Image Processing Reference
In-Depth Information
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
FIGURE 1.11: Digital neighborhood planes in an (18,6) 3-D grid.
su
cient number of points around p in the image. We can simply denote
the NPS of p as [p] considering k remains constant in an application. This
definition is also extended [148] for a set of points P = {p
1
,p
2
,...,p
n
} as
follows:
[P] = [p
1
]∩[p
2
]∩.....∩[p
n
]
The following two properties of the NPS are easily obtained from the
above definition. These are used in segmenting and characterizing 3-D surfaces
[148, 149, 19].
Lemma 1.1. if M = P ∪Q, then [M] = [P]∩[Q].
€
Lemma 1.2. If Q⊂ P, then [P] ⊆ [Q].
€
In [18] four more additional DNPs are identified, each corresponding to the
normal defined between the point and its diagonal neighbor in the 3 × 3 × 3
mask.
