Volume rendering []

An initial image is generated by casting a uniform but sparse grid of rays into the volume data, interpolating between the resulting colors and resampling at the display resolution. A sampling rate of one ray per four pixels corresponding to a sampling rate of one ray per four voxels, is typical. Subsequent images are generated by discarding interpolated colors, casting more rays and repeating the interpolation and resampling steps. Recursive subdivision and based on color differences is used to concentrate these additional rays in regions of high image complexity and recursive bi-linear interpolation is used to to form images from the resulting non-uniform array of colors.
The cost of computing each image in a refinement sequenz is equal to the sum of the costs of recursive subdivision, ray tracing and recursive interpolation.

Algorithm: The voxel array the following algorithm is applied to is already shaded and classified.

1. The image plane is divided into square sample regions measuring pixels on a side.
2. Parallel viewing rays are cast into the voxel array from the four corner pixels of each region.
3. Each ray is devided into equal-size sample intervals and color and opacity is computed at the center of each interval by tri-linear interpolation of the colors and opacities of the nearest eight voxels.
4. The resampled colors and opacities are then composited to yield a color for the ray.
5. If the range of colors returned by the four rays in a sample region is less than some , no further processing is performed on the region, otherwise the region is divided into four subregions and more rays are cast.
6. Subdivision is continues until the range of colors falls below or the size of the region reaches some .
7. An image is formed by interpolating between the available colors (to ensure continuity): The image plane is devided again into square regions measuring . Pixels are interpolated at the midpoints of the four sides and at the center of each region. The region is then subdivided into four subregions and the process is repeated. Subdivision continues until the region contains only one pixel.
8. To refine the image all interpolated pixels are cleared, the level of detail is increased by decreasing , and/or and repeating the the algorithm. To avoid that the same rays are cast several times a flag is maintained for each pixel.

Problems: High values of cause features to missed, high values of cause features to be ignored even if they are not missed and high values of cause features to be poorely resolved even if they are neither missed or ignored. Inapropriate values for these parameters cause suboptimal presentation of the data as well as unequal intervalls between successive frames in refinement sequenzes. Algorithms are needed that automatically select an optimum sequenz of values based on the characteristics of a particular dataset.

Results: