Name:
SIMG782 Introduction to Digital Image Processing
Midterm Examination
Fall Quarter 2003
Closed book and notes. Calculators are approved. Answer all questions.
1. The diagram at the right contains several curves that could be
used to transform the brightness values of a monochrome image by
the operation
B
=
T
[
A
] where
A
and
B
are image arrays. Shown
below are four pairs of histograms.
Identify the transformation
curve best associated with each pair and write the letter in the
space in the center column.
Curve C is the identity transform.
Curves A and B stretch the dark regions while curves D and E
compress the dark regions. Curve B stretches the light region while
curve D compresses the light region.
Compare these effects with
the changes in the histograms to select the transforms.
Answers
indicated below.
Input image histogram
Transform
Output image histogram
E
D
A
B
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2. The Sobel operator computes the following quantity at each location (
x, y
) in an image array,
A
:
G
x
[
j, k
] = (
A
[
j
+ 1
, k
+ 1] + 2
A
[
j
+ 1
, k
] +
A
[
j
+ 1
, k

1])

(
A
[
j

1
, k
+ 1] + 2
A
[
j

1
, k
] +
A
[
j

1
, k

1])
G
y
[
j, k
] = (
A
[
j

1
, k

1] + 2
A
[
j, k

1] +
A
[
j
+ 1
, k

1])

(
A
[
j

1
, k
+ 1] + 2
A
[
j, k
+ 1] +
A
[
j
+ 1
, k
+ 1])
G
[
j, k
] =

G
x
[
j, k
]

+

G
y
[
j, k
]

The position of
A
[
j, k
] is column
j
and row
k
of the array.
The operation is implemented as the convolution of the image array
A
with two masks,
M
x
and
M
y
followed by the
magnitude operation.
(a)
Write a
3
×
3
array for each mask,
M
x
and
M
y
.
The equations represent the formation of sums along rows or columns that are adjacent to pixel
[
x, y
]
and taking
the difference. This can be achieved by convolving with the masks below. True convolution would reflect the masks
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 Spring '09
 matteo
 Image processing, Sobel Operator, morphological image processing, image array

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