Streamline Variability Plots for Characterizing the Uncertainty in Vector Field Ensembles

We present a new method to visualize from an ensemble of flow fields the statistical properties of streamlines passing through a selected location. We use principal component analysis to transform the set of streamlines into a low-dimensional Euclidean space. In this space the streamlines are clustered into major trends, and each cluster is in turn approximated by a multivariate Gaussian distribution. This yields a probabilistic mixture model for the streamline distribution, from which confidence regions can be derived in which the streamlines are most likely to reside. This is achieved by transforming the Gaussian random distributions from the low-dimensional Euclidean space into a streamline distribution that follows the statistical model, and by visualizing confidence regions in this distribution via iso-contours. We further make use of the principal component representation to introduce a new concept of streamline-median, based on existing median concepts in multidimensional Euclidean spaces. We demonstrate the potential of our method in a number of real-world examples, and we compare our results to alternative clustering approaches for particle trajectories as well as curve boxplots.