VISUALIZATION OF 3D GRAY-TONE IMAGES - Fundamentals of Three-Dimensional Digital Image Processing - page 212

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Fig. 7.3. Interpolation of a density value. A density value of an interpolated voxel
P is calculated using density values of the nearest eight voxels.
The density value distribution along a curved surface is calculated in a sim-
ilar way based on interpolation. Examples used in medical image processing
include density value distribution along the surface of massive organs like liver,
and on the inner walls of tubular or cavity organs such as the bronchus, colon,
and stomach. To calculate density distributions along complicated surfaces is
needed in applications such as virtual endoscopy, multiplanar reconstruction,
and to unravel the colon [Harker00, Hayashi03, Oda06, Truong06, Wang98].
7.3.2 Surface
Rendering surfaces of solid objects is one of the major problems in com-
puter graphics. Nowadays a variety of methods is available and explained in
many computer graphics textbooks, in particular surface rendering [Foley84,
Watt98, Bankman00]. This method is used primarily for rendering the shape
of surface (a 3D curved surface) of a 3D solid object. If this surface is derived
from a 3D gray-tone image by a suitable method, the surface rendering is
useful also to visualize a 3D image. For example, if this surface represents
an equidensity surface, a rendered result shows one of the characteristics of a
density distribution in a 3D space.
Remark 7.4. Displaying a section of an image is regarded as rendering the
gray value distribution patterns seen on a cutting plane. In this sense the
visualization of a section is reduced to that of a surface. If we find a 3D
coordinate value of a point drawn on a 2D image plane, then a density value
for that point is derived directly from an original 3D image.