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Extraction of Dominant Extremal Structures in Volumetric Data using Separatrix Persistence
Computer Graphics Forum 31(8), December 2012
Extremal lines and surfaces are important in many applications, e.g., computer tomography, fluid dynamics, cell biology. We present a novel topological method to extract these features using discrete Morse theory.
We extend the notion of Separatrix Persistence from 2D to 3D. It allow to determine the most important (parts of) extremal lines and surfaces, and serves as a robust filtering measure of noise-induced structures. Our purely combinatorial method does not require derivatives or any other numerical computations.
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Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields
Computer Graphics Forum (Proc. Eurographics) 31(2), May 2012
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. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. Furthermore, our scheme gives rise to new types of curves. In particular, we introduce advected stream lines as a parameter-free variant of the time line metaphor.
This novel mathematical description allows for a large number of feature extraction and analysis tools for all characteristic curves, which were previously only available for stream and path lines. Possible applications include the computation of time line curvature fields and the extraction of cores of swirling advected stream lines.
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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.