Topology Control in Multiresolution Isosurface Extraction

Multiresolution modeling is a very important technique for interactive visualization of very large data sets. Multiresolution volume data structures allow the extraction of adaptively triangulated isosurfaces in large volume data sets at interactive frame rates, providing the user the ability to visualize the volume data in real-time. The isosurface is displayed at a coarse resolution for areas of low variance in the isovalue or for fast interaction, and at finer resolution for areas of high variability or detail inspections. Ideally, a coarse approximation of the isosurface has the same topological structure as in the highest resolution. Important topological properties such as the genus, or structure and number of connected components of an isosurface are often neglected in existing multiresolution isosurface extraction and rendering algorithms. This can result in sudden, and uncontrolled topological changes of the rendered isosurface whenever the global or local level-of-detail of the extracted isosurface changes. The scope of this paper is to propose an efficient technique which provides control over topological changes, in particular preservation of topolgical properties, in an interactive multiresolution isosurface extraction and rendering framework. We present two methods for topology preserving multiresolution isosurface extraction: the first is optimal in run-time and space cost, and the second is optimal with respect to the size of the extracted isosurface. Furthermore, we also present extensions of our method for controlled topology simplification.