Results and Discussion

The most important factor for the quality of contour images is the accuracy of gradient vectors. Quantizing gradients to a few bits for interactive rendering, limits the size of exponent $n$. High values of $n$ result in very sharp and thin contours. The quantization error of gradients close to the contour is therefore amplified and results in too bright or too dark voxel contributions. For a quantization to 12 bit, an exponent of approximately 4 provides a sufficiently narrow contour without producing disturbing artefacts (figure 4.24).

Figure 4.24: Interactive non-photorealistic rendering results

a) opacity=$I_c$	b) opacity=$g(\vert G(P)\vert)$
c) weighted sum of Phong and $I_c$	d) contours combined with an iso-surface
e) MIP of $I_c$	f) MIP of $I_c$ with color transfer function

Table 4.9: Rendering times for contour rendering

	volume size	voxels rendered	time
head/MIP	$256^2\times 225$	102k	85ms
head/back to front		366k	150ms
screws/MIP	$256^2\times 241$	337k	130ms
screws/back to front		942k	270ms

Due to more efficient skipping of black voxels and a simpler compositing operation for projecting a voxel, rendering using MIP is faster (see table 4.9) than when blending of voxel contributions is used. Although MIP allows to depict the most significant features of a volume (see figure 4.24e, f), the lack of occlusion and depth information in MIP images may be a disadvantage. The high interactivity of non-photorealistic rendering using MIP compensates for this disadvantage by adding time as an additional degree of freedom for the visualization (i.e., interactive view-point changes).

More flexibility is gained by using DVR (back to front compositing). The rendering times are acceptable (table 4.9), although slower than for MIP. Depending on the choice for voxel opacity, different effects can be achieved. By setting the opacity equal to $I_c$ (figure 4.24a) an effect similar to MIP is achieved, with the difference, that occlusion and spatial ordering of the voxels is taken into account. Contours in areas with a higher gradient magnitude are depicted brighter than in areas with lower gradient magnitude. If opacity is derived from $g(\vert G(P)\vert)$ only, the resulting image displays a blended set of surfaces with lighted contours (figure 4.24b). This approach can also be used with good results to enhance contours [11] in addition to Phong shading for surface rendering (figure 4.24c). For segmented data which allows to distinguish between different objects, non-photorealistic methods can be easily combined with other rendering methods, for example with conventional surface rendering (figure 4.24d).

The rendering times in table 4.9 have been measured using a Java implementation of the algorithms on a PII/400MHz PC with Sun JDK 1.3 for Windows.

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