DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
Written test, 6th of January 1998.
Course name : 04250 - Digital Image Analysis
Aids allowed : All usual aids
Weighting
: All questions are equally weighed.
Name
:...................................................
Signature
:...................................................
Desk no.
:...................................................
Question
Answer
1
2
3
4
5
6
7
8
9
10
Question
Answer
11
12
13
14
15
16
17
18
19
20
Possible answers to each question are numbered from 1 to 6. The chosen number of the answer
must be entered in the table above. In case you enter an incorrect number in the table this may
be corrected by "inking out" the wrong number and instead placing the correct number below.
Should there be any doubts in connection with a correction, the question will be considered as
not answered.
ONLY THE FRONT PAGE IS TO BE HANDED-IN.
If you decide to make a blank hand-in or leave the examination prematurely the front page must
in all circumstances be handed-in. Rough drafts, calculations and comments will NOT be
included in the evaluation. Only numbers included in the above table will be registered.
A correct answer will be equivalent to 5 points. An incorrect answer will be equivalent to -1
points. Questions unanswered as well as answer number six (equivalent to "do not know") will
not produce points. The number of points required for a satisfactorily answered exam is finally
determined by teacher and external examiner.
Please don't forget to state your name, signature and desk number on the paper.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.1
Given two normally distributed populations:
  1  2 0
 
Population1: N   , 
0
0
1





(1)
  1   1 0
 
Population2: N   , 
2
0
1





(2)
The prior probabilities are assumed equal and the losses by misclassification are assumed equal.
What is the expression for the curve separating R1 and R2?
1.
x 21 x22  3x1x 2 31x12 x 2 47  0
2.
7 x1 x 2  x1 5x 2 10  0
3.
5x1 3x 2  0
4.
1 2
9
x1  x1 4 x 2   log 2  0
2
2
5.
2 x12  x22  x1 x 2 8x1 7 x 2 3  0
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.2
Consider a camera constructed by means of a CCD chip. The following is extracts from the
chip's data sheet:
Spatial resolution:
756 pixels horizontal * 581 pixels vertical
Pixel size:
10  m * 10  m
Pixel positioning:
10  m (from centre to centre)
From a given distance an image is captured of an object with width 3.75 cm. The horizontal size
of the image is exactly 12 pixels. The camera is moved 1 m further away from the object and the
horizontal image size is now 10 pixels. Calculate the focal length, f of the lens. You can use the
pin hole model for the camera in the calculations.
1.
f = 8 mm
2.
f = 10 mm
3.
f = 12 mm
4.
f = 14 mm
5.
f = 16 mm
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.3
DPCM coding is used for coding of grey level images. The image f i, j  is traversed row by
row. The actual image value is predicted, fˆ i, j  and the difference f i, j  = f i, j  - fˆ i, j  is
coded. The neighbouring pixels of f i, j  (denoted x) are shown in the figure. (These pixels are
traversed row by row and from left to right with a as the first of the shown pixels.)
a b c
d x e
f g h
Which of the following predictors can not be used for DPCM coding?
1.
fˆ i, j   (b  d ) / 2
2.
fˆ i, j   (b  e) / 2
3.
fˆ i, j   d  (b  a) / 2
4.
fˆ i, j   b  d  a
5.
fˆ i, j   (a  b  c  d ) / 4
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.4
The inner orientation of a CCD camera is described by the following parameters:
c  400 ,
a1  0 , a3  0 , a5  0 and a7  0 ,
xh  305 and y h  412 ,
  0.02 and a  1.1 .
camera constant:
the radial symmetric distortion:
principal point co-ordinates:
affinity parameters:
Below is shown an extract of a digital image recorded with this camera.
yp
737 738 739 740 741
xp
503
20
23
37
45
51
504
25
27
36
43
46
505
38
30
35
39
42
506
41
36
33
29
33
507
39
37
32
28
26
Compute the grey level value for the pixel containing the image of an object point with the coordinates (-12,8,16) in the camera co-ordinate system.
Use the nearest neighbour method for interpolation.
1.
30
4.
36
2.
32
5.
39
3.
35
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.5
Below is shown a binary image. X is the set of black pixels.
A hit-or-miss transformation is performed with the following hit-or-miss structure element:
0 * *
* 1 *
* * 1
How many black pixels are left in the resulting image?
1.
3
2.
5
3.
6
4.
8
5.
9
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.6
Which of the listed satellite born scanner systems has the best geometric resolution (spatial
resolution)?
1.
Landsat MMS
2.
The weather satellite NOAH
3.
SPOT
4.
The weather satellite Nimbus
5.
Landsat TM
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.7
3
3
1
2
1
4
2
2
3
0
3
2
3
1
4
1
0
1
2
3
3
1
2
0
3
What is the coefficient of variation of the grey level function of the above grey level image?
1.
0.58
2.
0.25
3.
0.67
4.
0.74
5.
0.50
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.8
We will code the differences f i, j  to a DPCM coding of the image f i, j  by entropy coding.
For the construction of the code the following probabilities have been determined (we consider
positive difference values only): p (0) = 1/2, p(1) = 1/4, p(2) = 1/8, p(3) =1/16, p(esc) = 1/16,
where 'esc' is used as escape character when differences larger the 3 occur. Which of the
following binary codes has the shortest expected code length (and can still be decoded
unambiguously)?
1.
'0' '1' '2' '3' 'esc'
0
01
010
0010
0011
4.
'0' '1' '2' '3' 'esc'
000
001
010
011
100
2.
'0' '1' '2' '3' 'esc'
1
000
001
010
011
5.
'0' '1' '2' '3' 'esc'
1
01
001
0001
0000
3.
'0' '1' '2' '3' 'esc'
00
01
10
110
111
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.9
What parameters for the beta distribution results in a density function proportional to
x - x2
where 0 < x < 1 ?
1.
 ,   = (2,2)
2.
 ,   = (1,3)
3.
 ,   = (3,2)
4.
 ,   = (3,3)
5.
None.
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.10
In the image black pixels are foreground and white pixels are background. We use 8connectivity for the background. How many connected components are present in the
foreground?
1.
2
2.
4
3.
6
4.
3
5.
5
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.11
Which of the following is the only true statement?
1.
The loss function, L can not be a symmetric matrix.
2.
It is necessary to know or assume the prior distribution to compute the posterior
distribution.
3.
The Bayes solution to a classification problem leads either to a linear or quadratic
discriminant function.
4.
The Minimax solution to a classification problem always leads to a linear
discriminant function.
5.
Discriminant functions between more than two populations are always linear.
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.12
A camera with camera constant c  36 mm is set up with the projection centre in the coordinates:
(Xo, Yo, Zo) = (10, 5, 2).
The camera is rotated in relation to the object co-ordinate system:
, ,    90 ,90 ,90
Calculate the image co-ordinates (in mm) for a point with object co-ordinates:
(X, Y, Z) = (16, 6, 4).
1.
(0, 0)
2.
(10, 5)
3.
(-12, 6)
4.
(4, 8)
5.
(16, -8)
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.13
Which of the below statements about image analysis are true (T) and which are false (F)?
a) Real time image analysis requires 25 images/second.
b) The number of images/second necessary for real time image analysis depends on the
dynamics of the system in question.
c) Real time image analysis can be done only on very fast special designed computers.
d) Only binary images can be used in real time image analysis.
1.
(a,b,c,d) = (F,T,F,F)
2.
(a,b,c,d) = (F,F,F,F)
3.
(a,b,c,d) = (F,T,F,T)
4.
(a,b,c,d) = (F,F,T,F)
5.
(a,b,c,d) = (T,F,T,F)
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.14
0
1
2
1
4
4
1
4
5
6
3
3
3
0
4
6
4
1
3
5
4
2
2
1
2
What will be the value of the marked centre pixel after filtering with a 5 x 5 mode filter?
1.
1
2.
4
3.
3
4.
2
5.
3.5
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.15
In a vision system a part if the goal is to find 2 pixel wide vertical lines. The lines are black on
white background. The search is done in along a horizontal line in the image. Two algorithms
are examined.
a) O a (i)  h(i - 1) - h(i) - h(i  1)  h(i  2) .
b) O1 (j)  h(j  2)  h(j  1)  h(j)  h(j  1)
O b (i)  min(O 1 (j), O1 (j  2))
Calculate the outputs of the two algorithms (O a , O b )
1.
Image 1: (O a , O b ) = (0,80) Image 2: (O a , O b ) = (80,80) Image 3: (O a , O b ) = (80,0)
2.
Image 1: (O a , O b ) = (0,0) Image 2: (O a , O b ) = (80,80) Image 3: (O a , O b ) = (0,160)
3.
Image 1: (O a , O b ) = (0,0) Image 2: (O a , O b ) = (80,80) Image 3: (O a , O b ) = (80,0)
4.
Image 1: (O a , O b ) = (0,0) Image 2: (O a , O b ) = (80,80) Image 3: (O a , O b ) = (80,160)
5.
Image 1: (O a , O b ) = (0,0) Image 2: (O a , O b ) = 80,160) Image 3: (O a , O b ) = (80,0)
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.16
0
1
2
1
4
4
1
4
5
6
3
3
3
0
4
6
4
1
3
5
4
2
2
1
2
The discrete Fourier transform is performed on the above image. What will be the result in
F(0,0)?
1.
3.6
2.
7.3 x105
3.
0
4.
8.75
5.
2.84
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.17
Consider an image pair with known relative orientation. The basis vector described in the coordinate system of image 1 is (b, 0, 0).
The rotations of image 2 in relation to image 1 is denoted ();  around the x-axis, 
around the y-axis and  around the z-axis.
2
y
1
x
z
What is the necessary condition for the epipolar lines in image 2 to be parallel?
1.
=0
2.
 = 0
3.

4.
 = 
5.

6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.18
Which of the following choices is identical to ((((X  B)  B)  B)  B) ?
1.
((((X  B)  B)  B)  B)
2.
((((X  B)  B)  B)  B)
3.
XB
4.
((X  B)  B)
5.
(( X  B)  B)
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.19
?
The Euclidean distance transform 4SSEDT must be applied to the background (white pixels) in
the image above.
What is the value of the pixel marked "?" after two of the four masks have been applied?
1.
(0,-2)
2.
(0,2)
3.
(0,-3)
4.
(-1,-2)
5.
(-2,-1)
6.
Do not know.
DTU M.SC. - COURSE EXAM
Revised Edition
Year: 1997.
Course no.: 04250, Digital Image Analysis
Front page + 20 pages
QUESTION 97.20
Which of the following statements is false?
1.
For a linear frequency modulated signal the spatial resolution depends on the timeband width product (BT).
2.
By using the SAR technique instead of the SLAR technique the azimuth resolution is
improved 2400 times for a target with the slant-range distance of 20 km when a L
band radar system (1.25 GHz) with a 2m long antenna is used.
3.
Consider two homogenous areas in a SAR intensity image with 10 and 20 as the
average pixel values in the respective areas. The variance of the pixel values in the
brightest area is 4 times larger than the variance in the other area.
4.
The ground range resolution of a SAR (i.e., the spatial resolution on the ground
orthogonal to the flight direction) close to the aircraft is poorer than further away
from the aircraft.
5.
If the SAR system described in 2. is mounted on an aircraft moving with 720 km/h
the resulting Doppler band width will be 200 Hz.
6.
Do not know.