Results

Table 5.1: Compression survey. $^{*}$ Scalar value channel instead of gradients. $^{**}$ The attractor and basin data sets have been extracted from a volume with a vector of several scalar values at each voxel directly within the simulation application. No explicit volumetric representation is available outside the application.

data set	volume	obj.	bit/	bit/	bit/	file (w/o	ratio to
	size	voxels	pos	gradient	voxel	gradients)	gzipped
							volume
head-bone	$256^2$	378k	2.0	7.0	9.0	430k	1:22
	$\times 158$					(95k)	(1:97)
head-skin	$256^2$	231k	2.1	5.8	7.9	229k	1:40
	$\times 158$					(60k)	(1:154)
hand-bone	$256^2$	191k	2.5	7.8	10.3	246k	1:45
	$\times 232$					(60k)	(1:186)
hand-skin	$256^2$	170k	2.0	4.0	6.0	126k	1:89
	$\times 232$					(41k)	(1:273)
engine	$256^2$	298k	1.7	5.1	6.8	253k	1:13
	$\times 110$					(64k)	(1:51)
teapot	$256^3$	152k	1.7	3.4	5.1	80k	1:4
						(28k)	(1:11)
attractor	$256^3$	769k	1.8	4.9$^{*}$	6.7	639k	-$^{**}$
						(170k)
basin	$256^3$	292k	2.2	0.6$^{*}$	2.8	104k	-$^{**}$
						(80k)

Table 5.1 presents the compression rates obtained by applying the technique to a collection of data sets from different application fields. The head and hand data sets are CT scans containing objects typical for medical applications. Bone and skin surfaces extracted from the data are usually made up from 1-4% of all voxels. Using our compression scheme the boundary data is compressed by a factor of 20-90 compared to the original volume when compressed with gzip. If gradient information is not stored but approximated at the client the compression factor increases to 100-270. The cost of compressing voxel positions within such data sets is relatively independent of the surface shape (approximately 2-2.5bit/voxel). The cost for storing gradients depends on the smoothness and curvature of the surface and varies between 4 and 8bit/voxel. For objects with artificial, ``well-behaved'' surfaces like the CT scan of an engine block or the voxelized teapot, better compression is achieved for both voxel position and gradient data. The attractor and basin-of-attraction data, obtained from the simulation of a dynamical system, is also effectively compressed - especially as the basin boundary is derived from a binary classification of space and no gradient information has to be stored - it can be reconstructed from the surface shape at the client. Compression for each of the examples mentioned above takes approximately one second on a PIII/733 PC. Decompression timings for locally stored data are similar on the same PC. An applet which implements the described techniques and all compressed data sets discussed and depicted here are available at
(http://bandviz.cg.tuwien.ac.at/basinviz/compression/).

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