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SMOOTHING FILTERS IN
SPATIAL DOMAIN
Submitted by,
M.Madhu Bala
P.Malathi
R.Mathu Sini
V.Praseetha
1
Submitted to,
G. Murugeswari M.E,
Assistant Professor,
MS University,
Triunelveli.
Contents
What is Spatial filter
Mechanism of spatial filter
Smoothing filters in spatial
Linear filter
Non-linear filter
conclusion
2
Spatial Filter
A spatial filter is an image operation where each
pixel value I(u, v) is changed by a function of the
intensities of pixels in a neighborhood of (u, v).
Spatial filtering term is the filtering operations that
are performed directly on the pixels of an image.
3
Mechanism of Spatial Filtering
The process consists simply of moving the filter
mask from point to point in an image.
At each point (x,y) the response of the filter at that
point is calculated using a predefined relationship.
4
Smoothing Spatial Filter
Smoothing filters are used for
 blurring
 noise reduction.
Blurring is used in preprocessing steps to removal
of small details from an image prior to object
extraction and bridging of small gaps in lines or
curves
Noise reduction can be accomplished by blurring
5
Types of Smoothing Filter
There are 2 way of smoothing spatial filters
Linear Filters – operations performed on image
pixel
Order-Statistics (non-linear) Filters - based on
ranking the pixels
6
Linear Filter
Linear spatial filter is simply the average of the
pixels contained in the neighborhood of the filter
mask.
The idea is replacing the value of every pixel in an
image by the average of the gray levels in the
neighborhood defined by the filter mask.
7
Linear Filter (cont..)
This process result in an image reduce the sharp
transitions in intensities.
Two mask
Averaging filter
Weighted averaging filter
8
Averaging Filter
A major use of averaging filters is in the reduction
of irrelevant detail in image.
mxn mask would have a normalizing constant
equal to 1/mn.
Its also known as low pass filter.
A spatial averaging filter in which all coefficients are
equal is called a box filter.
9
Averaging Filter - Example
1 1 1
1 1 1
1 1 1

9
1
10
Weighted Averaging Filter
Pixels are multiplied by different coefficients, thus
giving more weight to some pixel at the expanses of
others.
The center pixel is multiplied by a higher value than
any other, thus giving the pixel more importance in
the calculation of average.
The other pixels are inversely weighted as a
function of their distance from center of mask
11
Weighted Averaging Filter
The general implementation for filtering an MxN
image with a weighted averaging filter of size m x
n is given by the expression
For complete filtered image apply x =
0,1,2,3……..m-1 and y=0,1,2,3,……..n-1 in the
above equation.


 
 

 a
as
b
bt
a
as
b
bt
tsw
tysxftsw
yxg
),(
),(),(
),(
12
Weighted Average Filter -
Example
1 2 1
2 4 2
1 2 1

16
1
13
Order-Statistics Filter
Order-statistics filters are nonlinear spatial filters.
It is based on ordering (ranking) the pixels
contained in the image area encompassed by
the filter,
It replacing the value of the center pixel with the
value determined by the ranking result.
14
Order- statics filter
The filter selects a sample from the window, does
not average
Edges are better preserved than with liner filters
Best suited for “salt and pepper” noise
15
Types of order-statics filter
Different types of order-statics filters are
Minimum filter
Maximum filter
Median filter
16
Minimum Filter
The 0th percentile filter is the min filter.
Minimum filter selects the smallest value in the
window and replace the center by the smallest
value
Using comparison the minimum value can be
obtained fast.(not necessary to sort)
It enhances the dark areas of image
17
Minimum Filter - Example
.
( mask size =3 x 3) ( mask size =7 x 7)
18
Maximum Filter
The maximum filter selects the largest value within
of pixel values, and replace the center by the
largest value.
Using comparison the maximum value can be
obtained fast.(not necessary to sort)
Using the 100th percentile results in the so-called
max filter
it enhances bright areas of image
19
Maximum Filter
mask (3 x 3) mask (7 x 7)
20
Median Filter
Three steps to be followed to run a median filter:
1. Consider each pixel in the image
2. Sort the neighboring pixels into order based upon
their intensities
3. Replace the original value of the pixel with the
median value from the list.
21
Median Filter - Process
22
Median Filter - Example
Median Filter size =7 x 7
23
Median Filter size =3 x 3
conclusion
A linear filter cannot totally eliminate impulse
noise, as a single pixel which acts as an
intensity spike can contribute significantly to the
weighted average of the filter.
Non-linear filters can be robust to this type of
noise because single outlier pixel intensities can
be eliminated entirely.
24
Original image
Median filter
Original image
Mean filter
25
26

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SMOOTHING FILTERS IN SPATIAL DOMAIN

  • 1. SMOOTHING FILTERS IN SPATIAL DOMAIN Submitted by, M.Madhu Bala P.Malathi R.Mathu Sini V.Praseetha 1 Submitted to, G. Murugeswari M.E, Assistant Professor, MS University, Triunelveli.
  • 2. Contents What is Spatial filter Mechanism of spatial filter Smoothing filters in spatial Linear filter Non-linear filter conclusion 2
  • 3. Spatial Filter A spatial filter is an image operation where each pixel value I(u, v) is changed by a function of the intensities of pixels in a neighborhood of (u, v). Spatial filtering term is the filtering operations that are performed directly on the pixels of an image. 3
  • 4. Mechanism of Spatial Filtering The process consists simply of moving the filter mask from point to point in an image. At each point (x,y) the response of the filter at that point is calculated using a predefined relationship. 4
  • 5. Smoothing Spatial Filter Smoothing filters are used for  blurring  noise reduction. Blurring is used in preprocessing steps to removal of small details from an image prior to object extraction and bridging of small gaps in lines or curves Noise reduction can be accomplished by blurring 5
  • 6. Types of Smoothing Filter There are 2 way of smoothing spatial filters Linear Filters – operations performed on image pixel Order-Statistics (non-linear) Filters - based on ranking the pixels 6
  • 7. Linear Filter Linear spatial filter is simply the average of the pixels contained in the neighborhood of the filter mask. The idea is replacing the value of every pixel in an image by the average of the gray levels in the neighborhood defined by the filter mask. 7
  • 8. Linear Filter (cont..) This process result in an image reduce the sharp transitions in intensities. Two mask Averaging filter Weighted averaging filter 8
  • 9. Averaging Filter A major use of averaging filters is in the reduction of irrelevant detail in image. mxn mask would have a normalizing constant equal to 1/mn. Its also known as low pass filter. A spatial averaging filter in which all coefficients are equal is called a box filter. 9
  • 10. Averaging Filter - Example 1 1 1 1 1 1 1 1 1  9 1 10
  • 11. Weighted Averaging Filter Pixels are multiplied by different coefficients, thus giving more weight to some pixel at the expanses of others. The center pixel is multiplied by a higher value than any other, thus giving the pixel more importance in the calculation of average. The other pixels are inversely weighted as a function of their distance from center of mask 11
  • 12. Weighted Averaging Filter The general implementation for filtering an MxN image with a weighted averaging filter of size m x n is given by the expression For complete filtered image apply x = 0,1,2,3……..m-1 and y=0,1,2,3,……..n-1 in the above equation.         a as b bt a as b bt tsw tysxftsw yxg ),( ),(),( ),( 12
  • 13. Weighted Average Filter - Example 1 2 1 2 4 2 1 2 1  16 1 13
  • 14. Order-Statistics Filter Order-statistics filters are nonlinear spatial filters. It is based on ordering (ranking) the pixels contained in the image area encompassed by the filter, It replacing the value of the center pixel with the value determined by the ranking result. 14
  • 15. Order- statics filter The filter selects a sample from the window, does not average Edges are better preserved than with liner filters Best suited for “salt and pepper” noise 15
  • 16. Types of order-statics filter Different types of order-statics filters are Minimum filter Maximum filter Median filter 16
  • 17. Minimum Filter The 0th percentile filter is the min filter. Minimum filter selects the smallest value in the window and replace the center by the smallest value Using comparison the minimum value can be obtained fast.(not necessary to sort) It enhances the dark areas of image 17
  • 18. Minimum Filter - Example . ( mask size =3 x 3) ( mask size =7 x 7) 18
  • 19. Maximum Filter The maximum filter selects the largest value within of pixel values, and replace the center by the largest value. Using comparison the maximum value can be obtained fast.(not necessary to sort) Using the 100th percentile results in the so-called max filter it enhances bright areas of image 19
  • 20. Maximum Filter mask (3 x 3) mask (7 x 7) 20
  • 21. Median Filter Three steps to be followed to run a median filter: 1. Consider each pixel in the image 2. Sort the neighboring pixels into order based upon their intensities 3. Replace the original value of the pixel with the median value from the list. 21
  • 22. Median Filter - Process 22
  • 23. Median Filter - Example Median Filter size =7 x 7 23 Median Filter size =3 x 3
  • 24. conclusion A linear filter cannot totally eliminate impulse noise, as a single pixel which acts as an intensity spike can contribute significantly to the weighted average of the filter. Non-linear filters can be robust to this type of noise because single outlier pixel intensities can be eliminated entirely. 24
  • 26. 26

Editor's Notes

  1. Minimum filtering causes the darker regions of an image to swell in size and dominate the darker regions
  2. Max filtering causes the lighter regions of an image to swell in size and dominate the lighter regions