1. CHAPTER 7
IMAGE ANALYSIS
Template Filters
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2. Moving templates for image filtering
gij = fi–1,j–1 h–1,–1 + fi–1,j h–1,0 + fi–1,j+1 h–1,1 +
+ fi,j–1 h0,–1 + fi,j h0,0 + fi,j+1 h0,1 +
+ fi+1,j–1 h1,–1 + fi+1,j h1,0 + fi+1,j+1 h1,1
The discrete convolution process in template filtering
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3. Typical template dimensions
Non-square templates viewed as
special cases of square ones
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4.       gij = hi,j;k,m fkm hi,j;k,m = hk–i,m–j gij = hk–i,m–j fkm
Template filters = Localized position-invariant linear transformations of an image
linear
gij = hi,j;k,m fkm
 
k m
position-invariant
hi,j;k,m = hk–i,m–j
gij = hk–i,m–j fkm
 
k m
localized
gij = hi,j;k,m fkm
 
k=i–p m=j–p
i+p j+p
Using a (p+1)(p+1) template
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5.       gij = hk–i,m–j fkm gij = hk,m fi+k,j+m g00 = hk,m fk,m
Template filters = Localized position-invariant linear transformations of an image
Combination of all properties
gij = hk–i,m–j fkm
 
k=i–p m=j–p
i+p j+p
k = k – i
m = m – j
gij = hk,m fi+k,j+m
 
k = –p m = –p
p p
renamed (i = 0, j = 0, k = k, m = m)
g00 = hk,m fk,m
 
k = –p m = –p
p p
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6. Template filters = Localized position-invariant linear transformations of an image
j–1 j
j+1
i+1 i
i–1
renamed
hij
g00 = hk,m fk,m
 
k = –p m = –p
p p
fij
g00 = h–1,–1 f–1,–1 + h –1,0 f–1,+1 + h –1,1 f–1,+1 +
+ h0,–1 f0,–1 + h0,0 f0, h0,+1 f0,+1 +
+ h+1,–1 f+1,–1 + h+1,0 f+1,0 + h+1,+1 f+1,+1
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7.         hk,m = 1 hk,m = 0 g00 = hk,m C = C g00 = hk,m C = 0
Low-pass filters
High-pass filters
hk,m = 1
 
k = –p m = –p
p p
hk,m = 0
 
k = –p m = –p
p p
homogeneous (low frequency)
areas preserve their value
fkm = C 
g00 = hk,m C = C
 
k = –p m = –p
p p
homogeneous areas are set to zero
high values emphasize high frequencies
fkm = C 
g00 = hk,m C = 0
 
k = –p m = –p
p p
Examples 1 25 9
Examples 1 -1 1 -2 8 4
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8. An example of low pass filters: The original band 3 of a TM image
is undergoing low pass filtering
by moving mean templates
with dimensions 33 and 55
Original
Moving mean 33
Moving mean 55
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9. An example of a high pass filter:
The original image is undergoing high pass filtering with a 33 template,
which enhances edges,
best viewed as black lines in its negative
Original
high pass filtering 33
high pass filtering 33 (negative)
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10. Templates expressing linear operators
Local interpolation and template formulation
fkm
interpolation
f(x, y)
hkm fkm 
k, m A
evaluation
gij
g(x, y)
g(0, 0)
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11. 2 2 A =  = + x2 y2 The Laplacian operator
 2
x y2
A =  =
Examples of Laplacian filters with varying template sizes
Original (TM band 4)
Laplacian 99
Laplacian 1313
Laplacian 1717
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12. Examples of Laplacian filters with varying template sizes
Original (TM band 4)
Laplacian 55
Original + Laplacian 55
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13. The Roberts and Sobel filters for edge detection
Roberts filter
Sobel filter
X 2+Y 2
X 2+Y 2 X Y X Y 1 -1 1 -1 -1 1 -2 2 -1 -2 1 2
Original (TM band 4)
Roberts
Sobel
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