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
Spectrum of images
Spectrum of images
Spectrum of images
Spectrum of images
Spectrum of images
Basic steps for filtering in the frequency domain
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.
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
Low pass filter
high pass filter
Filtering examples - revisited
Transfer function 5x5 lowpass filter
Filtering Examples
Filtering Examples
Filtering Examples
Transfer function high-pass filter
Filtering Examples
Filtering in frequency domain
Add the ½ of filter height to F(0,0) of the high pass filter
Correspondence between filter in spatial and frequency domains
Lowpass filtering
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
Lowpass filtering
Lowpass filtering
Lowpass filtering
Lowpass filtering
Lowpass filtering
Lowpass filtering
Lowpass filtering
Lowpass filtering
Lowpass filtering
Lowpass filtering
Lowpass filtering
Lowpass filtering
Highpass filtering
Highpass filtering
Highpass filtering
Highpass filtering
Highpass filtering
Highpass filtering
Highpass filtering
Highpass filtering
Highpass filtering
Homomorphic filtering
Homomorphic filtering
Homomorphic filtering
2 20( ( . ) / )( , ) ( ) 1 c D u v D
H L Lh u v e
C controls the sharpness of the slope
Homomorphic filtering