Real-Time Maximum Intensity Projection

The ability to depict blood vessels is of enormous importance for many medical imaging applications. CT and MR scanners are used to obtain volumetric data sets, which then allow the extraction of vascular structures. Especially data sets originating from MR, which are most frequently used for this purpose, exhibit some properties which make the application of standard volume visualization techniques like ray casting [26] or iso-surface extraction [33] difficult. MR data sets usually contain a significant amount of noise. Inhomogeneities in the sampled data make it difficult to extract surfaces of objects by specifying a single iso-value.

MIP exploits the fact, that within angiography data sets the data values of vascular structures are higher than the values of the surrounding tissue. By depicting the maximum data value seen through each pixel, the structure of the vessels contained in the data is captured. A straight-forward method for calculating MIP is to perform ray casting and search for the maximum sample value along each ray instead of the usual compositing process done in volume rendering. In contrast to direct volume rendering, no early ray termination is possible and the whole volume has to be processed. Depending on the quality requirements of the resulting image, different strategies for finding the maximum value along a ray can be used.

• Analytical solution: for each data cell which is intersected by the ray the maximum value encountered by the ray is calculated analytically. Trilinear blending of the cell vertices is usually assumed for data values within a cell, thus the maximum of a third degree polynomial has to be calculated. This is the most accurate but also computationally most expensive method [51].
• Sampling and interpolation: as usually done for ray casting, data values are sampled along a ray using trilinear interpolation. The cost of this approach depends on how many interpolations can be avoided that will not affect the ray maximum [51,67].
• Nearest neighbor interpolation: values of data points closest to the ray are used as maximum estimations. In combination with discrete ray traversal this is the fastest method. As no interpolation is performed, the voxel structure is visible in the resulting image as aliasing [5].

Recent algorithms for MIP employ a set of approaches for speeding up the rendering:

• Ray traversal and interpolation optimization: Sakas and others [51] interpolate only if the maximum value of the examined cell is larger than the ray-maximum calculated so far. For additional speed-up they use integer arithmetic for ray traversal and a cache-coherent volume storage scheme. Zuiderveld and others [67] apply a similar technique to avoid trilinear interpolations. In addition, cells containing only background noise are not interpolated. For further speed-up a low-resolution image containing lower-bound estimations for the maximum of clusters of rays is generated before the projection. Cells with maximum values below this bound can be skipped when the final image is generated. Finally a distance-volume is used to skip empty spaces efficiently.
• Using graphics hardware: Heidrich and others [24] use conventional polygon rendering hardware to simulate MIP. Several iso-surfaces for different threshold values are extracted from the data set. Before rendering, the geometry is transformed in a way, that the depth of a polygon corresponds to the data value of its iso-surface. MIP is approximated by displaying the z-buffer as a range of gray values. Recently the VolumePro board [48] became available as a purely hardware-based solution for MIP. The board is able to produce medium-quality MIP using shear/warp-based projection at interactive frame rates.
• Splatting and shear/warp: Several approaches [5,9] exploit the advantages of shear/warp rendering to speed up MIP. Cai and others [5] use an intermediate ``worksheet'' for compositing interpolated intensity contributions for projection of a single slice of the volume. The worksheet is then combined with the shear image to obtain the maxima. Several splatting modes with different speed/quality-tradeoffs are available, run-length encoding and sorting of the encoded segments by value are used to achieve further speed-up.

Figure 4.1: a: MIP of a test data set containing soft bounded cylinders; b: although depth shading provides some depth impression, the cylinders seem to intersect; c, d: While LMIP provides more information on the spatial structure, the results are sensitive to the threshold.

a) MIP	b) depth shaded MIP
c) LMIP - high threshold	d) LMIP - low threshold

As a MIP image contains no shading information, depth and occlusion information is lost (see figure 4.1a). Structures with higher data values lying behind a lower valued object appear to be in front of it. The most common way to ease the interpretation of such images is to animate the viewpoint while viewing (interactive frame-rates are essential here). Another approach is to modulate the data values by their depth to achieve a kind of depth shading [24] (see figure 4.1b). As the data values are modified before finding the maximum, MIP and depth-shaded MIP (DMIP) of the same data may display different objects.

Depth shading provides some hints on the spatial relation of objects. However it's performance is rather poor especially for tightly grouped structures. In such cases Closest Vessel Projection [51] or LMIP [52] can be used. Similar to MIP, for LMIP the volume is traversed along a ray, but the first local maximum which is above a user-defined threshold is depicted. If no value above the threshold is found along a ray, the global maximum along the ray is used for the pixel. With a high threshold value this method produces the same result as MIP, with a carefully selected one, less intense structures in front of more intense background are depicted, producing an effect similar to shading (see figures 4.1c, d). As this method is very sensitive to the setting of the threshold, the ability to interactively tune this parameter is extremely important.

In the following a novel approach to generate MIP images really fast is presented [42,43]. In Section 4.1.1 several algorithms for preprocessing the volume data to eliminate voxels, which will not contribute to a MIP, are discussed. Furthermore, a volume storage scheme which is based on RenderLists is presented which is optimized for skipping non-contributing voxels during rendering. In section 4.1.4 extensions of the algorithm for generating depth-shaded MIP and LMIP using the optimized data structure are discussed.

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