Image Processing Reference
In-Depth Information
5. Prove Lemma 5.9.
6. Prove Theorem 5.17.
7. Prove Theorem 5.18.
8. The speed of convergence of the iterative refinement algorithm to com-
pute the bounds of a and b of an Ellipse may be improved if more recent
estimates are used in the equations to compute the (k + 1)-th estimate
of the lower or upper bounds. Modify the iterative refinement algorithm
in this line and check by experiments that the speed is really improved.
9. The domain of a quarter circle with a known radius is a region in (α−
β)-plane where (α
1
− β
1
) is the center of the circle. Suppose that we
some how know ⌊α
1
⌋. Can you modify the iterative refinement
algorithm to obtain a scheme to compute the domain of a quarter circle
with a known radius?
⌋ and ⌊β
1
10. Consider an isothetic ellipse E defined by the following equation
(
x−
A
)
2
+ (
y−
B
)
2
= 1. The set of digital points resulting from its dig-
itization may be defined as
H(E) = {i,j|(
i−a
A
)
2
+ (
j −b
B
)
2
6 1,i,j, integers}.
The discrete moment of a H(E) may be defined as
i
k
j
l
.
µ
k,l
(H(E)) =
(i,j∈H(E))
Show that H(E
1
,H(E
2
)) are equivalent iff
(µ
0,0
(H(E
1
)),µ
1,0
(H(E
1
)),µ
0,1
(H(E
1
)),µ
2,0
(H(E
1
))) =
(µ
0,0
(H(E
2
)),µ
1,0
(H(E
2
)),µ
0,1
(H(E
2
)),µ
2,0
(H(E
2
)))
11. Refer to the previous problem. Present an algorithm to convert H(E)
to the Object Boundary Quantization and to Freeman's chain code.
12. Let A and B be two sets of points in 2-D. A and B are linearly separable
if there exists a straight line such that A lies entirely to one side of that
line while B lies entirely on the other side. Formulate iterative refinement
technique to solve this problem of linear separability.
