Biomedical Engineering Reference
In-Depth Information
5.
Let us consider a characteristic function in f
:
2
→{
0
,
1
}
defined over
2
. In this case, given a triangle, it can be verified
(do it as an exercise) that it has exactly two transverse edges or it does
not have transverse edges. Based on this property, write a pseudocode
for an algorithm to generate the polygonal curves, after computing the
intersections with the triangulation (see Section 7.2.3).
a CF triangulation of
6.
Would it be possible to design a T-surfaces model based on a cellular de-
composition of the image domain? What would be the advantages over the
traditional T-surfaces?
7.
Choose a gray scale image, binarize it applying several values of thresh-
olds. Later, with the same initial image, apply the following sequence of
operations and compare the results: Canny's edge detector of thresholds
30
and
80
; invert the result; apply over the result the erosion operation with a
cross structuring element. Observe the isolated regions with other values
of thresholds of your choice.
8.
Choose a binary image, apply the following sequence of operations and
describe the net effect (B is the structuring element of your choice):
(a) X
B
=
(
X
B
)
⊕
B
(b) X
B
=
(
X
⊕
B
)
B
(c) X
B
=
X
/
(
X
B
)
(d) X
B
=
(
X
B
ob
)
/
(
X
⊕
B
bk
)
, where B
ob
is the set formed from pixels
in B that should belong to the object, and B
bk
is the set formed from pixels
in B that should belong to the background.
9.
Considering the implicit representation of a curve, G
(
x
,
y
)
=
0
,
show that
the normal n and the curvature K can be computed by:
∇
G
(
x
,
y
)
∇
G
(
x
,
y
)
n
=∇
G
(
x
,
y
)
,
K
=∇·
,
respectively, where the gradient and the divergent (
∇·
)
are computed with
respect to the spatial coordinates
(
x
,
y
)
.
