Visual Evaluation of Downsampling Filters in Respect of the Topology of Scalar Fields

In general, downsampling filters for structured volumetric grids cannot preserve the topology of a scalar field; thus, the isosurfaces of the downsampled field will not only geometrically but also topologically differ from the isosurfaces of the original field. Since these topological differences are often more important than geometric deviations, the approximate preservation of topological features is an important feature of some downsampling filters in volume visualization. We apply a recently proposed visualization of the topology of scalar fields to visually evaluate three nonlinear downsampling filters, which have been proposed to preserve more topological features than linear downsampling filters. With the help of this evaluation, we can also determine the most suitable filter to compute previews for the mentioned topology visualization.