chapter 7 template filters image analysis a. dermanis
TRANSCRIPT
CHAPTER 7CHAPTER 7
Template FiltersTemplate Filters
IMAGE ANALYSISIMAGE ANALYSIS
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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
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
Moving templates for image filtering Moving templates for image filtering
The discrete convolution process in template filtering
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Typical template dimensions
Non-square templates viewed as special cases of square ones
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localized gij = hi,j;k,m fkm k=i–p m=j–p
i+p j+p
Template filters = Localized position-invariant linear transformations of an image
Using a (p+1)(p+1) templateUsing a (p+1)(p+1) template
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
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Template filters = Localized position-invariant linear transformations of an image
renamed (i = 0, j = 0, k = k, m = m)
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
g00 = hk,m fk,m k = –p m = –p
p p
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Template filters = Localized position-invariant linear transformations of an image
renamed
j–1 j j+1
i+1i
i–1
hij
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 f0,0 + h0,+1 f0,+1 +
+ h+1,–1 f+1,–1 + h+1,0 f+1,0 + h+1,+1 f+1,+1
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 f0,0 + h0,+1 f0,+1 +
+ h+1,–1 f+1,–1 + h+1,0 f+1,0 + h+1,+1 f+1,+1
g00 = hk,m fk,m k = –p m = –p
p p
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Examples
homogeneous areas are set to zerohigh values emphasize high frequencies
fkm = C
g00 = hk,m C = 0 k = –p m = –p
p p
hk,m = 0 k = –p m = –p
p p
Examples
1
25
1
9
homogeneous (low frequency) areas preserve their value
fkm = C
g00 = hk,m C = C k = –p m = –p
p p
1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1
1 1 1 1 2 1
1 8 1 2 4 2
1 1 1 1 2 1
High-pass filtersHigh-pass filters
hk,m = 1 k = –p m = –p
p p
Low-pass filtersLow-pass filters
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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 33 and 55
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 33 and 55
Original
Moving mean 33 Moving mean 55
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An example of a high pass filter:The original image is undergoing high pass filtering with a 33 template,which enhances edges, best viewed as black lines in its negative
An example of a high pass filter:The original image is undergoing high pass filtering with a 33 template,which enhances edges, best viewed as black lines in its negative
Original
high pass filtering 33 high pass filtering 33 (negative)
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evaluation
Local interpolation and template formulationLocal interpolation and template formulation
interpolation
Templates expressing linear operatorsTemplates expressing linear operators
fkm f(x, y)
A
g(x, y)g(0, 0)
gij
hkm fkmk, m
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Original (TM band 4)
Laplacian 99 Laplacian 1313 Laplacian 1717
Examples of Laplacian filters with varying template sizes Examples of Laplacian filters with varying template sizes
The Laplacian operator
2 2
x2 y2A = = +
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Original (TM band 4)
Laplacian 55 Original + Laplacian 55
Examples of Laplacian filters with varying template sizes Examples of Laplacian filters with varying template sizes
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The Roberts and Sobel filters for edge detection The Roberts and Sobel filters for edge detection
Original (TM band 4) Roberts Sobel
Roberts filter Sobel filter
0 0 0
0 1 0
0 0 -1
0 0 0
0 0 1
0 -1 0
X Y
-1 0 1
-2 0 2
-1 0 1
-1 -2 -1
0 0 0
1 2 1
X Y
X 2+Y
2 X 2+Y
2
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