Smoothing Filters in Spatial Domain

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 - 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

Smoothing Filters in Spatial Domain

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