Hybrid-Order Volume Rendering

Image-order and object-order algorithms have very distinct advantages and disadvantages. Therefore, some effort has been spent on combining the advantages of both approaches.

Figure 2.3: Illustration of the shear-warp mechanism. The volume slices are sheared so that all viewing rays are parallel to the major viewing axis. After the projection process has been performed, the distorted intermediate image is warped into the final image.
\includegraphics{state_of_the_art/images/shearwarp.eps}

Shear-warp [20] is such an algorithm. It is considered to be the fastest software-based volume rendering algorithm. It is based on a factorization of the viewing transformation into a shear and a warp transformation. The shear transformation has the property that all viewing rays are parallel to the principal viewing axis in sheared-object-space. This allows volume and image to be traversed simultaneously. Compositing is performed into an intermediate image. A two-dimensional warp transformation is then applied to the intermediate image, producing the final image. This basic mechanism is illustrated in Figure 2.3.

The aligned traversal is the basis for many optimizations: A runlength-encoding of the intermediate image allows an efficient early-ray termination approach. Additionally, runlength-encoding of the volume for each of the three major viewing axes allows skipping of transparent voxels. Additionally, an approach for empty space skipping which is based on a min-max octree has been presented. In contrast to runlength-encoding, this approach allows fast classification and does not require three copies of the volume.

The problem of shear-warp is the low image quality caused by using only bilinear interpolation for reconstruction, a varying sample rate which is dependent on the viewing direction, and the use of pre-classification. Some of these problems have been solved [51], however, the image quality is still inferior when compared to other methods, such as raycasting.