2D Frequency Domain Filtering and the 2D DFT
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The 2D DFT:
o The Transforms
o Frequency Content Location
o Properties of 2D DFT
o Examples of Properties

Frequency Domain Image Filters:
o 2D Filtering Concepts
o Smoothing
o Edge Detection
o Sharpening
o Filter Design



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Smoothing Through Lowpass Filters Brought to you by Team Phantom Cruiser and the Power of Steam

Top: Original image. Bottom: Image filtered with 5th order Butterworth lowpass filter, normalized cutoff frequency .3

But there are frequency domain filters that we can apply to the image without artifacting. Here we've created an equiradial 5th order lowpass Butterworth filter. As with a one dimensional Butterworth filter, this filter does not create ringing in the image, and so we can now start to examine the actual effects of lowpass filtering on an image.

As expected, when the car is multiplied in the frequency domain by the lowpass filter seen here to the right, it serves to smooth the image and blur out the sharply defined lines. In this way, a low pass filter can be used to create a blur effect on an image. When used subtely, this can have the effect of smoothing out high frequency noise in an image, such as dust or film grain. When used more grossly it can be used for general blur or, if the distribution of the filter around the DC is elliptical rather than circular, can create the effect of a directional motion blur.