DTU M.SC. - COURSE EXAM Revised Editionjmca/02501/exams/eksop.1999.UK.pdf · DTU M.SC. - COURSE EXAM Revised Edition Year: 1999. Course no.: 04250, Digital Image Analysis Front page

DTU M.SC. - COURSE EXAM Revised Edition

Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages Written test, 16th of December 1999. Course name : 04250 - Digital Image Analysis Aids allowed : All usual aids Weighting : All questions are equally weighed. Name : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signature : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Desk no. : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Question 1 2 3 4 5 6 7 8 9 10 Answer

Question 11 12 13 14 15 16 17 18 19 20 Answer

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.


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.1 A camera is made using a CCD-chip. The chip has the following data: Resolution : 756 pixels horizontal * 581 pixels vertical Pixels size : 11 µ m * 11 µ m Pixels placement : 11 µ m (centre to centre) Given a focal length (camera constant) of 8 mm, find the field of viewθ (diagonal). 1. θ = 76.50 2. θ = 66.50 3. θ = 56.50 4. θ = 46.50 5. θ = 36.50 6. Do not know.


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.2

In the image we see an object consisting of 5 black foreground pixels. what is the spatial dispersion matrix for this object?

1.

5445,3

2.

2.53

34

3.

4442,5

4.

5,34

45

5.

2,53

33

6. Do not know.


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.3 A point P has the following coordinates in the object coordinate system:

=

222

ZYX

In a camera coordinate system point P has the coordinates:

−−

=

448

zyx

The camera is rotated around a point Q, that is different from the projection centre. In the object coordinate system, Q’s coordinates are:

−=

31

2

dz

dy

dx

The camera coordinate system and the object coordinate system are orientated in the same way, i.e. the axis of the two systems are parallel and the axis have the same positive directions. Calculate the coordinates (q of point Q in the camera coordinate system. )q,q, zyx

1. (-12, -5, 5) 2. (-3, 4, 8) 3. (4, 5, 8) 4. (14, 12, 6) 5. (5, -8, 10) 6. Do not know


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.4 Lossy coding was applied to a digital map. A part of the decoded image is shown below. Which of the following techniques was applied as the first step of the coding?

1. Prediction for Differential Coding 2. Motion compensation 3. Conditional probabilities 4. DCT (8 x 8 pixels) 5. JBIG 6. Do not know.


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.5 We want to use a feature vector x to discriminate between four classes: 321 ,, πππ and 4π . The prior probabilities are 0.4, 0.2, 0.3 and 0.1 respectively, and the loss function is

Chosen class

1π 2π 3π 4π

1π 0 1 1 2

2π 1 0 1 2

3π 1 1 0 2 True

cla

ss

4π 4 4 4 0

Which one of the following five possibilities is not a Bayes discriminant function for any of the classes? 1. -0,8 f (x | 1π ) - 0,4 f (x | 2π ) - 0,6 f (x | 3π ) 2. -0,4 f (x | 1π ) - 0,3 f (x | 3π ) - 0,4 f (x | 4π ) 3. -0,2 f (x | 2π ) - 0,3 f (x | 3π ) - 0,4 f (x | 4π ) 4. -0,4 f (x | 1π ) -0,2 f (x | 2π ) - 0,4 f (x | 4π ) 5. -0,4 f (x | 1π ) -0,4 f (x | 2π ) - 0,4 f (x | 4π ) 6. Do not know.



We want to perform a Voronoi tessellation of the set of all pixels by three points - the three black pixels. How many pixels are associated with the upper-left point if we use a Euclidean distance transformation? 1. 13 2. 11 3. 15 4. 14 5. 17 6. Do not know.



We perform a hit-or-miss-transformation on the black pixels in the above with the composite structuring element

0 1 * 1 1 1 * 1 *

How many black pixels are there in the resulting image? 1. 6 2. 4 3. 3 4. 5 5. 2 6. Do not know.


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.8 Which of the statements below are true (T) and which are false (F):

a) 1'st order binary moments are good for real time vision.

b) Region growing is good for real time vision.

c) It is not possible to control unstable systems using vision.

d) Active signalling increases the time used for image processing significantly. 1. (a,b,c,d) = (T,T,T,F) 2. (a,b,c,d) = (F,T,T,F) 3. (a,b,c,d) = (T,F,F,F) 4. (a,b,c,d) = (T,F,T,T) 5. (a,b,c,d) = (F,T,F,T) 6. Do not know.



A 7*7 digitradial disto

1a = 0, 3a = The princip The image input transf

0. 0.8 y0. 1.1 x

−=+=

Which pixevalue in the 1. 9 2. 6 3. 7

9

4 9

4

Y

3

7

5

8

2

7

9

al imartion g

1.2 ⋅−

al poin

is corrormati

x1 x6+′⋅+′⋅

l value input

8

4

9

ge has the pixiven by the p

, 210−5 1a −=

t of the imag

ected for the on.

y0.6 y0.1

′⋅′⋅

is assigned t image is dete

8
4
4

el valarame

10.3 ⋅

e is (4

distor

o the rmine

4

3

8

7

9

ues asters:

and 3−

, 4).

tion, a

pixel (d by a

2

3

2

8
2
3

show

= 07a

nd the

neare)y,x ′′

8
8 3 7
5
7
9
6 9
5
9 7
6
8
9
6 5
7
4 9
6

2
3 4 5 6 7 1
1
2
3

4
5 6 7
n. The

reafter

st neig(2,1)=

4. 5. 6.

X

image is taken through a lens with the

rectified using the following output-to-

in the output image, when the pixel hbour interpolation?

8

4

Do not know


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.10 Which of the following monochannel mappings will map 0.0 into 0.0,1.0 into 1.0, and 0.5 into 0.8? 1. Hyperbolic mapping with parameter 0.25 2. Hyperbolic mapping with parameter 0.22 3. Gamma mapping with parameter 0.5 4. Gamma mapping with parameter 1.2 5. Logarithmic mapping with parameter 0.4 6. Do not know


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.11 Which one of the following texture statistics is invariant to any gamma mapping of the pixel values? 1. Correlation 2. Diagonal moment 3. Sum average 4. Inertia 5. Maximum probability 6. Do not know.


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.12 A camera is calibrated using a plane test field. The photo is taken from an unknown distance. The optical axis of the camera is pointed at right angle (perpendicular) to the test field. Which of the listed inner orientation parameters cannot be estimated from a single photo? 1. The affinity angle 2. The coefficients in the distortion polynomial 3. The aspect ratio 4. The principal point 5. The camera constant 6. Do not know


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.13 A binary image is coded using (a very simple) run-length code applied to each row of the image. The values of the pixels are independent. The probabilities are given by P(white) = 0.8 and P(black) = 0.2, independently of neighbouring pixels. We code the run-values 1,2 and esc for both black and white runs using a different code for each colour. The esc symbol is used for runs larger than 2. Consider the situation that a black run has been completed so the next binary pixel is white. What is the entropy for the next symbol (1,2 or esc) ? (The entropy determines a lower bound for the expected number of bits used to code the symbol.) 1. 1.3 bit 2. 1.6 bit 3. 1.8 bit 4. 2 bits 5. 3 bits 6. Do not know.


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.14 The discrete Fourier transform is performed on a 480 x 640 (rows x columns) image. A peak is found at frequency (u,v) = (27,0). What is the length in pixels of one period of this frequency? 1. 23.7 2. 3.7 3. 13.2 4. 14.3 5. 17.8 6. Do not know.


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.15 A SAR has an antenna with a length of 4 m in the azimuth direction. It is operating at an altitude of 13,000 m. The radar system has a bandwidth of 150 MHz. At which one of the following ground-range distances will the spatial resolutions in the azimuth direction and in the ground-range direction be the same? 1. 13,000 m 2. 7,506 m 3. 3,357 m 4. 6,500 m 5. 4,436 m 6. Do not know.


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.16 Which filter will in one step do the same as a 3 x 3 mean filter 1 1 1

1 1 1

1 1 1

followed by a Laplacian 0 -1 0

-1 4 -1

0 -1 0

? 1. 0 -1 -1 -1 0 -1 2 1 2 -1 -1 1 0 1 -1 -1 2 1 2 -1 0 -1 -1 -1 0 2. -1 -1 -1 -1 -1 -1 2 2 2 -1 -1 2 4 2 -1 -1 2 2 2 -1 -1 -1 -1 -1 -1 3. 1 1 1 1 1 1 0 -2 0 1 1 -2 4 -2 1 1 0 -2 0 1 1 1 1 1 1

4. 1 0 1 0 5 0 1 0 1 5. 0 0 -1 0 0 0 -1 2 -1 0 -1 2 0 2 -1 0 -1 2 -1 0 0 0 -1 0 0 6. Do not know


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.17 In an industrial vision system objects on a conveyor belt are detected using a single line in the camera. The camera conforms to the CCIR standard i.e. the line is scanned every 40 ms (the line scan time is considered negligible). The minimum length of the objects bmin are 0.1 m. The distance between objects are greater than bmin . What is the maximum conveyor belt speed Vmax requiring that all objects are detected (seen in at least one scan). 1. Vmax = 2.5 m/s. 2. Vmax = 3.5 m/s 3. Vmax = 3.0 m/s 4. Vmax = 4.0 m/s 5. Vmax = 2.0 m/s 6. Do not know.



1 1 1 1 0 0

0 1 0 1 1 1

0 1 0 1 1 0

0 0 0 1 1 1

1 1 0 1 0 1

0 0 0 1 1 1

The gray level run length matrix in the horizontal direction can be computed on the image above. What is the short runs emphasis? 1. 0.43 2. 0.88 3. 0.79 4. 0.62 5. 0.65 6. Do not know.



On the set of black pixels X in the image above we perform the operation

) )( BBX oo • )B with structuring element

How many pixels are there in the result? 1. 9 2. 13 3. 16 4. 11 5. 7 6. Do not know.


Year: 1999. Course no.: 04250, Digital Image Analysis Front page + 20 pages QUESTION 99.20 The absolute orientation parameters for a stereo model are:

−−

=

113

ZYX

0

0

0

; Ω and M = 2; 0;0;0 =Κ=Φ=

A point P in the object coordinate system has the coordinates

=

555

ZYX

The stereo model is constructed from 2 images taken by a pinhole camera with c = 2. Find the image coordinates of point P in the left camera (image 1) where the relative orientation parameters are defined. 1. (-4, 0) 2. (0, 3) 3. (-1, 3) 4. (-4, -3) 5. (3, -4) 6. Do not know

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DTU M.SC. - COURSE EXAM Revised Editionjmca/02501/exams/eksop.1999.UK.pdf · DTU M.SC. - COURSE EXAM Revised Edition Year: 1999. Course no.: 04250, Digital Image Analysis Front page