Contrast Enhancement and Dimensionality Reduction by Principal Components

Abstract

This chapter presents the transformation based on principal components as a tool for dimensionality reduction and contrast enhancement. A multiband image with m lines and n columns is treated as mxn multivariate observations of dimension, the number of bands. Using an RGB image, the data are seen as points in the 3D space. The effect of data correlation is associated to unsaturated colors, opening the path for the technique of contrast enhancement by spectral rotation. The transformation by principal components is presented: a linear combination of the original data which produces new data of the same dimension. The relationship between eigenvalues, eigenvectors, and variances of the new components is then discussed. A simple proof that the new bands are uncorrelated is presented using standard linear algebra arguments. A step-by-step procedure in R for obtaining the principal component transformation of the original image is presented. The possibility of compressing the data by discarding bands is discussed both in the original data and in the data transformed by principal components: each of the bands before, during, and after transformation is exhibited and analyzed.

There is no quality in this world that is not what it is merely by contrast. Nothing exists in itself. Herman Melville.