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
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