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Fig. 13.14 Shell rendering examples. Top row, shell SR [174]: skull CT data (left) and CT data of a “dry” child’s skull (right). Bottom row, shell DVR [175]: CT skull (left), and MR head (right)
13.7 Texture Mapping
The pioneering work of exploiting texture hardware for DVR was performed by Cullip and Neumann [90] and Cabral et al. [91]. When graphics hardware does not support trilinear interpolation, 2D texture mapping (2DTM) must be adopted. In this case, the volume is decomposed into three stacks of perpendicularly object-aligned polygons. For the current viewing direction, the stack whose slicing direction (normal) must be within 45 degrees of the current viewing direction is chosen for rendering. During rasterization, each of the polygon slices is textured with the image information obtained from the volume via bilinear interpolation. Finally, the textured slices are alpha-blended in a back-to-front order to produce the final image.
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Fig. 13.15 The working pipeline of 3DTM for 3D head rendering
Fig. 13.16 Medical image rendered with 3DTM: (a) CT skull; (b) MR brain; (c) CT jaw, and (d) MR cerebral blood vessel
Figure 13.15 describes the working pipeline, and Fig. 13.16 illustrates the rendering results with this algorithm. 3DTM uploads the volume to the graphics memory as a single 3D texture, and a set of polygons perpendicular to the viewing direction is placed within the volume and textured with the image information by trilinear interpolation. Compared with 2DTM, there are no orientation limitations
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for the decomposed polygon slices, making the texture access more flexible. The compositing process is similar to 2DTM, in that the set of textured polygon planes are alpha-blended in a back-to-front order.
13.7.1 Performance Analysis
Compared with 3DTM, the main advantage of 2DTM is higher rendering speed and lower hardware requirements, since it uses efficient in-slice bilinear interpolations, instead of expensive trilinear interpolations. However, this algorithm is prone to aliasing artifacts at the edges of the slice polygons, and has to maintain three copies of the volume in graphics memory. The shift of viewing directions causes the algorithm to switch from one texture stack to another, resulting in the “popping” artifacts mentioned earlier. In 3DTM, the extracted slices can have arbitrary orientations and only a single copy of the data is required; therefore, there are no artifacts caused by the texture stack switching during the viewing direction changing process. In addition, the extracted slices are textured with trilinear instead of bilinear interpolation, so the mapped texture information has a higher accuracy. For orthographic projections, the viewport-aligned slices can be employed to achieve a consistent sampling step, but because the sampling distance cannot be uniform for projective views, “striping” artifacts are introduced. This limitation may be overcome using spherical rendering primitives [92], albeit with an increased computational cost.
13.7.2 Applications
In the published literature, there are three main types of medical applications for TM-based DVR. The first is multimodal medical image rendering and tissue separation. Sato et al. [93] designed a multidimensional TF to identify tissue structures in multimodal medical images generated with 3DTM. A two-level rendering technique was integrated with 3DTM by Hauser et al. [94], allowing different rendering techniques to be selected for different tissues based on segmentation information. Later, Hadwiger et al. [95] improved this 3DTM-based two-level DVR algorithm in the aspects of image quality and performance, minimizing the number of rendering passes and the computational cost of each pass, adding dynamic filtering, and using depth and stencil buffering to achieve correct compositing of objects created with different rendering techniques.
The second application area is in the display of specific tissues and organs for diagnosis and therapy. Holmes et al. [96] used 3DTM to achieve a real-time display of transurethral ultrasound (TUUS) for prostate treatment. This technique was also used by Etlik et al. [97] to find bone fractures, and also by Wenger et al. [98] to visualize diffusion tensor MRI (DTI) data in the brain. Wang et al. [99] exploited