weinkauf

T. Weinkauf and H. Theisel
Streak Lines as Tangent Curves of a Derived Vector Field
IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization 2010) 16(6), November - December 2010
Received the Vis 2010 Best Paper Award.

Stream and path lines can be described as tangent curves of a vector field. Such a description of streak lines is not yet available, which excludes them from most of the feature extraction and analysis tools that have been developed in our community.

We develop the first description of streak lines as tangent curves of a derived vector field. Furthermore, we apply a number of feature extraction and analysis tools to the new streak line vector field including the extraction of cores of swirling streak lines and the computation of streak line curvature fields.

paper  •  image gallery  •  data sets

Data sets often contain noise that hinders their processing and analysis. When the nature of the noise is unknown, it is difficult to distinguish between noise and actual data features.

We propose a smoothing method for 2D scalar fields that gives explicit control over the data features, i.e., critical points and the topological structure they induce. Feature significance is rated according to topological persistence.

This is the first topological smoothing method that guarantees a C1-continuous output scalar field with the exact specified features and topological structures.

Feature Flow Fields are a well-accepted approach for extracting and tracking features.

In the original approach, the stream lines around the feature line may diverge from it; creating a numerically unstable situation.

We introduce Stable Feature Flow Fields which guarantee that the neighborhood of a feature line has always converging behavior. This way, we have an automatic correction of numerical errors: if the integration moves slightly off the feature line, it automatically moves back to it during the ongoing integration.

Separatrix Persistence measures the feature strength of every point along a separatrix in a topological skeleton.

It aids in identifying the most important minimal/maximal lines of a scalar function. Using discrete Morse theory, these extremal lines can be computed without derivatives.

We used this to extract salient edges on surfaces as minimal/maximal lines of the principal curvatures.