Initially, volume visualization focussed on surface-fitting, which is done by extracting surfaces which are boundaries between different materials in the volume. Surface-fitting algorithms include among others, Marching Cubes, Contour Connecting (Kep75), Marching Tetrahedra (TPG98) and Dividing Cubes. The most frequently used method of surface extraction is the Marching Cubes algorithm for contour mapping (LC87). Surfaces are approximated by sets of polygons, fitted to constant-value contour surfaces of the volumetric data set. A threshold value is selected and polygons representing the high contrast contours are situated within each cubic voxel whose vertices span the threshold. Cubes whose vertices do not span the threshold are omitted from intersection computations. The strength of surface-fitting algorithms is that the surface corresponding to a given threshold is derived in a single pass and therefore can be rapidly displayed from any viewpoint using the highly evolved rendering techniques of computer graphics.
However, surface-fitting algorithms only work well for volumetric data that contains well-defined surfaces. They handle small or fuzzy details very poorly. For example, a teddy bear rendered with surface-fitting looks as if it is wearing a wet-suit. Surface-fitting algorithms can easily introduce incorrect topology, spurious holes and incorrectly detached pieces of surface. Artifacts caused by small details being added or removed are considered unacceptable in medical applications.
To avoid these problems direct volume rendering creates two dimensional images straight from the volume data without deriving explicit surfaces, but by casting light rays through the volume. DVR algorithms try to project the most important characteristics of the volumetric data. One such algorithm is Direct 2-D Display of 3-D Objects. This method follows parallel rays perpendicular to the view screen into the three dimensional volume and records the density value of the first encountered non-zero voxel (TT84). A similar method of ray traversal is Maximum Intensity Projection (MIP), which displays an image containing the highest density found along each ray. Additive Reprojection averages the density along each ray producing X-ray like picture (LDHR78). Other algorithms attribute an attenuation coefficient to each voxel, often called opacity, to allow for occlusion (DSSW86). Depth shading has been also considered (VMW83). These methods run fast but produce images of limited intelligibility.
An innovative and more complex algorithm for volume rendering was discovered by Marc Levoy in 1988 (Lev88). His method displays surfaces from volume data, using transparent layers, sophisticated classification and compositing methods, illumination and light transport models, without requiring an intermediate surface representation. The new features of his volume rendering algorithm revolutionalized the volume visualization field since they reproduced well the amorphous character of complex data set representing materials like clouds, fluids and gases.