6.2 Feature space

Question 1

Feature space terminology 1/2

Answer 1

• Also called band space
• Provides a different way to visualize image data
• Can be mathematically analyzed or transformed to isolate groups of pixels with similar spectral behavior
• Each axis represents values from one band
• Based on its value, each pixel is plotted in the feature space

Question 2

Feature space terminology 2/2

Answer 2

• Different object classes are located in different parts of the feature space.
• Feature space has n dimensions (n is the number of bands)
• Difficult to visualize more than three dimensions
• Each image pixel is described by a vector in feature space
• Dimension of the vector = number of bands
• Pixel value in bands = values of the vector

Question 3

Feature space statistics: mean vector

check example 1 &2

Answer 3

–Describes the expected position

–Do not consider the distribution

Question 4

Feature space statistics: Covariance matrix

check example 1 & 2

Answer 4

–Diagonal values are variances –> distribution of values in each band

–Off diagonal values are covariances –> describe how one band varies in relation to the other

–High covariance: strong relationship between bands

Question 5

Principle Component Analysis (PCA)

Answer 5

• PCA transforms a collection of correlated bands into a smaller set of uncorrelated bands
• The transformed image represents most of the information present in the original dataset
• PCA reduces data dimensionality i.e. number of bands.