Computing a Stable Distance on Merge Trees

Bollen, Brian; Tennakoon, Pasindu; Levine, Joshua A.

doi:10.1109/tvcg.2022.3209395

Title: Computing a Stable Distance on Merge Trees

Journal Article · Wed Oct 05 00:00:00 EDT 2022 · IEEE Transactions on Visualization and Computer Graphics

DOI:https://doi.org/10.1109/tvcg.2022.3209395· OSTI ID:1998147

Bollen, Brian ^[1]; Tennakoon, Pasindu ^[1];

^[1]

University of Arizona, Tucson, AZ (United States)

Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological summaries cannot and 2) to still be robust to perturbations in the dataset. The combination of these two properties, known respectively as stability and discriminativity, has led to theoretical distances which are either thought to be or shown to be computationally complex and thus their implementations have been scarce. In order to design similarity measures on merge trees which are computationally feasible for more complex merge trees, many researchers have elected to loosen the restrictions on at least one of these two properties. The question still remains, however, if there are practical situations where trading these desirable properties is necessary. Here we construct a distance between merge trees which is designed to retain both discriminativity and stability. While our approach can be expensive for large merge trees, we illustrate its use in a setting where the number of nodes is small. This setting can be made more practical since we also provide a proof that persistence simplification increases the outputted distance by at most half of the simplified value. As a result, we demonstrate our distance measure on applications in shape comparison and on detection of periodicity in the von Kármán vortex street.

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Research Organization:: Univ. of Arizona, Tucson, AZ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0019039

OSTI ID:: 1998147

Journal Information:: IEEE Transactions on Visualization and Computer Graphics, Vol. 29, Issue 1; ISSN 1077-2626

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Merge trees
scalar fields
distance measure
stability
edit distance
persistence

Title: Computing a Stable Distance on Merge Trees

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