Image Processing Reference
In-Depth Information
FIGURE 7.18: Potteries with thick walls. (See color insert.)
Reprinted from
International Journal of Arts and Technology
,
4
: 196-215, G. Kumar et al., Copyright 2011, with
permission from Inderscience Publishers.
and the distance of G from the axis of revolution, α, but it also depends on
the shape of G. If each pair of consecutive points comprising G has the radius
difference unity, then the number of missing voxels increases, which, in turn,
increases the total number of voxels defining S
G
.
7.3 Summary
The algorithm for construction of an outer cover executes in O(n) time
for a given grid size and requires computations in the integer domain only,
thereby providing an effective approach for 3-D shape analysis through voxel-
level approximation. Multi-grid analysis of the cover reveals a gradual increase
in the topological complexity as the grid size decreases. This is a specialty of
the algorithm as it reveals the characteristics of the object surface based on
the concavities of the cover. Extension of the algorithm to an adaptive grid
system may also prove to be useful for applications related to rough sets in
the 3-D domain.
The algorithm on wheel-throwing in digital space shows how certain e
-
cient techniques of digital geometry can be used for graphics and computer-
vision problems in 3-D space. Some test results given in this chapter demon-
strate its e
ciency and robustness in creating a digital pottery defined as a dig-
