Lecturer: Wanasanan Thongsongkrit Email : email@example.com Office room : 410
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) 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.
2. 3. 4. 5. 6.
• 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
Add the ½ of filter height to F(0,0) of the high pass filter
Correspondence between filter in spatial and frequency domains
Smoothing Frequency-domain filters: Ideal Lowpass filter
image power circles
Result of ILPF
Butterworth Lowpass Filter: BLPF
Spatial representation of BLPFs