Image Processing Reference
In-Depth Information
3.2.5.1
(n)-characterization [76, 79]
This is the simplest characterization of a chain code and is given by the
number of elements in it.
g
MPO
(n) = n
g
BLUE
(n) = (π/4)
√
2n = 1.111n
For both estimators, RDEV tends to be a constant as n →∞. This means
that the accuracy of these estimators cannot be increased beyond a certain
point, even by increasing the sampling density. RDEV (g
MPO
(n)) = 16% and
RDEV (g
BLUE
(n)) = 11%.
3.2.5.2 (n
e
,n
o
)-characterization [76, 79]
In (n
e
,n
o
)-characterization, the number of 0s in a chain code is computed
as n
e
and the number of 1s in a chain code is computed as n
o
. This is also
known as odd-even characterization.
√
1
2
3
if (n
e
,n
o
) = (0,1)
g
MPO
(n
e
,n
o
) =
(n
e
+ n
o
)
2
+ n
o
elsewhere
√
2
n
{
m + 1
n
−1
m + 1
n
−2
m
−1
m
n
+
m−1
−1
m−1
n
g
BLUE
(n
e
,n
o
)
=
tan
n
tan
tan
n
−
1
2
log(1 + (
m + 1
)
2
) + log(1 + (
m
n
)
2
)−
1
2
log(1 + (
m−1
)
2
)}
n
n
−1
).
RDEV for both these estimators are O(n
3.2.5.3
(n,q,p,s)-characterization [76, 79]
The MPO estimator for this characterization is given by
1 + (
p
q
)
2
g
MPO
(n,q,p,s) = n
As (p/q) is a better estimate of the slope of a line, this estimator is the best
of all. The asymptomatic error for this estimator is O(n
−3/2
).
3.3 Three-Dimensional Digital Straight Line Segments
In this section, we review a few preliminary notions of three-dimensional
geometry and introduce digitization schemes in 3-D. Digitization of a 3-D line
yields a set of discrete points in 3-D. These points are usually denoted by a