Digital Image Processing
4. Image Enhancement in the Frequency Domain
- 3. Filtering 영상처리 연구실
1410685 최홍철
Computer Engineering, Sejong University
Filtering
 Filter concept in the frequency domain
2/19
Filtering
 Convolution operation of the image and the convolution mask in
the spatial domain is processed by multiplication in the
frequency domain
f ( x, y )
h( x, y )
g ( x, y )
g ( x, y )  h( x, y )  f ( x, y )
F (u , v )
H (u , v )
G (u , v )
G (u , v )  H (u , v ) F (u , v )
3/19
Filtering
 Filter appearance in the spatial domain and frequency domain
4/19
Filtering
 Creation of a filter mask
• Convolution mask is used in the spatial domain is converted
to a mask in the frequency domain via the DFT
• Generate directly in the frequency domain
- DFT is not necessary for the mask
- It is often used to conceptually simple
5/19
Filtering
 1-D filter mask(ideal case)
H(f)
cutoff frequency
f
f
Low Pass Filter
High Pass Filter
H(f)
H(f)
f
f
Band Pass Filter
Band Stop Filter
6/19
Filtering
 Characteristics of 1-D filter mask
• Low pass filter : The low-frequency component in the input
image is passed through but the high-frequency component is
removed.
• High pass filter : The high-frequency component in the input
image is passed through but the low-frequency component is
removed.
• Band pass filter : Passes only a specific frequency component
from the input image.
• Band stop filter: Removes only a specific frequency
component from the input image.
• cutoff frequency : The frequency that H(f) value is changed
from 1 to 0(or changed to ½)
7/19
Filtering
 Characteristics of 1-D filter mask
frequency sweep signal
After the low-pass filter applied
After the high-pass filter applied
After the band-pass filter applied
After the band-stop filter applied
8/19
Filtering
 2-D filter and processing result
9/19
Filtering
 Zone-plate image
10/19
Filtering
 Zone-plate image
• Zero frequency component in the center of the image
• The far distance from the center, the frequency component is
increased
• Used effectively for the purpose of testing the characteristics
of the filter
• Identifying the display properties of the display device
• An expression of zone plate image creation(The origin is
center of image)
f ( x , y )  127 . 5 (1  cos(

V
11/19
Low-pass
filtered
image
12/19
x2 

H
y 2 ))
Original
image
13/19
High-pass
filtered
image
14/19
Original
image
15/19
Laplacian
filtered
image
16/19
Filtering
 Practical filter
• Sharp cut-off filter as the ideal is unrealistic
• The ringing generated during the implementation of a computer
• Most of the filters are a combination of the previous four filters
• Low-pass filter : Removing noise, Reduction of image,
Compression of image, etc.
• High-pass filter : Extracting of edge, etc.
• Band-stop/pass filter : Color separation of the NTSC signal
• Universal filter used by the image processing
- Butterworth filter
- Gaussian filter
17/19
Filtering
 Example of Ideal Low Pass Filter (:ILPF)
18/19
Filtering
 ILPF and its spatial domain representation
19/19