@ARTICLE{weinkauf11b,
  author = {T.~Weinkauf and H.~Theisel and A.~Van~Gelder and A.~Pang},
  title = {{S}table {F}eature {F}low {F}ields},
  journal = {IEEE Transactions on Visualization and Computer Graphics},
  year = {2011},
  volume = {17},
  pages = {770--780},
  number = {6},
  month = {June},
  abstract = {Feature Flow Fields are a well-accepted approach for extracting and
              tracking features. In particular, they are often used to track critical
              points in time-dependent vector fields and to extract and track vortex
              core lines. The general idea is to extract the feature or its temporal
              evolution using a stream line integration in a derived vector field
              -- the so-called Feature Flow Field (FFF). Hence, the desired feature
              line is a stream line of the FFF. As we will carefully analyze in
              this paper, the stream lines around this feature line may diverge
              from it. This creates an unstable situation: if the integration moves
              slightly off the feature line due to numerical errors, then it will
              be captured by the diverging neighborhood and carried away from the
              real feature line. The goal of this paper is to define a new FFF
              with the guarantee that the neighborhood of a feature line has always
              converging behavior. This way, we have an automatic correction of
              numerical errors: if the integration moves slightly off the feature
              line, it automatically moves back to it during the ongoing integration.
              This yields results which are an order of magnitude more accurate
              than the results from previous schemes. We present new stable FFF
              formulations for the main applications of tracking critical points
              and solving the Parallel Vectors operator. We apply our method to
              a number of data sets.},
  keywords = {feature extraction, feature flow fields, topology, parallel vectors, time-dependent vector fields},
  url = {http://tinoweinkauf.net/}
}