VOLUME MODELS FOR VOLUMETRIC DATA

To display, transform, and compare volumetric data, it is often convenient or necessary to use different representations derived from the original discrete voxel values. In particular, several methods have been proposed to compute and display an isosurface defined by some threshold value. This article describes a method to represent the volume enclosed by an isosurface as the union of simple volume primitives. The needed properties (displayed image, volume, surface, and so forth) are derived from this representation. A survey of properties that might be needed or useful for such representations shows that some important properties are lacking in the representations used so far. Basic properties include efficiency of computation, storage, and display. Some other properties of interest include stability (the fact that the representation changes little for a small change in the data, such as noise or small distortions), the ability to determine the similarities between two data sets, and the computation of simplified models. The authors illustrate this concept with a representation based on the union of spheres derived from a Delaunay tetrahedralization of the boundary points. This representation is stable and can be simplified by clustering methods.