Localized Topological Simplification of Scalar Data

This paper describes a localized algorithm for the topological simplification of scalar data, an essential pre-processing step data analysis (TDA). Given field f and selection extrema to preserve, proposed (LTS) derives function g that is close only exhibits selected set extrema. Specifically, suband superlevel components associated with undesired are first locally flattened then correctly embedded into global field, such these regions guaranteed-from combinatorial perspective-to no longer contain any In contrast previous approaches, LTS independently processes domain actually need be simplified, which already results in noticeable speedup. Moreover, due nature algorithm, can utilize shared-memory parallelism simplify simultaneously high parallel efficiency (70%). Hence, significantly improves interactivity exploration parameters their effect on subsequent analysis. For tasks, brings overall execution time plethora TDA pipelines from minutes down seconds, average observed speedup over state-of-the-art techniques up ×36. Furthermore, special case where preserved based persistence, adapted version partially computes persistence diagram simplifies features below predefined threshold. The effectiveness LTS, its efficiency, resulting benefits demonstrated several simulated acquired datasets different application domains, including physics, chemistry, biomedical imaging.