On the (Un)Suitability of Strict Feature Definitions for Uncertain Data - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 46

min , max -30 30

Fig. 4.2 Salient edges of a surface are detected using a topological analysis of the principal curva-
tures

κ min ,κ max . After computing the curvature fields ( left ), we extract their topological skeletons
using discrete Morse theory ( middle ). It consists of critical points and separatrices—the latter being
lines of minimal/maximal curvature. We quantify the significance of these lines using separatrix
persistence and remove all parts below a certain threshold. This effectively removes all noise-
induced structures and yields all perceptually salient concave and convex edges of the input surface
( right )

example. Later, it has also been applied to filter extremal lines in general scalar fields
such as the elevation maps of Mars [ 6 ].

4.3 Conclusion

While strict feature definitions introduce a notion of certainty by their mere definition,
they are not necessarily antagonistic to the concept of uncertainty. We reviewed three
strategies for dealing with strict feature definitions in the presence of noisy/uncertain
data: the development of fuzzy analogs to strict feature definitions, the aggregation of
features, and the filtering of features. The latter is usually done by means of a notion
of “feature strength”, which is not only useful to remove noise-induced structures,
but may also be applied to build a hierarchy of features.

References

1. Doleisch, H., Gasser, M., Hauser, H.: Interactive feature specification for focus+context visu-
alization of complex simulation data. In: Data Visualization 2003. Proceeding Visualisation
Symposium 03, pp. 239-248 (2003)
2. Eberly, D.: Ridges in Image andData Analysis. Kluwer Acadamic Publishers, Dordrecht (1996)
3. Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification.
Discrete Comput. Geom. 28 (4), 511-533 (2002)
4. Forman, R.: Morse theory for cell-complexes. Adv. Math. 134 (1), 90-145 (1998)
5. Garth, C., Tricoche, X., Scheuermann, G.: Tracking of vector field singularities in unstructured
3D time-dependent datasets. Proc. IEEE Vis. 2004 , 329-336 (2004)
6. Gnther, D., McGuire, P.C., Walter, S., Weinkauf, T., Hege, H.C.: Extraction of valley networks
in mars elevation maps. In: European Planetary Science Congress (Poster). Rome, Italy (2010)
7. Haller, G.: Distinguished material surfaces and coherent structures in three-dimensional fluid
flows. Phys. D 149 (4), 248-277 (2001)
8. Helman, J., Hesselink, L.: Visualizing vector field topology in fluid flows. IEEE Comput.
Graphics Appl. 11 , 36-46 (1991)
9. Milnor, J.: Morse Theory. Princeton University Press (1963)
10. Miura, H., Kida, S.: Identification of tubular vortices in turbulence. J. Phys. Soc. Jpn. 66 (5),
1331-1334 (1997)