Image Processing Reference

In-Depth Information

Exercise 3:
An image is first rotated 10° and then scaled with a factor 2 in both

horizontal and vertical direction. Next, the image is scaled with a factor 0.5 in

both horizontal and vertical direction and rotated

−

10°. Do we now have the same

image as we started out with?

Exercise 4:
An image is first rotated 10° and then scaled with a factor 2 in both

horizontal and vertical direction. Would the same image appear if the order of the

rotation and scaling is reversed (i.e., first scaling and then rotation)?

Exercise 5:
An input image
f(x,y)
consists of a black background with a white

rectangle on top. The corners of the rectangle are located at:
(
50
,
50
)
,
(
50
,
60
)
,

(
60
,
50
)
and
(
60
,
60
)
. We want to scale the image with a factor 2 in the horizontal

direction and a factor 1.5 in the vertical direction. What will the area of the white

rectangle be after the scaling?

Exercise 6:
f(x,y)
is rotated 15
◦
around the point
(
55
,
55
)
. Where will the corner

(
50
,
50
)
be located after the rotation?

Exercise 7:
f(x,y)
is sheared with
B
x
=

2 and
B
y
=−

1
.
5. Where will the corner

(
50
,
50
)
be located after the shearing?

Exercise 8:
In an image the following pixel values are present:
f(
10
,
10
)

=

10,

f(
10
,
11
)

=

12,
f(
11
,
10
)

=

11 and
f(
11
,
11
)

=

9. During a backward mapping

f(
10
.
3
,
10
.
8
)
. What value will
g(
100
,
100
)
have if

we use i) zero-order interpolation? ii) first-order interpolation?

Exercise 9:
The mapping between two coordinate systems
(x, y)
and
(x
,y
)
is de-

fined via the LUT below. Which position does the point
(x, y)

it is found that
g(
100
,
100
)

=

=

(
8
,
6
)
correspond

to in
(x
,y
)
?

(x, y) (
1
,
4
)
3
,
4
)
6
,
4
)
10
,
4
)
2
,
7
)
5
,
7
)
10
,
7
)
3
,
10
)
5
,
10
)
9
,
9
)

(x
,y
)
0
,
1
)
3
,
1
)
5
,
1
)
10
,
2
)
1
,
4
)
4
,
4
)
9
,
5
)

(
1
,
7
)

(
3
,
8
)

(
7
,
7
)

Additional exercises:
What is camera calibration? What can it be used for and how

does it work?