SECTION 1.5 GRAPHING TECHNIQUES; GRAPHING TECHNIQUES; TRANSFORMATIONS TRANSFORMATIONS.
CHAPTER 10 Principal Components BAND TRANSFORMATIONS A. Dermanis.
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Transcript of CHAPTER 10 Principal Components BAND TRANSFORMATIONS A. Dermanis.
CHAPTER 10CHAPTER 10
Principal ComponentsPrincipal Components
BAND TRANSFORMATIONSBAND TRANSFORMATIONS
A. Dermanis
Principal Components Principal Components
2
1
12
21
2
1
cossin
sincos
sin cos
sin cos
x
x
xx
xx
x
x
( )x R x
A two-dimensional illustration of the principal component transformation
A. Dermanis
1 2 3( , , ) x R x
The principal components transformation (a three-dimensional illustration)
Principal Components Principal Components
1
2
3
b
b
b
x
PC1
PC2
PC3
x
A. Dermanis
The original bands of a Landsat Thematic Mapper Image before applying the principal components transformation
The original bands of a Landsat Thematic Mapper Image before applying the principal components transformation
TM1 TM2 TM3 TM4
TM5 TM7 TM6
A. Dermanis
The new bands resulting from the principal components transformation The new bands resulting from the principal components transformation
PC1 PC2 PC3 PC4 PC5 PC6 PC7
σj2 2543.73 192.64 68.11 9.61 5.12 3.25 1.08
σj 50.44 13.88 8.26 3.10 2.26 1.80 1.04
PC1 PC2 PC3 PC4 PC5 PC6 PC7
σj2 2543.73 192.64 68.11 9.61 5.12 3.25 1.08
σj 50.44 13.88 8.26 3.10 2.26 1.80 1.04
PC1 PC2 PC3
PC1 – PC2 – PC3
PC4 PC5 PC6 PC7
A. Dermanis
A color composite presentation of the three first principal component bands (R=1, G=2, B=3), containing a significant part of the original image informationIt presents a type of classification of the image
A color composite presentation of the three first principal component bands (R=1, G=2, B=3), containing a significant part of the original image informationIt presents a type of classification of the image
PC1 PC2 PC3
A. Dermanis
The original bands of a SPOT 4 image
The original bands of a SPOT 4 image
Correlation matrix:
standard deviations and variances:
175.066.092.0
75.0197.081.0
66.097.0170.0
92.081.070.01
R
σi σi2
8583 7367523615 1306523513 1234442622 68765
A. Dermanis
The resultingl bands from the principal
components transformation
The resultingl bands from the principal
components transformation
standard deviations and variances:
σi σi2
97.94 9592.7129.79 887.23 9.79 95.90 4.51 20.30
correlation matrix == identity matrix
(R = I)
PC1 PC2
PC3 PC4
A. Dermanis
A color composite of the first three principal components (R=1, G=3, B=2) where colors correspond to land cover classes.
Blue and green represent water and vegetation, while red corresponds to dry soil.
In particular the part of the forest destroyed by a recent fire is clearly outlined in the dark red area north-east of the city
A color composite of the first three principal components (R=1, G=3, B=2) where colors correspond to land cover classes.
Blue and green represent water and vegetation, while red corresponds to dry soil.
In particular the part of the forest destroyed by a recent fire is clearly outlined in the dark red area north-east of the city
PC1 PC2 PC3
A. Dermanis