04-1 - Frequency domain filtering fundamentals

# 04-1 - Frequency domain filtering fundamentals -...

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4/28/2008 1 Frequency domain filtering fundamentals Spring 2008 ELEN 4304/5365 DIP 1 by Gleb V. Tcheslavski: [email protected] http://ee.lamar.edu/gleb/dip/index.htm Preliminaries For a digital image f ( x,y ) the basic filtering equation is 1 { } (, ) (,) (,) gxy HuvFuv = ℑ Where H ( u,v ) and F ( u,v ) are DFTs of the image and of the filter. Their product is defined by array (element-by-element) multiplication. Specifications of H ( u,v ) are simplified considerably when using functions symmetric about their centers This requires Spring 2008 ELEN 4304/5365 DIP 2 when using functions symmetric about their centers. This requires that F ( u,v ) is also centered, which is accomplished by multiplying the input image by (-1) x+y before computing its transform.

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4/28/2008 2 Simple filters Considering the following image with centered (and scaled) DFT Spring 2008 ELEN 4304/5365 DIP 3 Simple filters One of the simplest filters would be H ( u,v ) having 0 at the center and 1 elsewhere. Such filter will reject the DC (constant) term and l thi l h d leave everything else unchanged. Since the DC term represents an average intensity, setting it to zero results in reduction of average intensity to zero. Spring 2008 ELEN 4304/5365 DIP 4 Therefore, the resulting image appears darker. Actually, aero average implies negative intensities.
4/28/2008 3 Simple filters Low frequencies in the transform are related to slowly varying intensity components of image. High frequencies are caused by

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04-1 - Frequency domain filtering fundamentals -...

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