Results

The algorithm described was implemented and timed on an Intel P4 1900 MHz machine and assessed in the trans-bronchial biopsy application using a 364×264×144 data set of a human chest. The important background objects (aorta, pulmonary arteries and tumor) were pre-segmented. For the tumor, a watershed-from-markers algorithm was used, the vessels were segmented using the thresholding-based technique (see section 4). Three sequences, each consisting of 100 images ( 512×512 pixels), were rendered and timed: one sequence displaying only the surface of the trachea, one displaying only the background objects, and one displaying the surface semi-transparently over the background objects. Figure 7 shows three snap shots out of each sequence, table 1 gives timings.

Figure 7: three image sequences

Table 1: frame times in seconds for sequences of images

algorithm used	minimum	maximum	average
surface only	0.873	1.249	0.968
background objects only	1.224	1.769	1.502
surface and background objects	2.186	2.896	2.532

Cell-based first-hit ray casting performs similarly to conventional first-hit ray casting (where rays are tracked from the eye point to the intersection points with iso-surfaces) in the surface-only scenario. Conventional ray casting, however, is outperformed quite significantly, if background objects are rendered. The main reason for the good performance are the short paths that rays have to traverse. Average numbers of local rays per pixel range between 1.1 and 1.4 for surface only and background only and between 2.5 and 3 for the semi-transparent views. Performance is heavily influenced by the number of objects and the number of different thresholds, since these determine, how many macro-cells have to be processed. Also, the macro-cell size has an influence on rendering speed, as it determines the number of macro-cells, the length of local rays and the efficiency of early scan line termination.