Image Processing Reference
In-Depth Information
Algorithm 4: Sequential Updates for Iterative Refinement
Algorithm Sequential I R
c
l
= y
0
; { Initialize c
l
}
repeat
m
u
= min
i
(y
i
+ 1−c
l
)/i; { compute m
k+1
from c
l
}
u
c
l
= max
i
(y
i
−m
u
i) { compute c
k+2
from m
k+1
u
}
l
until changes in m
u
and c
l
become negligible.
c
u
= y
0
+ 1;
repeat
m
l
= max
i
(y
i
−c
u
)/i; { compute m
k+1
from c
u
}
l
from m
k+1
l
c
u
= min
i
(y
i
+ 1−m
l
i) { compute c
k+2
}
u
until changes in m
l
and c
u
become negligible.
end ( Algorithm Sequential I R )
points (i,y
i
) and (j,y
j
+1). We show that m
k+1
≤ m ≤ m
l
and c
k+2
≥ c ≥c
u
.
Let us call this version the sequential I R with simultaneous solution.
In reality, often the m and c values obtained by solving such simultaneous
equations are better approximations of m
l
and c
u
than m
k+
l
and c
k+
u
. Since
our iteration scheme is strictly monotone, the use of m and c as new initial
values can only hasten the convergence. See Fig. 3.8 for a comparison of the
speed of convergence of these three versions of the I R algorithms.
l
u
FIGURE 3.8: Convergence speed of I R algorithms.
3.2.5 Length Estimators
Consider that the length of a CSLS l is to be estimated given its digiti-
zation D. D is the DSLS and may be represented by a chain code C. But
