chapter 4 image enhancement in frequency domain digital image processing
Post on 19-Dec-2015
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CHAPTER 4Image Enhancement in Frequency Domain
Digital Image Processing
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Spectrum of images
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Spectrum of images
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Spectrum of images
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Spectrum of images
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Spectrum of images
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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)
2. computer F(u,v), the DFT of the image3. multiply F(u,v) by a filter function H(u,v)4. compute the inverse DFT of the result in (3)5. obtain the real part of the result in (4)6. multiply the result in (5) by (-1)x+y to cancel the
multiplication of the input image.
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Notch filter
otherwise 1
N/2 (M/2, v)(u, if 0),(
) vuH
• 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
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Low pass filter
high pass filter
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Filtering examples - revisited
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Transfer function 5x5 lowpass filter
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Filtering Examples
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Filtering Examples
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Filtering Examples
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Transfer function high-pass filter
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Filtering Examples
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Filtering in frequency domain
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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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Lowpass filtering
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Lowpass filtering1 1
2
0 0
Total Power = ( , )M N
u v
F u v
α= 92.0, 94.6, 96.4, 98, 99.5
% total power
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Lowpass filtering
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Lowpass filtering
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Lowpass filtering
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Lowpass filtering
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Lowpass filtering
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Lowpass filtering
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Lowpass filtering
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Lowpass filtering
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Lowpass filtering
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Lowpass filtering
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Lowpass filtering
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Lowpass filtering
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Highpass filtering
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Highpass filtering
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Highpass filtering
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Highpass filtering
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Highpass filtering
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Highpass filtering
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Highpass filtering
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Highpass filtering
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Highpass filtering
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Homomorphic filtering
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Homomorphic filtering
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Homomorphic filtering
2 20( ( . ) / )( , ) ( ) 1 c D u v D
H L Lh u v e
C controls the sharpness of the slope
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Homomorphic filtering