Image Processing Reference
In-Depth Information
r 2
r 3
r 1
q 2
p 2
q 1
p 1
q 5
p 3
q 3
, q 4
q=r 0
r 4
q 0
p
p 0
p 4
p 9 ,
p 5
q 9
p 8
q 8
p 6
q 6
r 7
r 6
r 5
p 7
q 7
(a)
(b)
FIGURE 1.8: (a) The order of searching a foreground pixel in the neigh-
borhood of a border pixel at p with a background neighbor at q in an (8,4)
digital grid. The order follows clockwise movement starting from q. (b) The
sequence of pairs of border pixels (p i ,q i ), where p i belongs to the foreground,
and q i belongs to background, respectively, for the point set as shown in Fig.
1.7. (See color insert.)
ing or path following is required to obtain the chain code of a sequence of
border points. The advantage of this scheme is in its linear representation.
Using chain codes various local and global properties of digital curves can be
derived. In Chapter 3 and 4 we discuss its use in characterization of a digital
straight line segment and estimation of its length. The drawback of represent-
ing a curve using chain code is that it is sometimes quite long and sensitive
to small disturbances. It is also di cult to perform set operations like union
and intersection using the coded data.
1.3.3.3
Neighborhood Plane Set (NPS)
Like 2-D grids, in 3-D also, discrete orientations of primitive planar patches
are used to encode the local surface features. In [148] in a (26,6) 3-D digital
grid 9 neighborhood planes around a point p are identified, whose normals
are in the directions of one of its 18-neighbors. These planes are called digital
neighborhood planes (DNP) of p. They are illustrated in Fig. 1.11.
The neighboring condition of p determines the plane in which p lies. Let
P i be the set of points assigned to the i-th neighboring plane as described in
Figure 1.11. In a digital picture, P = (G 3 ,18,6,O), the neighborhood plane
set (NPS) of a point p belonging to an object O, is defined as:
[p] k = {i||N 18 (p)∩O∩P i | > k)}, k ≥ 3.
Here, |S|defines the cardinality of set S. The value of k usually lies between
3 and 5. It may be noted that in the above, N(p) denotes the set of neighboring
points of p. The NPS of a 3-D point refers to the set of DNPs that have a
 
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