Extracting iso-valued features in 4-dimensional scalar fields

Abstract

Isosurfaces are an important tool for finding features in 3D scalar data. The paper describes how recursive contour meshing is applied to extract similar features in 4-dimensional space. In the case of time-varying isosurfaces f(x, y, z, t)=c, the technique constructs a solid mesh for the isosurface that sweeps a volume in space-time. An instance of an isosurface at a particular time results from applying a second constraint against this volume. The envelope defined by the time-varying isosurface can be captured in a similar way: when a time-varying isosurface f=c reaches is maximum extent, the function's partial derivative with respect to time must be zero. This second constraint and produces a surface containing the extrema of the isosurfaces. Multi-resolution models and inter-penetrating blobby objects can also be extracted from 4-dimensional representations.