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# Digital Image Processing Basics

Module by: Robert Nowak. E-mail the author

Summary: The module provides an introduction to the concepts of digital imaging processing through basic equations and examples.

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## Digital Image Processing

A sampled image gives us our usual 2D array of pixels fmn f m n :

We can filter fmn f m n by applying a 2D discrete-space convolution as shown below (where hmn h m n is our PSF):

gmn=hmn*fmn=k=l=hmknlfkl g m n h m n f m n k l h m k n l f k l
(1)

### Example 1: Sampled Image

We also have discrete-space FTS:

Fuv=m=n=fmne(ium)e(ivm) F u v m n f m n u m v m
(2)
where Fuv F u v is analogous to DTFT in 1D.

### note:

"Convolution in Time" is the same as "Multiplication in Frequency"
gmn=hmn*fmn g m n h m n f m n
(3)
which, as stated above, is the same as:
Guv=HuvFuv G u v H u v F u v
(4)

### Example 2: 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 below:

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