From the tables above, it is clear that the basic Marching Cubes algorithm is considerably faster than the algorithms which construct topologically connected surfaces. When connected surfaces are required, edge-hashing and cache-ring extraction methods produce comparable timing results. This second point is somewhat surprising, given the increased book-keeping coding necessary for maintaining the rings. We conclude that the lack of performance degradation (and actually a small performance improvement) is due to improved cache performance.
In analyzing the performance of the parallel methods, we see that speedups are sub-optimal for all of the algorithms. Analyzing the Extract timings, we see that Marching Cubes had the best speedup, with very little extra computation required when the work was spread across processors. As expected, edge-hashing and cache-rings had added computation when split across processors. This increase reflects the overhead of sharing data at boundaries during triangle extraction, and merging the boundary data during surface construction.
Examining the Wall Clock timings and total Extraction timings from the various methods, it is clear that we didn't have exceptional load-balancing performance. This is an artifact of the uneven distribution of data values, as would be expected from radiological patient images.
A final point of interest is that these performance numbers come from execution on 90 MHz R8000 processors. These MIPS processors are relatively lenient in the penalties they impose for an L1 cache miss. This is primarily due to the fact that they are running at a relatively slow clock rate. The more stringent cache miss penalties imposed on faster processors will further improve the relative performance of cache-ring methods over hashing methods.