MODELS OF IMAGES AND IMAGE OPERATIONS - Fundamentals of Three-Dimensional Digital Image Processing - page 26

Fig. 2.6. Simple arc.
(2) Digitization by grid : Superimpose a grid on an image plane. Each grid
point is regarded as a center point of a pixel. At an every cross point of
a line figure and the grid, the nearest grid point is given a 1-pixel. The
resulting digital line figure is then 8-connected.
Both methods are utilized with a 3D image. In the first case, a voxel (a
cube) that a line figure passes through becomes a 1-voxel and the other a
0-voxel (voxel digitization). A 6-connected figure † is always obtained, if we
disregard the probability that a line figure passes exactly through a vertex or
afacesharedbytwovoxels.
In the second method, a 3D grid plane is put on the 3D space, and cross
points between a line figure and the 3D grid are calculated. Each 3D grid
point is regarded as the center point of a cubic voxel. Then at each cross
point between the 3D grid and the line figure, the nearest grid point is se-
lected and a 1-voxel is put there. A resultant line figure obtained by this digi-
tization method is always 26-connected † . More detailed discussion is found in
[Jonas97].
Remark 2.3 (Simple arc). In the simplest form of a line figure, only two
voxels have one 1-voxel in their k -neighborhoods and all other voxels have
exactly two 1-voxels in their k -neighborhoods. We call such a figure simple
( k -connected † ) digital curve ,orbriefly simple arc . Two voxels that have only
one neighboring 1-voxel are called edge voxel (edge point) and others are called
connecting voxels (connecting point) (Fig. 2.6).
The direction from an arbitrary 1-voxel on a digital line figure toward
the other 1-voxel in the k -neighborhood can be represented by using a code
specific to each direction (such as integers 1 , 2 ,..., 26 ) (Fig. 2.7). This code is
called the direction code or chain code . A simple digital arc is exactly defined
by the start point and a sequence of the chain code.
Desirable properties of the digitization of a 3D line figure were explained
in [Jonas97] as introduced below.
† The term “ k -connected” will be explained in detail in Section 4.1.2.