Digital Image Processing Basics 2.1 2002/12/20 2003/02/28 Rob "The Kid" Nowak nowak@rice.edu Michael Haag mjhaag@rice.edu Rob "The Kid" Nowak nowak@rice.edu 2d convolution 2d fourier transforms 2d FT sampling 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.

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 :