Even though volume rendering as a visualization tool is more than ten years old, only recently has research focused on making the space of transfer functions easier to explore. He et al.  generated transfer functions with genetic algorithms driven either by user selection of thumbnail renderings, or some objective image fitness function. The Design Gallery  creates an intuitive interface to the entire space of all possible transfer functions based on automated analysis and layout of rendered images. A more data-centric approach is the Contour Spectrum , which visually summarizes the space of isosurfaces in terms of metrics like surface area and mean gradient magnitude, thereby guiding the choice of isovalue for isosurfacing, and also providing information useful for transfer function generation. Another recent paper  presents a novel transfer function interface in which small thumbnail renderings are arranged according to their relationship with the spaces of data values, color, and opacity.
The application of these methods is limited to the generation of 1D transfer functions, even though 2D transfer functions were introduced by Levoy in 1988 . Levoy introduced two styles of transfer functions, both two-dimensional, and both using gradient magnitude for the second dimension. One transfer function was intended for the display of interfaces between materials, the other for the display of isovalue contours in more smoothly varying data. The previous work most directly related to this paper facilitates the semi-automatic generation of both 1D and 2D transfer functions [13,26]. Using principles of computer vision edge detection, the semi-automatic method strives to isolate those portions of the transfer function domain which most reliably correlate with the middle of material interface boundaries.
Other scalar volume rendering research that uses multi-dimensional transfer functions is relatively scarce. One paper discusses the use of transfer functions similar to Levoy's as part of visualization in the context of wavelet volume representation . More recently, the VolumePro graphics board uses a 12-bit 1D lookup table for the transfer function, but also allows opacity modulation by gradient magnitude, effectively implementing a separable 2D transfer function . Other work involving multi-dimensional transfer functions uses various types of second derivatives in order to distinguish features in the volume according to their shape and curvature characteristics [11,30].
Designing colormaps for displaying non-volumetric data is a task similar to finding transfer functions. Previous work has developed strategies and guidelines for colormap creation, based on visualization goals, types of data, perceptual considerations, and user studies [2,29,32].
Direct manipulation widgets are geometric objects rendered with a visualization and are designed to provide the user with a 3D interface [4,10,28,31,34]. For example, a frame widget can be used to select a 2D plane within a volume. Widgets are typically rendered from basic geometric primitives such as spheres, cylinders, and cones. Widget construction is often guided by a constraint system which binds elements of a widget to one another. Each sub-part of a widget represents some functionality of the widget or a parameter to which the user has access.
Many volume rendering techniques based on graphics hardware utilize texture memory to store a 3D dataset. The dataset is then sampled, classified, rendered to proxy geometry, and composited. Classification typically occurs in hardware as a 1D table lookup.
2D texture-based techniques slice along the major axes of the data and take advantage of hardware bilinear interpolation within the slice . These methods require three copies of the volume to reside in texture memory, one per axis, and they often suffer from artifacts caused by under-sampling along the slice axis. Trilinear interpolation can be attained using 2D textures with specialized hardware extensions available on some commodity graphics cards . This technique allows intermediate slices along the slice axis to be computed in hardware. These hardware extensions also permit diffuse shaded volumes to be rendered at interactive frame rates.
3D texture-based techniques typically sample view-aligned slices through the volume, leveraging hardware trilinear interpolation . Other proxy geometry, such as spherical shells, may be used with 3D texture methods to eliminate artifacts caused by perspective projection . The pixel texture OpenGL extension has been used with 3D texture techniques to encode both data value and a diffuse illumination parameter which allows shading and classification to occur in the same look-up . Engel et al. showed how to significantly reduce the number of slices needed to adequately sample a scalar volume, while maintaining a high quality rendering, using a mathematical technique of pre-integration and hardware extensions such as dependent textures .
Another form of volume rendering graphics hardware is the Cube-4 architecture  and the subsequent VolumePro PCI graphics board . The VolumePro graphics board implements ray casting combined with the shear warp factorization for volume rendering . It features trilinear interpolation with supersampling, gradient estimation, shaded volumes, and provides interactive frame rates for scalar volumes with sizes up to .