Connexions

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

What is a lens?

Lenses

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

What is in a lens?

Lens makers point to Connexions 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 Connexions member, a community, or a respected organization.

This content is ...
Affiliated with (?)
This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.

  • This module is included inLens: Rice University OpenCourseWare
    By: OpenCourseWare ConsortiumAs a part of collection:"Intro to Digital Signal Processing"

    Click the "Rice University OCW" link to see all content affiliated with them.

    Rice University OCW
Tags

(?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Digital Image Processing Basics

Module by: Robert Nowak

Summary: 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 fmn f m n (Figure 1):
smiley.png
Figure 1: We illustrate a "pixelized" smiley face.
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=-∞∞hm-kn-lfkl g m n h m n f m n k l h m k n l f k l (1)
Example 1: Sampled Image 
sec2_eg1.png
Figure 2: Illustrate the "pixelized" nature of all digital images.
We also have discrete-space FTS:
Fuv=∑m=-∞∞∑n=-∞∞fmnⅇ-ⅈumⅇ-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 
cam_mag.png
Figure 3
To get a better image, we can use the fftshift command in Matlab to center the Fourier Transform. The resulting image is shown in Figure 4:
cam_mag_center.png
Figure 4

Comments, questions, feedback, criticisms?

Send feedback