Variational Feature Extraction in Scientific Visualization

• Applicant: Professor Dr.-Ing. Tobias Günther
• Subject Area: Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 557324483

Scientific visualization is concerned with the development of general algorithms for the analysis of large spatial data sets that arise in various scientific disciplines, such as atmospheric sciences or fluid dynamics. A common approach is to reduce the amount of information by concentrating on so-called features. In practice, however, feature extraction often requires pre-processing, such as reference frame optimization, or post-processing, such as smoothing, reconnection, or iterative refinement. For reproducibility and improved robustness, we believe that such operations should be modeled in the feature definition itself. Thus, with this project, we continue our work on a variational feature formulation that is versatile and flexible, enabling the combination of common and new feature definitions with a comprehensive set of application-agnostic regularizers. We model the solution to the proposed variational minimization both explicitly and implicitly, which requires different numerical approaches and has different implications regarding the handling of topological changes and the dependence on the initialization. We apply the approaches in different application domains, including atmospheric sciences and fluid dynamics to understand the inherent advantages and limitations of the different feature representations. We divide the project into three steps. First, we expand on explicit feature representations, for which we investigate alternative feature definitions, improve numerical extraction procedures, and apply the approach to the atmospheric sciences. Second, we investigate implicit feature representations, in which features arise as level sets in an unknown scalar field. Third, we extend the variational framework by concurrently optimizing not only the feature but also the field from which the features are extracted. This project has the potential to spur multiple lines of follow-up research on feature definitions, regularizations, feature representations, numerical extraction algorithms, and novel applications. The goal of this project is to create a paradigm shift in how features are defined, extracted, and analyzed to enable scientists from atmospheric sciences and fluid dynamics to obtain novel, detailed, and insightful views into their large-scale data.

• DFG Programme: Research Grants