#### Selected Images

Selected Works Across all Times and Places

#### Multi-field Pattern Matching based on Sparse Feature Sampling

We present an approach to pattern matching in 3D multi-field scalar data. Existing pattern matching algorithms work on single scalar or vector fields only, yet many numerical simulations output multi-field data where only a joint analysis of multiple fields describes the underlying phenomenon fully.

#### Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields

Data acquisition, numerical inaccuracies, and sampling often introduce noise in measurements and simulations.

#### MovExp: A Versatile Visualization Tool for Human-Computer Interaction Studies with 3D Performance and Biomechanical Data

In Human-Computer Interaction (HCI), experts seek to evaluate and compare the performance and ergonomics of user interfaces.

#### Extended Branch Decomposition Graphs: Structural Comparison of Scalar Data

We present a method to find repeating topological structures in scalar data sets. More precisely, we compare all subtrees of two merge trees against each other - in an efficient manner exploiting redundancy.

#### An Edge-Bundling Layout for Interactive Parallel Coordinates

Parallel Coordinates is an often used visualization method for multidimensional data sets. Its main challenges for large data sets are visual clutter and overplotting which hamper the recognition of patterns in the data.

#### Extraction of Dominant Extremal Structures in Volumetric Data using Separatrix Persistence

Extremal lines and surfaces are features of a 3D scalar field where the scalar function becomes minimal or maximal with respect to a local neighborhood.

#### Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields

We present the first general scheme to describe all four types of characteristic curves of flow fields - stream, path, streak, and time lines - as tangent curves of a derived vector field.

#### Stable Feature Flow Fields

Feature Flow Fields are a well-accepted approach for extracting and tracking features. In particular, they are often used to track critical points in time-dependent vector fields and to extract and track vortex core lines.

#### Streak Lines as Tangent Curves of a Derived Vector Field

Characteristic curves of vector fields include stream, path, and streak lines. Stream and path lines can be obtained by a simple vector field integration of an autonomous ODE system, i.e., they can be described as tangent curves of a vector field.

#### Topology-based Smoothing of 2D Scalar Fields with C1-Continuity

Data sets coming from simulations or sampling of real-world phenomena often contain noise that hinders their processing and analysis.

#### Separatrix Persistence: Extraction of Salient Edges on Surfaces Using Topological Methods

Salient edges are perceptually prominent features of a surface. Most previous extraction schemes utilize the notion of ridges and valleys for their detection, thereby requiring curvature derivatives which are rather sensitive to noise.

#### Smoke Surfaces: An Interactive Flow Visualization Technique Inspired by Real-World Flow Experiments

Smoke rendering is a standard technique for flow visualization. Most approaches are based on a volumetric, particle based, or image based representation of the smoke.

#### Cores of Swirling Particle Motion in Unsteady Flows

In nature and in flow experiments particles form patterns of swirling motion in certain locations. Existing approaches identify these structures by considering the behavior of stream lines.

#### Vortex and Strain Skeletons in Eulerian and Lagrangian Frames

We present an approach to analyze mixing in flow fields by extracting vortex and strain features as extremal structures of derived scalar quantities that satisfy a duality property: they indicate vortical as well as high-strain (saddle-type) regions.

#### Topological Structures in Two-Parameter-Dependent 2D Vector Fields

In this paper we extract and visualize the topological skeleton of two-parameter-dependent vector fields.

#### Extracting Higher Order Critical Points and Topological Simplification of 3D Vector Fields

This paper presents an approach to extracting and classifying higher order critical points of 3D vector fields.

#### Extraction of Parallel Vector Surfaces in 3D Time-Dependent Fields and Application to Vortex Core Line Tracking

We introduce an approach to tracking vortex core lines in time-dependent 3D flow fields which are defined by the parallel vectors approach.

#### Topological Methods for 2D Time-Dependent Vector Fields Based on Stream Lines and Path Lines

This paper describes approaches to topologically segmenting 2D time-dependent vector fields. For this class of vector fields, two important classes of lines exist: stream lines and path lines.

#### Galilean Invariant Extraction and Iconic Representation of Vortex Core Lines

While vortex region quantities are Galilean invariant, most methods for extracting vortex cores depend on the frame of reference.

#### Grid-Independent Detection of Closed Stream Lines in 2D Vector Fields

We present a new approach to detecting isolated closed stream lines in 2D vector fields. This approach is based on the idea of transforming the 2D vector field into an appropriate 3D vector field such that detecting closed stream lines in 2D is equivalent to intersecting certain stream surfaces in 3D.

#### Stream Line and Path Line Oriented Topology for 2D Time-Dependent Vector Fields

Topological methods aim at the segmentation of a vector field into areas of different flow behavior. For 2D time-dependent vector fields, two such segmentations are possible: either concerning the behavior of stream lines, or of path lines.

#### Topological Construction and Visualization of Higher Order 3D Vector Fields

We present the first algorithm for constructing 3D vector fields based on their topological skeleton.

#### Boundary Switch Connectors for Topological Visualization of Complex 3D Vector Fields

One of the reasons that topological methods have a limited popularity for the visualization of complex 3D flow fields is the fact that their topological structures contain a number of separating stream surfaces.

#### Saddle Connectors - An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields

One of the reasons that topological methods have a limited popularity for the visualization of complex 3D flow fields is the fact that such topological structures contain a number of separating stream surfaces.