MIP of Contours

If contours should be rendered, voxel intensities are not constant data values from the volume as commonly used for MIP projection. Intensities $I_c$ result from a function which depends on the viewing direction and gradient magnitude. This property makes a global pre-sorting of voxels by intensity impossible. However, proper ordering of the voxels can be used to group and efficiently skip groups of voxels mapped to black either by windowing of the gradient magnitude (modifying $g()$) or by the influence of the current viewing direction.

For maximum intensity projection, the order of projecting voxels is not relevant as $max(a,b)=max(b,a)$. Thus, voxels do not have to be ordered and projected in spatial order. Instead, voxels with the same or a similar gradient direction are grouped. This exploits the fact, that voxels which are not part of a contour for the current viewing direction, are mapped to low-intensity values. Entire groups of voxels with a similar gradient direction can be skipped, if the intensity $(1 - \vert G(P) \cdot V\vert)^n$ of a representative of this group is below some threshold $\varepsilon$ (see figure 4.22). The quantization of gradient vectors for rendering leads to the required clustering of voxels into groups with the same gradient representation. For typical data sets, over 75% of all voxels can be skipped by exploiting just this scheme. Furthermore, within a group of voxels with the same gradient representation (a RenderListEntry), voxels can be sorted by gradient magnitude. If projection of voxels within a group starts with voxels with the highest gradient magnitude, processing of the RenderListEntry can be stopped as soon as the first voxel with an intensity $I_c$ below $\varepsilon$ has been projected.

Figure 4.22: Voxel ordering for MIP (2D). Voxels are grouped by (quantized) gradient direction into RenderListEntrys. Within a group, voxels are sorted by gradient magnitude. Only groups with $(1 - \vert G(P) \cdot V\vert)^n> \varepsilon$ are rendered, within a group rendering is stopped after the first voxel with $I_c<\varepsilon$ is encountered.

This arrangement of voxels allows to skip non-contributing parts of the data with utmost efficiency. The disadvantage of this optimization is the restriction of the compositing process to maximum intensity selection. Due to the arbitrary spatial ordering of the voxels, blending of voxel contributions is not feasible with this scheme. mailto:mroz@cg.tuwien.ac.at.