Topology preserving and controlled topology simplifying multiresolution isosurface extraction

Abstract

Multiresolution methods are becoming increasingly important tools for the interactive visualization of very large data sets. Multiresolution isosurface visualization allows the user to explore volume data using simplified and coarse representations of the isosurface for overview images, and finer resolution in areas of high interest or when zooming into the data. Ideally, a coarse isosurface should have the same topological structure as the original. The topological genus of the isosurface is one important property which is often neglected in multiresolution algorithms. This results in uncontrolled topological changes which can occur whenever the level-of-detail is changed. The scope of this paper is to propose an efficient technique which allows preservation of topology as well as controlled topology simplification in multiresolution isosurface extraction.

Automating Transfer Function Design Based on Topology Analysis

“…Gerstner and Pajarola [8] defined a bisection scheme that enumerates all grid points of a rectilinear grid in a tetrahedral hierarchy. Using piecewise linear interpolation in tetrahedra, critical points can be detected.…”

“…Gerstner and Pajarola [8] developed criteria for detecting critical points of piecewise linear scalar fields defined on tetrahedral meshes and used them in mesh simplification. We provide a comprehensive analysis of the topological behavior of piecewise trilinear interpolation and develop criteria to detect critical isovalues for these scalar fields.…”

“…Gerstner and Pajarola [8] considered piecewise linear interpolation applied to tetrahedral grids, which also leads to C 0 -continuous functions. Considering piecewise linear interpolation, critical points can only occur at mesh vertices.…”

“…When applying Gerstner and Pajarola's criterion [8] for connected components in an edge graph for the resulting implicit tetrahedrization, we obtain Fig. 4.…”

Volumetric video compression for interactive playback

“…This property significantly reduces the space and time required for searching cells containing the isosurface by using a small number of seed cells. Multiresolution [7] and view-dependent techniques [30] are useful to reduce the number of triangles in an isosurface.…”