CHAPTER 10 Principal Components BAND TRANSFORMATIONS A. Dermanis

Principal Components A two-dimensional illustration of the principal component transformation A. Dermanis

The principal components transformation (a three-dimensional illustration) Principal Components 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 TM1TM2TM3TM4 TM5TM7TM6 A. Dermanis

The new bands resulting from the principal components transformation PC1PC2PC3PC4PC5PC6PC7 σ j σ j PC1PC2PC3PC4PC5PC6PC7 σ j σ j PC1PC2PC3 PC1 – PC2 – PC3 PC4PC5PC6PC7 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 information It 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 information It presents a type of classification of the image PC1PC2PC3 A. Dermanis

The original bands of a SPOT 4 image The original bands of a SPOT 4 image Correlation matrix: standard deviations and variances: σ i σ i A. Dermanis

The resultingl bands from the principal components transformation standard deviations and variances: σ i σ i correlation matrix = = identity matrix (R = I) PC1PC2 PC3PC4 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 PC1PC2PC3 A. Dermanis