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Issue No. 12 - Dec. (2011 vol. 17)
ISSN: 1077-2626
pp: 2045-2052
Jan Reininghaus , Zuse Institute Berlin, Germany
Natallia Kotava , University of Kaiserslautern, Germany
David Guenther , Zuse Institute Berlin, Germany
Jens Kasten , Zuse Institute Berlin, Germany
Hans Hagen , University of Kaiserslautern, Germany
Ingrid Hotz , Zuse Institute Berlin, Germany
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.
Scale space, persistence, discrete Morse theory.

I. Hotz, D. Guenther, H. Hagen, N. Kotava, J. Reininghaus and J. Kasten, "A Scale Space Based Persistence Measure for Critical Points in 2D Scalar Fields," in IEEE Transactions on Visualization & Computer Graphics, vol. 17, no. , pp. 2045-2052, 2011.
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