Splatting was also employed by Birkfellner et al. [79] to generate digitally rendered radiographs (DRRs) rapidly in the iterative registration of medical images, and the authors later exploited graphics hardware to accelerate the splat-based creation of DRRs [80]. Audigier and his colleagues [81] used splatting with raycasting to guide the interactive 3D medical image segmentation, providing users with feedback at each iterative segmentation step. Since basic splatting algorithms suffer from “color bleeding” artifacts, Westover originally employed an axis-aligned sheet buffer to solve this problem. However, this technique needs to maintain three stacks of sheets and introduces “popping” artifacts. To address this issue, Mueller and his colleagues [82] aligned the sheet buffers parallel to the image plane instead of parallel to the axes, and they later accelerated this image aligned splatting algorithm with modern GPUs [83]. They also proposed a postshaded pipeline for splatting to improve the resultant image [77].

13.6 Shell Rendering

Shell rendering [84] is an efficient software-based hybrid of surface and volume rendering proposed by Udupa and Odhner. The shell rendering algorithm is based on a compact data structure referred to as a shell, which is a set of nontransparent voxels near the extracted object boundary with a number of attributes associated with each related voxel for visualization. The shell data structure can store the entire 3D scene or only the hard (binary) boundary. For a hard boundary, the shell is crisp and only contains the voxels on the object surface, and shell rendering degenerates to SR. For a fuzzy boundary, the shell includes voxels in the vicinity of the extracted surface, and shell rendering is identified as DVR. Figure 13.14 shows examples of shell SR and DVR.

13.6.1 Application and Improvements

Lei et al. [85] employed this algorithm to render the segmented structures of vessels and arteries of contrast-enhanced magnetic resonance angiography (CE-MRA) image. However, the explicit surface extraction creates errors. To address the problem, Bullitt et al. [86] selectively dilated the segmented object boundaries along all axes, and visualized the extracted fuzzy shell with raycasting. To accelerate the shell rendering speed, Falcao and his colleagues [87] added the shear-warp factorization to the shell data structure, and Botha and Post [88] used a splat-like elliptical Gaussian to compute the voxel contribution energy to the rendered image. Later, Grevera et al. [89] extended the point-based shell element to a new T-shell element comprised of triangular primitives for isosurface rendering, referred to as T-Shell rendering.