MP230 Modern Diagnostic Imaging Systems, Fall 2010.
Homework #1
Due: Septemer 8 by 5:00 pm
Part I:
Thoroughly answer all questions. Clearly and
neatly
show your work.
Part II & III:
Fully answer all questions and print out a copy of your Matlab code,
including any figures or tables.
I.
PROBLEMS (PP 5661 OF PRINCE)
1.) Evaluate the following:
Z
∞
∞
Z
∞
∞
f
(
x, y
)
δ
(
x

2
, y
+ 3)
dxdy
Z
∞
∞
Z
∞
∞
f
(
x, y
)
*
δ
(
x
+ 4
, y

1)
dxdy
2.) 2.12
3.) a.) Qualitatively describe how a convolution with the following kernels would
affect a digital image:
i.)
0
0
0
0
1
0
0
0
0
ii.)
1
0
0
0
0
0
0
0
0
iii.)
1
1
1
1
1
1
1
1
1
b.) Write an equation for the kernels in part a. Assume the distance between adjacent pixels is 1.
c.) What is the center pixel value of the following image convolved with the third kernel?
a
b
c
d
e
f
g
h
i
4. 2.19
5. 2.22
Extra Credit: 2.23
1
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II.
MATLAB EXCERCISE: SPATIAL RESOLUTION
Define a zerofilled 256x256 matrix using the command, zeros.
Set 5 vertical bars of
thickness 1 separated from each other by 9 pixels to the value 1. Label this matrix as
Bars
.
1.
Display the image, Bars.
Your matrix can be displayed as a 2D grayscale image
by using the commands,
imagesc
and
colormap
.
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 Fall '10
 MacFall
 Image processing, Impulse response, Dirac delta function, point spread function, Modern Diagnostic Imaging Systems

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