Uncertain Mode Surfaces in 3D Symmetric Second-Order Tensor Field Ensembles

Abstract: The analysis of 3D symmetric second-order tensor fields often relies on topological features such as degenerate tensor lines, neutral surfaces, and their generalization to mode surfaces, which reveal important structural insights into the data. However, uncertainty in such fields is typically visualized using derived scalar attributes or tensor glyph representations, which often fail to capture the global behavior. Recent advances have introduced uncertain topological features for tensor field ensembles by focusing on degenerate tensor locations. Yet, mode surfaces, including neutral surfaces and arbitrary mode surfaces are essential to a comprehensive understanding of tensor field topology. In this work, we present a generalization of uncertain degenerate tensor features to uncertain mode surfaces of arbitrary mode values, encompassing uncertain degenerate tensor lines as a special case. Our approach supports both surface and line geometries, forming a unified framework for analyzing uncertain mode-based topological features in tensor field ensembles. We demonstrate the effectiveness of our method on several real-world simulation datasets from engineering and materials science.