A Scale Space Based Persistence Measure for Critical Points in 2D Scalar Fields

Authors:
Jan Reininghaus;Natallia Kotava;David Guenther;Jens Kasten;Hans Hagen;Ingrid Hotz
Affiliations:
Zuse Institute Berlin, Germany;University of Kaiserslautern, Germany;Zuse Institute Berlin, Germany;Zuse Institute Berlin, Germany;University of Kaiserslautern, Germany;Zuse Institute Berlin, Germany
Venue:
IEEE Transactions on Visualization and Computer Graphics
Year:
2011

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Abstract

This paper introduces a novel importance measure for critical points in 2D scalar fields. This measure is based on a combination of the deep structure of the scale space with the well-known concept of homological persistence. We enhance the noise robust persistence measure by implicitly taking the hill-, ridge- and outlier-like spatial extent of maxima and minima into account. This allows for the distinction between different types of extrema based on their persistence at multiple scales. Our importance measure can be computed efficiently in an out-of-core setting. To demonstrate the practical relevance of our method we apply it to a synthetic and a real-world data set and evaluate its performance and scalability.