Topology-based Exploration of Volume Data
Gunther H. Weber, Gerik Scheuermann, Bernd Hamann, and Hans Hagen
AbstractWhen examining a scalar field using isosurfaces, it is often difficult to identify isovalues where relevant isosurface behavior occurs. Using Morse theory, it is possible to identify critical points. These critical points indicate isosurface topology changes: the creation of new surface components, merging of surface components or the formation of holes in a surface component. Therefore, they highlight "interesting" isosurface behavior and are helpful in exploration of large trivariate data sets. We present a method that detects critical points in a scalar field defined by piecewise trilinear interpolation over a rectilinear grid. The resulting list of critical points is then used to aid users in examining a data set with isosurfaces. We further use critical isovalues to automatically generate transfer functions for direct volume rendering. We also extend the concept of critical points to critical regions. This allows us to classify regions of constant value and use our method for a wider variety of data sets.
- Gunther H. Weber, Gerik Scheuermann, Automating Transfer Function Design Based on Topology Analysis, in: Geometric Modeling for Scientific Visualization, 2004.
- Bernd Hamann, Gunther H. Weber, Gerik Scheuermann, Detecting Critical Regions in Scalar Fields, in: Data Visualization 2003 (Proceedings of VisSym), pp. 85--94, 2003.
- Gunther H. Weber, Gerik Scheuermann, Bernd Hamann, Hans Hagen, Exploring Scalar Fields Using Critical Isovalues, in: IEEE Visualization 2002, pp. 171--178, 2002.
- Gunther H. Weber, Gerik Scheuermann, Topology-Based Transfer Function Design, in: Proceedings of the Second IASTED International (VIIP 2002) Conference on Visualization, Imaging, and Image Processing 2002, pp. 527--532, 2002.