This document discusses spatial filtering for image enhancement. It begins by introducing filters and explaining that filtering can modify or enhance images by highlighting certain features or removing others. It then explains that spatial filtering involves applying a filter mask to an image point by point. The mechanism of spatial filtering is described as calculating filter responses at each point (x,y) using a predefined relationship between pixels under the mask and mask coefficients. Linear spatial filtering is discussed where each pixel is replaced by a constant value. Convolution is introduced as the process of applying filters to an image. The approaches and types of spatial filtering are outlined. In summary, spatial filtering uses a mask that is applied point by point to an image to calculate new pixel values using neighboring pixel values and

1. Image enhancement using
Spatial filtering
By
Md. Fazle Rabbi
16CSE057

2. 4.2
Introduction To Filters
• Filtering is a technique used for modifying or enhancing an
image like highlight certain features or remove other
features.
• Image filtering include smoothing, sharpening, and edge
enhancement
• Term ‘convolution ‘ means applying filters to an image .
• It may be applied in either
spatial domain
frequency domain

3. 4.3
SPATIAL DOMAIN FILTERS

4. 4.4
SPATIAL FILTER
The spatial filter is just moving the filter mask from point to
point in an image.
The filter mask may be 3x3 mask or 5x5 mask or to be 7x7
mask.
Example
3x3 mask in a 5x5 image

5. 4.5
MECHANISM OF SPATIAL FILTERING
Filter at each point
(x , y) are calculated
by predefined
relationship
This process shows
moving filter mask
point to point

6. 4.6
Spatial Filtering
• Similar to neighborhood operation
• A mask or filter or template or kernel or window
defines the neighborhood
• Mask size is usually m × n
o m = 2a+1, n = 2b+1
• Output pixel value is determined from the pixels under
the mask

7. 4.7
The Approaches of Spatial Filtering
O A neighborhood (small rectangle)
O
A predefined operation performed on
image pixels.
Spatial filter consist of two steps
Filtering creates a new pixel value replaced by old pixel value

8. 4.8
Image Enhancement using Spatial Filtering
Mask
Image
Origin
Image f(x,y)

9. 4.9
Image Enhancement using Spatial Filtering
Mask
Image
Origin
Image f(x,y)
w(-1,-1) w(-1,0) w(-1,1)
w(0,-1) w(0,0) w(0,1)
w(1,0) w(1,1)
Mask Coefficients
showing coordinate
arrangement
w(1,-1)

10. 4.10
Image Enhancement using Spatial Filtering
Mask
Image
Origin
Image f(x,y)
f(x-1,y-1) f(x-1,y) f(x-1,y+1)
f(x,y-1) f(x,y) f(x,y+1)
f(x+1,y-1) f(x+1,y) f(x+1,y+1)
Pixels of image
section under
Mask

11. 4.11
Image Enhancement using Spatial Filtering
Mask
Image
Origin
Image f(x,y)
w(-1,-1) w(-1,0) w(-1,1)
w(0,-1) w(0,0) w(0,1)
w(1,0) w(1,1)
f(x-1,y-1) f(x-1,y) f(x-1,y+1)
f(x,y) f(x,y+1)
f(x+1,y-1) f(x+1,y) f(x+1,y+1)
Mask
Coefficients
Pixels under Mask
w(1,-1)
f(x,y-1)

12. 4.12
Types Of Spatial Filters
There are two types of filter,
1.Linear Spatial Filter
2.Non Linear Spatial Filter
 Each pixel in an image can be replaced with
constant value then it is called as linear spatial
filter otherwise it is called as non-linear.

13. 4.13
LINEAR SPATIAL FILTERING

14. 4.14
LINEAR SPATIAL FILTERING

15. 4.15
LINEAR SPATIAL FILTERING

16. 4.16
CONVOLUTION

17. 4.17
CONVOLUTION

18. 4.18
Image Enhancement using Spatial Filtering
Mask
Image
Origin
Image f(x,y)
w(-1,-1) w(-1,0) w(-1,1)
w(0,-1) w(0,0) w(0,1)
w(1,0) w(1,1)
f(x-1,y-1) f(x-1,y) f(x-1,y+1)
f(x,y) f(x,y+1)
f(x+1,y-1) f(x+1,y) f(x+1,y+1)
Mask
Coefficients
Pixels under Mask
w(1,-1)
f(x,y-1)

19. 4.19
Image Enhancement using Spatial Filtering
w(-1,-1) w(-1,0) w(-1,1)
w(0,-1) w(0,0) w(0,1)
w(1,0) w(1,1)
f(x-1,y-1) f(x-1,y) f(x-1,y+1)
f(x,y) f(x,y+1)
f(x+1,y-1) f(x+1,y) f(x+1,y+1)
Mask
Coefficients
Pixels under Mask
w(1,-1)
f(x,y-1)
Response of the filter
at point (x, y):
)
1
,
1
(
)
1
,
1
(
)
,
1
(
)
0
,
1
(
)
,
1
(
)
0
,
1
(
)
1
,
1
(
)
1
,
1
(














y
x
f
w
y
x
f
w
y
x
f
w
y
x
f
w
R



20. 4.20
Image Enhancement using Spatial Filtering
w(-1,-1) w(-1,0) w(-1,1)
w(0,-1) w(0,0) w(0,1)
w(1,0) w(1,1)
f(x-1,y-1) f(x-1,y) f(x-1,y+1)
f(x,y) f(x,y+1)
f(x+1,y-1) f(x+1,y) f(x+1,y+1)
Mask
Coefficients
Pixels under Mask
w(1,-1)
f(x,y-1)
Response of the filter
at point (x, y):
)
1
,
1
(
)
1
,
1
(
)
,
1
(
)
0
,
1
(
)
,
1
(
)
0
,
1
(
)
1
,
1
(
)
1
,
1
(














y
x
f
w
y
x
f
w
y
x
f
w
y
x
f
w
R


**This type of response is called linear filtering

21. 4.21
Image Enhancement using Spatial Filtering
A more general
equation for
response:
w(-1,-1) w(-1,0) w(-1,1)
w(0,-1) w(0,0) w(0,1)
w(1,0) w(1,1)
f(x-1,y-1) f(x-1,y) f(x-1,y+1)
f(x,y-1) f(x,y) f(x,y+1)
f(x+1,y-1) f(x+1,y) f(x+1,y+1)
Mask
Coefficients
w(1,-1)


 




a
a
s
b
b
t
t
y
s
x
f
t
s
w
y
x
g )
,
(
)
,
(
)
,
(
g(x,y)
M
N
2b+1
2a+1

22. 4.22
Image Enhancement using Spatial Filtering



mn
i
i
i z
w
R
1
w1 w2 w3
w4 w5 w6
w8 w9
Mask
Coefficients
w7
Or, for a general case of
mask size mXn:
z1 z2 z3
z4 z5 z6
z8 z9
z7



9
1
i
i
i z
w
R

23. 4.23
Thank You