Lecturer: Wanasanan Thongsongkrit Email : wanasana@eng.cmu.ac.th Office room : 410

Basic steps for filtering in the frequency domain

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Basics of filtering in the frequency domain

1. multiply the input image by (-1)x+y to center the transform to u = M/2 and v = N/2 (if M and N are even numbers, then the shifted coordinates will be integers) computer F(u,v), the DFT of the image from (1) multiply F(u,v) by a filter function H(u,v) compute the inverse DFT of the result in (3) obtain the real part of the result in (4) multiply the result in (5) by (-1)x+y to cancel the multiplication of the input image.

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2. 3. 4. 5. 6.

Notch filter

• this filter is to force the F(0,0) which is the average value of an image (dc component of the spectrum) • the output has prominent edges • in reality the average of the displayed image can’t be zero as it needs to have negative gray levels. the output image needs to scale the gray level

0 if (u, v) = (M/2, N/2 ) H (u, v) = 1 otherwise 4

Low pass filter

high pass filter

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Add the ½ of filter height to F(0,0) of the high pass filter

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Correspondence between filter in spatial and frequency domains

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Smoothing Frequency-domain filters: Ideal Lowpass filter

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image power circles

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Result of ILPF

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Example

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Butterworth Lowpass Filter: BLPF

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Example

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Spatial representation of BLPFs

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Gaussian