Combinatorial Feature Flow Fields: Tracking Critical Points in Discrete Scalar Fields

Please always quote using this URN: urn:nbn:de:0297-zib-12151
  • We propose a combinatorial algorithm to track critical points of 2D time-dependent scalar fields. Existing tracking algorithms such as Feature Flow Fields apply numerical schemes utilizing derivatives of the data, which makes them prone to noise and involve a large number of computational parameters. In contrast, our method is robust against noise since it does not require derivatives, interpolation, and numerical integration. Furthermore, we propose an importance measure that combines the spatial persistence of a critical point with its temporal evolution. This leads to a time-aware feature hierarchy, which allows us to discriminate important from spurious features. Our method requires only a single, easy-to-tune computational parameter and is naturally formulated in an out-of-core fashion, which enables the analysis of large data sets. We apply our method to a number of data sets and compare it to the stabilized continuous Feature Flow Field tracking algorithm.

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Metadaten
Author:Jan Reininghaus, Jens Kasten, Tino Weinkauf, Ingrid Hotz
Document Type:ZIB-Report
Tag:data analysis; feature detection; time-varying data; topology-based techniques
MSC-Classification:05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15) / 05C85 Graph algorithms [See also 68R10, 68W05]
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Dxx Dynamical systems with hyperbolic behavior / 37D15 Morse-Smale systems
Date of first Publication:2011/02/10
Series (Serial Number):ZIB-Report (11-02)