Image Processing Reference
In-Depth Information
Triangulated object (69451 faces)
Resolution 0.3 (6096 surface voxels)
Resolution 0.5 (15488 surface voxels) Resolution 1.0 (58560 surface voxels)
FIGURE 7.4: Voxelation of
bunny
at different resolutions. (See color insert.)
[31, 45]. In general, these algorithms follow the principle of marching cube
that triangulates a 3-D iso-surface based on cubic cell decomposition, their
local configurations, and displacement [45, 136, 158]. Approaches to reduce
computational time have been suggested by several researchers [91, 135, 212].
Nevertheless, the algorithm can be enhanced to handle multi-resolution rec-
tilinear data [211] and data sets in higher dimensional space [12, 11]. More
recently, the problem of approximating a 3-D digital object by a polyhedral
surface has also been investigated by several researchers [189, 190]. It has been
proved that obtaining an optimal polyhedral reconstruction with trapezoidal
or triangular facets is strongly NP-hard [33]. Several other methods have been
used for digitization of 3-D objects including majority interpolation, a mod-
ification of the marching cubes algorithm, ball union, tri-linear interpolation,
bcc and fcc grids, etc. [199, 198, 200].
