March 21, 2001  Lab 3

Fourier Methods

Low-pass and high-pass filters

Use a circular image to create a suitable ideal low pass filter and apply it to the Fourier transform of the following picture. Then do the IFT. 
 

Assuming that your cutoff is sufficiently high to preserve most of the picture, you will see considerable ringing due to the sharp cutoff. Before trying to remove this ringing, apply a high pass filter to the original image.  If you invert your circle image, you will have a high frequency filter. (You must however keep the value at (0,0) since that location specifies the average brightness of the image.) Filter the image and look at the result. You should basically see the outline of objects with considerable ringing. To reduce the ringing, try blurring the circle image in both cases with a simple Gaussian filter, or you can perform the filtering with second-order Butterworth high and low pass filters of suitable cutoff and avoid having to do any smoothing. 

Periodic Noise Removal.

The following four pictures show periodic noise.

Note that for color images, the halftone screens have different orientations, so FFTs have to be taken of each RGB color and each color filtered separately.  A montage is an effective way to show the image color sets.

Touch up your results.

Last modified on April 10, 2001