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(ELEC317)2002_final.pdf
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ELEC 317 Exam (Fall 2002) Name: ___________________________
Student No.: _______________________ Signature: _________________________

1. (10%) Linear time invariant system

a.
(5%) Your friend says that the paddling device of a row boat is a linear time invariant system. You decide that what your friend says is correct. What are your reasons that it is a linear time invariant system? (Simple answer to explain what the input and output are, why linear, and why time invariant)

b.
(5%) Suppose you decide that what your friend says is wrong. What are your reasons that it is not a linear time invariant system? (Simple answer)



Fig. 2a Fig. 2b Fig. 2c

Fig. 2d Fig. 2e Fig. 2f
Fig. 2a is the original Lena image. Fig. 2b to 2f are obtained by performing horizontal lowpass, horizontal highpass, vertical lowpass, vertical highpass, and simple all-direction lowpass filtering.
a.
(2%) What was the filtering used to obtain Fig. 2b? Why?

b.
(2%) What was the filtering used to obtain Fig. 2c? Why?

c.
(2%) What was the filtering used to obtain Fig. 2d? Why?

d.
(2%) What was the filtering used to obtain Fig. 2e? Why?

e.
(2%) What was the filtering used to obtain Fig. 2f? Why?

f.
(2%) Give an example of a simple all-direction lowpass filter.

g.
(2%) Give an example of a horizontal lowpass filter.

h.
(2%) Give an example of a horizontal highpass filter.

i.
(2%) Give an example of a vertical lowpass filter.

j.
(2%) Give an example of a vertical highpass filter.



3. (20%) Medial axis and morphological operations. Draw on the exam paper.
a.
(4%) Draw the medial axis of the following figure. Draw on the exam paper.

b.
(4%) Perform erosion using the structuring element on the right hand side. The origin of the structuring element is the dark pixel (in the center). Draw on the exam paper.

c.
(4%) Perform dilation using the structuring element on the right. Draw on the exam paper.

d. (4%) Perform opening using the structuring element on the right. Draw on the exam paper.

e.
(4%) Perform closing using the structuring element on the right. Draw on the exam paper.







4. (20%) Edge detection and image filtering The image A is a 4x4 image containing two objects and an edge between the two objects. You will be asked to perform some filtering on A. When filtering the image boundary, you can assume the boundary pixels are extended as shown.
. . . . . . . ...
......
150 150 150 153 153 150 150 149 149
149
a.
(10%) Perform edge detection on A using the Roberts filters. Show all your steps.

b.
(5%) Perform a 3x3 median filtering on A.

c.
(5%) Perform a 3x3 filtering on A using the filter ones(3, 3)/9.


150 149 147 144 144

.

. . . . . . ...

149 147 144

.

151 153 32

153 151 153 32 32

A

extended A=
=

148 34 33

35 37 38

14935 37 38 38

5. (20%) True or False (Do thi