EEE 508 - Digital Image & Video Processing and Compression
http://lina faculty asu edu/eee508/
http://lina.faculty.asu.edu/eee508/
Basic Concepts
Prof.
P
f Li
Lina Karam
K
School of Electrical, Computer, & Energy Engineering
Arizona State University
karam@asu.edu
EEE 508
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Copyright 2004-2012 by Prof. Lina Karam
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Basic image/video processing system
Analog Image
CAMERA
x(n1,n2)
STORAGE
DIGITIZER
PROCESS
Sampling +
Quantization
x(t1,t2)
• Display
• Perform analysis
• Reconstruct x(t1,t2)
•
x(t
(t1,tt2) : ANALOG SIGNAL
x : real value
(t1,t2) : pair of real continuous space (time) variables
•
x(n1,n2) : DISCRETE SIGNAL (DIGITAL)
x : discrete (quantized) real or integer value
(n1,n
n2) : pair of integer indices
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Examples
•
Sampled Black & White Photograph: x(n1,n2)
x (n1,n2) scalar indicating piel intensity at location (n1,n2)
For example: x = 0
Black
x=1
White
0<x<1
•
In-between
Sampled color video/TV signal
xR(n1, n2, n3)
xG(n1, n2, n3)
xB(n1, n2, n3)
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How do we process images?
•
Use DSP concepts as tools
•
Exploit
p
visual perception
p
p
properties
p p
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How many possible images are there?
•
We represent pixels as amplitude values (gray scale).
256 levels
1
0
128 levels
1
0
64 levels
1
0
32 levels
1
•
•
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How much to sample (quantize) the gray scale?
H
Humans
can di
distinguish
ti
i h in
i the
th order
d off 100 llevels
l off gray
(about 40 to 100).
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How many possible images are there?
•
An image has pixels and dimensions, say 200x200 and
assume 64 pixel values (64 gray levels).
¾
¾
¾
¾
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A 1x1 image → about 64 images
A 1x2 image → about (64)2 images
A 200x200 image → about (64)40000 images
A large but finite number due to human perceptive properties.
properties
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EEE 508 - Digital Image Processing and Compression
Basic 2D DSP Concepts
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2D Image Representation
x(n1,n2) has 2 axes (n1,n2) + amplitude axis
x(n1,n2)
7
12
6 10
5
6 5 6
n2
n2
6
10
12
5
7
6
5
6
n1
n1
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Special 2D Signals
n2
•
2D unit impulse
⎧1, n1 = n2 = 0
x(n1 , n2 ) = δ (n1 , n2 ) = ⎨
else
⎩0,
Note:
n1
δ (n1 , n2 ) = δ (n1 )δ (n2 )
n2
•
Line impulses
¾ vertical line impulse:
n1
x(n1 , n2 ) = δ ( n1 )
n2
¾ horizontal line impulse:
n1
x( n1 , n2 ) = δ ( n2 )
¾ other line impulses:
δ (n1 + n2 ), δ (n1 − n2 ), δ (2n1 − n2 ), δ ( Pn1 + Qn2 )
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Special 2D Signals
• 2D unit step
n2
⎧1, n1 , n2 ≥ 0
u (n1 , n2 ) = ⎨
else
⎩0,
Note:
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n1
u (n1 , n2 ) = u (n1 )u (n2 )
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Some useful definitions
•
A 2D signal x(n1,n2) is separable if x(n1, n2) = f(n1)g(n2)
•
A finite-extent signal is a signal with a finite number of nonzero samples (all images are finite extent signals in
practice).
practice)
•
Region of support of a signal:
¾ If R is the region of support of a signal x(n1, n2),
) then
x(n1, n2)=0 for (n1, n2) ∉R (i.e., outside R).
¾ The region of support of a signal is the set of points where it
can be nonzero.
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Basic 2D Operations
• Shifting
x(n1,n2)
x(n1-1,n2) n2
n2
n1
x(n1-1,n2-1)
n2
n1
n1
• Flipping
x(n1,n2)
x(-n1,n2)
n2
1
x(-n1,-n2)
n2
n2
1
n1
n1
n1
1
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