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Topology-based Exploration of Volume Data

Gunther H. Weber, Gerik Scheuermann, Bernd Hamann, and Hans Hagen

Abstract

Image When 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.

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Gunther H. Weber