Image Processing Math Tools

1
LECTURE 3
Image Processing / Math Tools
2

• Convolution
• Correlation
• Histograms
• Point Operations
• Algebraic Operations
• Geometric Operations
• 2-D Fourier Transform
• Other Transform

3
Graphical illustration of convolution. The shaded
areas indicate regions where the product is not
zero
f (?)
g (?)
1
1/2
(a)
(b)
?
?
1
1
g (- ?)
g (x- ?)
1/2
1/2
(c)
(d)
?
?
-1
-1
4
Graphical illustration of convolution. The shaded
areas indicate regions where the product is not
zero
f (?)g(x - a)
f (?)g(x - a)
0? x ? 1
1? x ? 2
1
1
1/2
1/2
(e)
(f)
?
?
1
1
-1
x
x
x-1
f (x) ? g(x)
1/2
(g)
x
1
2
5
Illustration of the folding, displacement, and
multiplication steps needed to perform
two-dimensional convolution
g(?,?)
f(?,?)
B
(b)
A
(a)
?
?
?
?
f(?,?)g(x - ? ,y - ?)
g(x - ? ,y - ?)
B
x
(d)
?
(c)
x
?
y
?
y
?
Volume f(x,y) ? g(x,y)
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GRAY LEVEL HISTOGRAM
Number of Pixels in Image
0
255
Gray Level
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HISTOGRAM
UNIQUE
IMAGE
HISTOGRAM
NON UNIQUE
NON - ISOMORPHIC
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EXAMPLE
9
Point Operations Algebraic Operations Geometric
Operations
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Histogram Manipulation Point Operations
NONLINEAR
Histogram Flattening CDF
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Effect of a point operation on the histogram
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255
255
0
0
255
0
13
Where
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LINEAR POINT OPERATION
AND