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1.1 Digital image processing basics

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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

Sampled image

Illustrate the "pixelized" nature of all digital images.
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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"
g m n h m n f m n
which, as stated above, is the same as:
G u v H u v F u v

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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