Smoothing in Digital Image Processing

Digital Image Processing
• Digital Image Processing denotes the process of digital images with
the use of digital computer.
• Digital images are contains various types of noises which are
reduces the quality of images. Noises can be removed by various
enhancement techniques.
• Noise is anything in the image that are unwanted or undesired
information
Examples:
– Light fluctuations
– Sensor noise
– Transmission
1

Smoothing
• Smoothing is often used to reduce noise within an image.
• Image smoothing is a key technology of image enhancement,
which can remove noise in images. So, it is a necessary
functional module in various image-processing software.
• Image smoothing is a method of improving the quality of
images.
• Smoothing is performed by spatial and frequency filters
2

Spatial filtering
• Spatial filtering term is the filtering operations that are
performed directly on the pixels of an image. The process
consists simply of moving the filter mask from point to point
in an image.
– Smoothing spatial filters
– Sharpening spatial filters
3

Smoothing Spatial Filters
• Smoothing filters are used for noise reduction and blurring
operations.
• It takes into account the pixels surrounding it in order to make
a determination of a more accurate version of this pixel.
• By taking neighboring pixels into consideration, extreme
“noisy” pixels can be filtered out.
• Unfortunately, extreme pixels can also represent original fine
details, which can also be lost due to the smoothing process
4

Cont…
Smoothing spatial filters
Linear Nonlinear
Mean Weiner Gaussian Min Max Median
5

Smoothing Linear Filters
• Smoothing linear spatial filter is the average of
the pixels contained in the neighborhood of
the filter mask.
• Averaging filters or low pass filters.
– Mean filter
– Gaussian filter
6

Mean Filter/Box Filter
• Mean filtering is simply to replace each pixel value in an
image with the mean (`average') value of its neighbors,
including itself.
• 3×3 normalized box filter:
20 40 10
10 20 20
10 20 30
20 40 10
10 20 20
10 20 30
7

Cont…
• Image smoothed with 33, 55, 99 and
11 11 box filters
8

Cont…
• Often a 3×3 square matrix is used, although larger
matrix (e.g. 5×5 squares) can be used for more
severe smoothing.
• Drawback:
– smoothing reduces fine image detail
9

Gaussian Filter
• A Gaussian filters smoothens an image by calculating
weighted averages in a filter box.
• It is used to `blur' images and remove detail and noise.
• Gives more weight at the central pixels and less weights to the
neighbors.
• The farther away the neighbors, the smaller the weight.
• Gaussian Blurs produce a very pure smoothing effect without
side effects.
10

Gaussian Smoothing Example
Original Sigma = 3
11

Smoothing Non Linear Filters
• Nonlinear spatial filters are Order-statistics filters whose
response is based on ordering (ranking) the pixels contained
in the image area encompassed by the filter, and then
replacing the value of the center pixel with the value
determined by the ranking result.
– Min and Max Filter
– Median Filter
– Midpoint Filter
12

Min and Max Filter
• The minimum filter selects the smallest value within the pixel
values and maximum filter selects the largest value within of
pixel values.
• Max filter is useful for finding the brightest points in an image
i.e. it removes salt noise.
• Min filter is useful for finding the darkest points in an image
i.e. it removes pepper noise.
• Both filters require a data sort.
13

Median Filter
• It smooth a few pixels whose values differ significantly from
their surroundings without affecting the other pixels.
• Best suited for “salt and pepper” noise
• Salt-and pepper noise can occur due to a random bit error in a
communication channel
14

Comparison Of Median And Box Filter
Noisy image 5x5 median filtered 5x5 box filter
15

Midpoint Filter
• The Midpoint filter blurs the image by replacing each
pixel with the average of the highest pixel and the
lowest pixel (with respect to intensity) within the
specified window size.
• Midpoint = (darkest + lightest)/2
16

Frequency filtering
• The basic model for filtering in the frequency domain
where F(u,v): the Fourier transform of the image to be
smoothed
H(u,v): a filter transfer function
• Smoothing is fundamentally a low pass operation in the
frequency domain.
• It is computationally faster than spatial domain.
17

Operation of frequency filter
18

Major filter categories
• Typically, filters are classified by examining their
properties in the frequency domain:
(1) Low-pass for smoothing
(2) High-pass for sharpening
(3) Band-pass
(4) Band-stop
19

Example
20
Original signal
Low-pass filtered
High-pass filtered
Band-pass filtered
Band-stop filtered

Cont…
• There are several standard forms of low pass filters (LPF).
– Ideal low pass filter
– Butterworth low pass filter
– Gaussian low pass filter
21

Ideal Low pass Filters (ILPFs)
• The simplest low pass filter is a filter that “cuts off” all high-frequency
components of the Fourier transform that are at a distance greater than a
specified distance D0 from the origin of the transform.
• The transfer function of an ideal low pass filter
where D(u,v) : the distance from point (u,v) to the center of their frequency
rectangle
22






),(if0
),(if1
),(
0
0
DvuD
DvuD
vuH
 2
1
22
)2/()2/(),( NvMuvuD 

  n
DvuD
vuH 2
0/),(1
1
),(


Butterworth Low pass Filters (BLPFs)
25

Butterworth Low pass
Filters (BLPFs)
n=2
D0=5,15,30,80,and 230
26

2
0
2
2/),(
),( DvuD
evuH 

Gaussian Lowpass Filters (FLPFs)
28

Gaussian Low pass
Filters (FLPFs)
D0=5,15,30,80,and 230
29

Conclusion
• Image smoothing algorithms offer a wide variety of
approaches for modifying images to achieve visually
acceptable images. The choice of such techniques is
a function of the specific task, image content,
observer characteristics, and viewing conditions.
30

References
[1] S. Shenbagavadivu, Dr. M. Renuka Devi, “AN INVESTICATION OF NOISE
REMOVING TECHNIQUS USED IN SPATIAL DOMAIN IMAGE PROCESSING”,
International Journal of Computer Science and Mobile Computing, Vol. 2,
Issue. 7, July 2013, pg.378 – 384
[2] Aditya Goyal, Akhilesh Bijalwan, Mr. Kuntal Chowdhury, “A Comprehensive
Review of Image Smoothing Techniques”, International Journal of
Advanced Research in Computer Engineering & Technology Volume 1,
Issue 4, June 2012
[3] http://homepages.inf.ed.ac.uk/rbf/HIPR2/mean.htm
[4] http://www.nptel.ac.in/courses/117104069/chapter_8/8_16.html
[5] http://www.markschulze.net/java/meanmed.html
[6] www.cse.unr.edu/~bebis/CS474/Lectures/FrequencyFiltering
[7] staffweb.ncnu.edu.tw/jcliu/course/dip2006/freq_intro
[8] www.csie.ntnu.edu.tw/~violet/IP93/Chapter04
[9] http://paulbourke.net/miscellaneous/imagefilter
[10] Rafael C Gonzalez, “Digital Image Processing”, Pearson Education India,
2009, ISBN no. 8131726959, 9788131726952 31

Smoothing in Digital Image Processing

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