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Intro to digital signal processing Dsp systems i Digital image processing basics
The module provides an introduction to the concepts of digital imaging processing through basic equations and examples.
Digital image processing
A sampled image gives us our usual 2D array of pixels
f
m
n (
We illustrate a "pixelized" smiley face.
We can filter
f
m
n by applying a 2D discrete-space
convolution as shown below (where
h
m
n is our PSF):
g
m
n
h
m
n
f
m
n
k
∞
∞
l
∞
∞
h
m
k
n
l
f
k
l
We also have discrete-space FTS:
F
u
v
m
∞
∞
n
∞
∞
f
m
n
u
m
v
m where
F
u
v is analogous to
DTFT in 1D.
"Convolution in Time" is the
same as
"Multiplication in Frequency"
which, as stated above, is the same as:
Magnitude of ft of cameraman image
To get a better image, we can use the
fftshift command in Matlab to center
the Fourier Transform. The resulting image is shown in
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Source:
OpenStax, Intro to digital signal processing. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10203/1.4
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