Problem 1. (spring2009)
Fill in the blank (9 points, 0.5 each)
a.
Give 2 examples on imaging in bands other than the visible
band:
1

infrared
2

radio
b.
In order to image an object, the object is illuminated by an
energy source and the energy reflected from or
transmitted
through the object is collected by specialized sensors.
c.
The cones receptors in the eye are responsible for
fine details.
d.
A cert
a
in
object is exposed to a light source whose illumination
is given by i(x,y)=x
2

y
2
. If the transmittance of the omje
ct is
given by t(x,y)=1/x

y, then the image function f(x,y) is given by
x+y.
e.
Reducing the number of quantization levels
used to represent
an image results in
False countering.
f.
The formula for computing the pixel value in bilinear
interpolation is
ax+by+cxy+d
and the coefficients are
determined by the nearest
four
neighbors.
g.
If the minimum and maximum available gray levels are
0 and
100,respectively, then the histogram equalization transforms
its histogram into
flat
histogram with a mean value of
5
0.
h.
The result of
applying T(r)
=(2/r+1)

1
to
an image is
represented
using the normalized gray levels [0,1] is
negative.
i.
The filtering result of a certain 3x3 mask h(x,y) on an image
f(x,y) is expressed by g(x,y)= 2*f(x,y)

f(x

1,y

1)+3*f(x+1,y

1).
Draw th
is mask
below showing its coefficients.

1
0
0
0
2
0
3
0
0
j.
If the DFT for the function f(x,y)=[1,

3,5;0,8,

9;2,

5,1] is
computed then F(0,0)=

9.
k.
The effect of multiplying a MxM image f(x,y) by j
x+y
on its
original Fourier transform F(u,v) is
shifting
to M/4.
l.
Zero padding is an essential step in frequency processing to
avoid
aliasing.
m.
For a Butterworth
high pass filter with fixed radius , ringing can
be reduced by
decreasing n.
n.
The filter H(u,v) is expressed by mathematically as H(u,v)=
1

(u
2
+
v
2
)
. If this filter is used to process an image, then the
result is similar processing the image with
low pass filter.
Problem 1. (spring20
10
)
True or false
(4 marks)
:
1

If the gray levels are represented by 6 bits then the mean of
the equalized histogram is 32
.
T
2

The human body reflect
s
gamma ray.
F(transmit).
3

The cones receptors are responsible for
low illumination.
F(RODS).
The derivative amplifies the noise. Explain why(3marks)
The derivative in time domain is jwF(w) in frequency domain
and the noise is high
frequency component so it amplifies the
noise w*n(w).
There
is another formula used to compute the
DFT:
1/ (MN)
0.5
*F
(u,
v) how
we can know which Formula is used?
(3marks)
we draw the DFT then if F(0,0)=MN
*average(f(x,y)) it's the
original formula but i
f F(0,0)=
MN
0.5
*average(f(x,y)) it's the
new formula.
Problem
2
. (spring2009)
The image f(x,
y) is shown below. Compute the result of the
following operations at the specified pixel location only.
Assume truncation for boundary pixels
(4marks).
8
5
8
0
7
8
8
9
9
1
0
2
3
1
1
9
4
8
2
3
2
9
2
9
3
5
1
4
6
8
8
4
6
2
4
1
7
7
5
7
3
4
3
2
3
2
6
5
9
1

3*3 smoothing at pixel (3, 3).
2

5*5 median filtering at pixel (6, 6).
3

Magnitude of gradient at pixel (1,
4) computed using
Roberts' operator.
4

Laplacian at pixel
(2,
2)
.
1

pixel (3,3)= 4 smoothing (1+0+9+9+8+4+3+9+2)/9
2

pixel (6,6)=3 median(3,5,1,4,4,6,2,4,5,7,3,4,2,6,5,9)=
4.
3

pixel(1,4)=0 GX=2,GY=

7,2

7=

5.
4

pixel (2, 2)=9 laplacian=

4*9+1+9+5+9
.
Problem
3
. (spring2009)
It's desired to modify an image with a
histogram h(r) such that
the histogram of the processed image h(s) = (3/(L

1)
3
)*s
2
. Derive
the transformation function T(r) to achieve this task.
Problem
6
. (spring2009)
Each of the images shown on the left has been filtered to produce the
result shown to the right. Write down the name and the mathematical
expression for the filter that would produce the given result in each
case.
1

notch reject filter (periodic noise).
2

low pass filter(smoothing).
3

low pass filter(Gaussian without ringing).
4

high pass filter( darkening the picture).
5

band pass filter.
Problem 7. (spring2009)
The Fourier transform of an image is shown below. Draw the Fourier
transform after each performing of the following
operations:
15

15

15

10

5 0 5 10 15
1

Ideal
low pass filter with D0=5.
Draw circle from the origin with radius=5. Inside it
pass
outside it reject.
2

Ideal high pass filter with D0=5.
Draw circle from the origin with radius=5. Inside it
reject
outside it
pass
.
15

15

15

10

5 0 5 10 15
3

Ideal band pass filter with D0=10
and w=2.
Draw
2
circle
s
centered at 10 and

10
with radius 1
. Inside it
pass
outside
it
reject
.
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