Exploring Uncertainty Visualization for Degenerate Tensors in 3D Symmetric Second-Order Tensor Field Ensembles

Symmetric second-order tensors are fundamental in various scientific and engineering domains, as they can represent properties such as material stresses or diffusion processes in brain tissue. In recent years, several approaches have been introduced and improved to analyze these fields using topological features, such as degenerate tensor locations, i.e., the tensor has repeated eigenvalues, or normal surfaces. Traditionally, the identification of such features has been limited to single tensor fields. However, it has become common to create ensembles to account for uncertainties and variability in simulations and measurements. In this work, we explore novel methods for describing and visualizing degenerate tensor locations in 3D symmetric second-order tensor field ensembles. We base our considerations on the tensor mode and analyze its practicality in characterizing the uncertainty of degenerate tensor locations before proposing a variety of visualization strategies to effectively communicate degenerate tensor information. We demonstrate our techniques for synthetic and simulation data sets. The results indicate that the interplay of different descriptions for uncertainty can effectively convey information on degenerate tensor locations.