Volume visualization

Volume visualization actually is a sub-field of computer graphics. Traditionally, computer graphics algorithms expect a scene description in form of geometric objects which then is used to generate suitable images through rendering. Volume visualization algorithms, on the other hand, deal with volumetric description of objects, that is, scalar (for instance density) or vectorial (for instance flow direction) properties or combinations of these at certain positions in 3D space.

These positions in space (often called sample points or grid locations) form a grid which often is regular, meaning that cells are axis-aligned and spacings between cells are the same in all three directions. Also, quite often used is a recti-linear grid, which also is axis-aligned but the spacings along the axes may be arbitrary. Some applications areas, for instance computational fluid dynamics, produce data on a curvi-linear grid, which is a recti-linear grid transformed by a non-linear transformation but having its topology preserved. Other application areas, like, e.g., finite element or volume analysis, produce unstructured grids which have no implicit topology so topology must be specified explicitly.

There are primarily three sources of volumetric data:

• Sampled data of real objects or phenomena, for example, from medical and industrial scanning technologies like computed tomography (CT), magnetic resonance imaging (MRI) or positron emission tomography (PET).
• Data originating from a computer simulation like, for example, in meteorology (for instance for storm prediction), materials science (for instance for exploring new materials) or fluid dynamics (for instance for studying flow around objects).
• Voxelized geometric objects, which differ from traditional geometric objects that object specific information is decoupled from the rendering process and that rendering time is independent from scene complexity [56].

The advantage gained by a volumetric representation is, that objects have information inside of them. If an object specified in a traditional geometric way is cut through, ``you are going to cut through the surface and be faced with empty space'' [31], whereas when one cuts through an volumetric model she cuts through tissue and sees everything there is to see. This allows also to render amorphous phenomena like smoke, clouds, or gas which are impossible to specify geometrically. Nevertheless, surface-based visualization is still possible [27,28] and these two approaches can even easily be combined.

The application areas where volumetric data can be used are numerous. In medical imaging 3D scans of patients can be used for diagnosis or treatment planning without having to perform a surgery from the outset. In geoscience seismic measurements can be visualized, non-destructive inspection is definitely an auspicious alternative for industrial developments and the visualization of electron density maps is also quite valuable in chemistry. Also, computer graphics applications, such as computer aided design (CAD) and flight simulation (many others could be named) can take advantages of volumetric approaches [24].

The main disadvantages of volumetric specifications are, that algorithms, such as ray casting, are computationally quite demanding, although recent hardware developments already allow real-time ray casting [46,47,50], and that, of course, the memory demand is quite high. Also, the discretization entails several problems like limitations of accuracy (for instance for volume or area measurements) or aliasing. Further, all geometric information is lost which would be more accurate in cases like normal or distance computations.