@InCollection{guenther12a,
  author    = {D.~Günther and J.~Reininghaus and S.~Prohaska and T.~Weinkauf and H.-C.~Hege},
  title     = {Efficient Computation of a Hierarchy of Discrete 3D Gradient Vector Fields},
  booktitle = {Topological Methods in Data Analysis and Visualization II},
  publisher = {Springer},
  year      = {2012},
  editor    = {R.~Peikert and H.~Hauser and H.~Carr and R.~Fuchs},
  series    = {Mathematics and Visualization},
  pages     = {15--30},
  abstract  = {This paper introduces a novel combinatorial algorithm to compute a
              hierarchy of discrete gradient vector fields for three-dimensional
              scalar fields. The hierarchy is defined by an importance measure
              and represents the combinatorial gradient flow for different levels
              of detail. The presented algorithm is based on Forman's discrete
              Morse theory, which guarantees topological consistency and algorithmic
              robustness. In contrast to previous work, our algorithm combines
              memory and runtime efficiency. It thereby lends itself to the analysis
              of large data sets. A discrete gradient vector field is also a compact
              representation of the underlying extremal structures - the critical
              points, separation lines and surfaces. Given a certain level of detail,
              an explicit geometric representation of these structures can be extracted
              using simple and fast graph algorithms.},
  url = {http://tinoweinkauf.net/publications/absguenther12a.html},
}