Skip to content Skip to navigation


You are here: Home » Content » Digital Image Processing Basics


Recently Viewed

This feature requires Javascript to be enabled.

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.

Note: You are viewing an old version of this document. The latest version is available here.

Digital Image Processing

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

Figure 1: We illustrate a "pixelized" smiley face.
Figure 1 (smiley.png)

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

Example 1: Sampled Image

Figure 2: Illustrate a the "pixelized" nature of all digital images.
Figure 2 (sec2_eg1.png)

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
where Fuv F u v is analogous to DTFT in 1D.


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

Example 2: Magnitude of FT of Cameraman Image

Figure 3
Figure 3 (cam_mag.png)

To get a better image, we can use the fftshift command in Matlab to center the Fourier Transform. The resulting image is shown below:

Figure 4
Figure 4 (cam_mag_center.png)

Content actions

Download module as:

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens


A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks