Topology Control of Volumetric Data

Abstract

Three-dimensional scans and other volumetric data sources often result in representations that are more complex topologically than the original model. The extraneous critical points, handles, and components are called topological noise. Many algorithms in computer graphics require simple topology in order to work optimally, including texture mapping, surface parameterization, flows on surfaces, and conformal mappings. The topological noise disrupts these procedures by requiring each small handle to be dealt with individually. Furthermore, topological descriptions of volumetric data are useful for visualization and data queries. One such description is the contour tree (or Reeb graph), which depicts when the isosurfaces split and merge as the isovalue changes. In the presence of topological noise, the contour tree can be too large to be useful. For these reasons, an important goal in computer graphics is simplification of the topology of volumetric data.

The key to this thesis is that the global topology of volumetric data sets is determined by local changes at individual points. Therefore, we march through the data one grid cell at a time, and for each cell, we use a local check to determine if the topology of an isosurface is changing. If so, we change the value of the cell so that the topology change is prevented.

In this thesis we describe variations on the local topology check for use in different settings. We use the topology simplification procedure to extract a single component with controlled topology from an isosurface in volume data sets and partially-defined volume data sets. We also use it to remove critical points from three-dimensional volumes, as well as time-varying volumes. We have applied the technique to two-dimensional (plus time) data sets and three dimensional (plus time) data sets.