Volume visualization

Volume visualization is a method of extracting information from volumetric datasets through interactive graphics and imaging, and is concerned with the representation, manipulation, and rendering of these datasets [Gallagher 1995; Kaufman 1991; Rosenblum 1994]. Volume data are 3D entities that may have information inside them, may not consist of surfaces and edges, or may be too voluminous to be represented geometrically. Volume visualization encompasses an array of techniques for peering inside the dataset and for interactively extracting meaningful information from it using transformations, cuts, segmentation, translucency, measurements, and the like. The primary sources of volume data are three: sampled data of real objects or phenomena, computed data produced by a computer simulation, and modeled data generated from a geometric model. Examples of applications generating sampled data are medical imaging (e.g., CT, MRI), biology (e.g., confocal microscopy), geoscience (e.g., seismic measurements), industry (e.g., nondestructive inspection), and chemistry (e.g., electron density maps) [Kaufman 1991]. Some examples of applications generating computed datasets, typically by running a simulation on a supercomputer, are meteorology (e.g., storm prediction), computational fluid dynamics (e.g., water flow), and materials science (e.g., new materials). Recently, many traditional computer graphics applications, such as computer-aided design and flight simulation [Cohen and Shaked 1993; Kaufman et al. 1993], have been exploiting the advantages of volumetric techniques for modeling, manipulation, and visualization, an approach called volume graphics [Kaufman et al. 1993]. Volumetric data is typically a set S of samples (x, y, z, v), representing the value v of some property of the data at a 3D location (x, y, z). If v is simply a 0 or a 1, with 0 indicating background and 1 indicating the object, the data is called binary data. The data may instead be multivalued, with v representing some measurable property of the data, such as density, color, heat, or pressure. The value v may even be a vector, representing, for example, velocity at each location. In general, the samples may be taken at random locations in space, but in many cases S is isotropic, containing samples taken at regularly spaced intervals along three orthogonal axes. Since S is defined on a regular grid, a 3D array (called volume buffer, cubic frame buffer, 3D raster) is typically used to store the values. S is therefore referred to as the array of values S(x, y, z), which is defined only at grid locations. A function may be defined to describe the value at any continuous location by approximating v at a location (x, y, z) using some interpolation function to S, such as zero-order (nearest-neighbor), piecewise function known as first-order (trilinear), or higher-order interpolation. The region of constant value that surrounds each sample in zero-order interpolation is known as a volume cell (voxel for short), with each voxel being a rectangular cuboid having six faces, twelve edges, and eight corners. The terms, voxel, grid location,