Image Processing Reference
In-Depth Information
Fig. 7.1.
Voxel surface representation.
of 1-voxels corresponding to an object and a set of 0-voxels corresponding to
the background. Here we represent each voxel by a sample point at the center
of a voxel.
Considering a set of
2
2
voxels (sample points) and arranging the
values0and1onthem,thereare256(=2
8
) possible patterns. However,
by inverting 0 and 1 and taking into account the geometrical symmetry of
patterns, it is found that only 14 patterns are essentially different from each
other (Fig. 7.2). Therefore, it is sucient to fix the locations before a trian-
gular patch is inserted corresponding to each of these 14 patterns and store
them in the computer memory. These
2
×
2
×
2
local patterns do not ex-
ist independently, meaning that neighboring patterns strongly relate to each
other according to some deterministic rules. By using this relation and the list
of local patterns an effective algorithm was developed to generate triangular
patches sequentially with raster scanning an image. This algorithm is called
a
marching cubes algorithm
and is commonly used [Lorensen87, Watt98].
×
2
×
Remark 7.2.
Strictly speaking, it is necessary to meet several additional con-
ditions when using the algorithm. First, the inside and the outside relation
should not contradict between adjacent patches. Second, a solid figure sur-
rounded by a surface defined by a set of patches should have the same topo-
Search WWH ::
Custom Search