Data Representation

Figure 8.1: Data structure for efficient volume rendering. During preprocessing, potentially relevant voxels are extracted from the volume and stored into a list (an array). For each voxel, the position, and a set of attributes are stored. The voxels are ordered by one of the attributes, the ``key'' attribute. This might be, for example, data value, or one of the coordinates. Groups of voxels with an identical key value are joint into RenderListEntrys. All RenderListEntrys sorted by the key value form a RenderList.

All voxels which have been classified as relevant are extracted from the volume and stored in a secondary data structure. The structure is simply a list, or array, containing attribute information for the extracted voxels. Each entry corresponds to one extracted voxel, and holds the voxel's position, data value, gradient information and/or other attributes. If different objects are distinguished within the volume, separate lists are created for the voxels of each object. The voxels are sorted by one of the attributes (for example, data value, or one of the coordinates), voxels within the list can be grouped into blocks, so-called RenderListEntrys, with the same value of a ``key'' attribute (figure 8.1). To save memory, the key attribute has to be stored just once for all voxels of the group. All RenderListEntrys, sorted by the value of the key attribute form a RenderList.

For rendering, only information contained within the list is used. Different compositing methods require a specific ordering of the voxels:

• For DVR, a consistent front-to-back or back-to-front order is required. Voxels are sorted according to depth (or the axis most parallel to the viewing direction, for shear/warp-based rendering).
• For MIP, the spatial ordering of voxels is not relevant. By sorting voxels by value several important advantages are gained. The voxels can be splatted in the order of ascending data values as the array is traversed for rendering. Therefore comparing the value of the actual voxel with the screen content is not necessary at all. Instead of directly mapping data values to a linear ramp of gray values for viewing ( $d_{min}\Rightarrow g_{min}$, $d_{max}\Rightarrow g_{max}$), medical data sets are usually viewed using a window to improve contrast and to focus on certain details. The window is defined by a center value $c$ and a width $w$ which maps all data values below $c-w/2$ to black, all data values above $c+w/2$ to white, and the data in between to a gray ramp. As realistic window functions (such as used by doctors) map significant portions of the data to black, the corresponding parts of the voxel array can be skipped during rendering at almost zero cost.
• For non-photorealistic volume rendering which enhances object contours, opacity of a voxel may depend on the direction of the gradient vector. By grouping voxels according to gradient direction, entire groups of transparent voxels can be skipped.

mailto:mroz@cg.tuwien.ac.at.