour tree, for which well-known algorithms exist that are theoretically efficient (O(n log n)) and fast in practice.

A practical approach to Morse-Smale complex computation: scalability and generality.

The Morse-Smale (MS) complex has proven to be a useful tool in extracting and visualizing features from scalar-valued data. However, efficient computation of the MS complex for large scale data remains a challenging problem. We describe a new algorithm and easily extensible framework for computing MS complexes for large scale data of any dimension where scalar values are given at the vertices of a closure-finite and weak topology (CW) complex, therefore enabling computation on a wide variety of meshes such as regular grids, simplicial meshes, and adaptive multiresolution (AMR) meshes.

Efficient computation of Morse-Smale complexes for three-dimensional scalar functions.

The Morse-Smale complex is an efficient representation of the gradient behavior of a scalar function, and critical points paired by the complex identify topological features and their importance. We present an algorithm that constructs the Morse-Smale complex in a series of sweeps through the data, identifying various components of the complex in a consistent manner. All components of the complex, both geometric and topological, are computed, providing a complete decomposition of the domain.

Topologically clean distance fields.

Analysis of the results obtained from material simulations is important in the physical sciences. Our research was motivated by the need to investigate the properties of a simulated porous solid as it is hit by a projectile. This paper describes two techniques for the generation of distance fields containing a minimal number of topological features, and we use them to identify features of the material.

A topological approach to simplification of three-dimensional scalar functions.

This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of a function's associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the Morse-Smale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex.