Locally Adapted Reference Frame Fields using Moving Least Squares

Julio Rey Ramirez, Peter Rautek, Tobias Günther and Markus Hadwiger

IEEE Transactions on Visualization and Computer Graphics, Vol.32, No.1 (Proceedings IEEE VIS 2025), to appear , 2026

The detection and analysis of features in fluid flow are important tasks in fluid mechanics and flow visualization. One recent class of methods to approach this problem is to first compute objective optimal reference frames, relative to which the input vector field becomes as steady as possible. However, existing methods either optimize locally over a fixed neighborhood, which might not match the extent of interesting features well, or perform global optimization, which is costly. We propose a novel objective method for the computation of optimal reference frames that automatically adapts to the flow field locally, without having to choose neighborhoods a priori. We enable adaptivity by formulating this problem as a moving least squares approximation, through which we determine a continuous field of reference frames. To incorporate fluid features into the computation of the reference frame field, we introduce the use of a scalar guidance field into the moving least squares approximation. The guidance field determines a curved manifold on which a regularly sampled input vector field becomes a set of irregularly spaced samples, which then forms the input to the moving least squares approximation. Although the guidance field can be any scalar field, by using a field that corresponds to flow features the resulting reference frame field will adapt accordingly. We show that using an FTLE field as the guidance field results in a reference frame field that adapts better to local features in the flow than prior work. However, our moving least squares framework is formulated in a very general way, and therefore other types of guidance fields could be used in the future to adapt to local fluid features.

@article{Rey2025MLSObservers,
  title = {Locally Adapted Reference Frame Fields using Moving Least Squares},
  author = {Rey Ramirez, Julio and Rautek, Peter and G{\"u}nther, Tobias and Hadwiger, Markus},
  journal = {IEEE Transactions on Visualization and Computer Graphics (Proceedings IEEE VIS 2025)},
  year = {2026},
  volume = {32},
  number = {1},
  pages = {to appear}
}